© BOB TICER

ISBN: 978-0-9701254-5-9

APRIL 2, 2013

http://BobTicer.com

The author is self-educated with little more math than high school algebra and a course in applied calculus. He retired from a farmer’s COOP called AGRIPAC in 1999 after working seasonal at the cannery from 1961. He has learned from an effort of correcting mistakes in providing a clearer path for others to follow.

Besides learning from history, he explains the causes of gravity, electrodynamic phenomena in general and how light and mass are observable parts of a plenum. He offers the means of a unified field theory in view that renormalization of size used to resolve a problem of infinities in electrodynamics is correct and that the singularity interpreted as a necessary consequence of the Schwartzschild Metric, as a solution to Einstein’s general field equations, is incorrect.

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TABLE OF CONTENTS

FORWARD

INTRODUCTION

- IN LIGHT OF PHYSICS

- CRITERIA OF THEORY

- CONSISTENCY OF THEORY

- THE OBJECTIVE

THEORIES OF MOTION

- IMPETUS AND INERTIA

- THE COPERNICAN REVOLUTION

- KEPLER’S CELESTIAL MECHANICS

- TERRESTRIAL MECHANICS

- WEIGHING THE DEBATE

NEWTON’S MECHANICS

- LAWS OF MOTION

- CENTRIPETAL ACCELERATION

- KEPLER’S SCHEME

- A GALILEAN INTERPRETATION

- THE ESCAPE VELOCITY

- EXPLAINING GRAVITY

- KINEMATICS

NATURE FROM WITHIN

- THE KINETIC THEORY OF GASES

- THE SUBSTANCE OF HEAT

- ATTRACTION AND REPULSION

- LATENT HEAT

- FROM PHLOGISTON TO CALORIC

- FROM CALORIC TO ATOMIC THEORY

- THE FATE OF THE CALORIC

- CONSERVING ENERGY

- ENTROPY

FROM WAVE THEORY TO RELATIVITY

- LIGHT AND WAVE THEORY

- TRANSVERSE WAVES

- THE ELASTIC MEDIUM

- ELECTROMAGNETIC ROTATION

- ADVANCING THEORY

- EXPLAINING EXPERIMENT

- LORENTZ AND EINSTEIN’S EXPLANATIONS

SPACE-TIME RELATIVITY

- THE MICHELSON-MORLEY EXPERIMENT

- SIMULTANEITY

- LORENTZ TRANSFORMATIONS

- COVARIANCE

- ADDING VELOCITIES

- THE CLOCK PARADOX

- CONSTANT SPEED CHANGE

- THE DOPPLER EFFECT

MASS-ENERGY DYNAMICS

- RELATIVE MASS

- MASS-ENERGY AND LIGHT

- CONSERVING LIGHT ENERGY

GENERAL RELATIVITY

- INVARIANCE

- THE SCHWARTZSCHILD METRIC

- SRT AND GRT ANALOGIES

QUANTUM ORIGINS

- HEAT AND LIGHT

- THE STEFAN-BOLTZMANN LAW

- WIEN’S DISPLACEMENT LAW

- PLANCK’S SOLUTION

- COMPARING FORMULAS

QUANTUM PHYSICS

- THE BOHR ATOM

- THE PHOTOELECTRIC EFFECT

- THE COMPTON EFFECT

- WAVE MECHANICS

- SCHRODINGER’S WAVE EQUATIONS

- SPIN AND ANTIMATTER

- PROBABILITY INTERPRETATION

- UNCERTAINTY

PLENUM COSMOLOGY

- CIRCULAR MOTION IN A PLENUM

- LIGHT, MATTER AND ENERGY

- EQUIVALENCE

- VACUUM EFFECTS

- NEUTRINO-LIGHT COMPOSITES

- MASS AND VOLUME RATIOS

- MEAN FREE PATH

THE COSMIC COINCIDENCE

- THE HUBBLE CONSTANT

- EXPLAINING THE COSMIC COINCIDENCE

- THE GRAVITATIONAL INTERPRETATION

- A NON COINCIDENCE

- A QUANTUM INTERPRETATION

- UNITY

ACKNOWLEDGEMENTS

FORWARD

When Shayla got off the school bus she laid down on the sidewalk with the neighbor kid. He was doing her homework.

I had to convince Shayla that you learn by doing and that she was not learning by letting someone else do her homework.

As for the reason she did not do her homework, it was because she had a mental block with math. I told her math was a small step by step process and that taking each small step would lead to success, but that getting behind would result in a mental block.

She did not understand how to subtract 60 from 80, but she knew how to subtract 6 from 8. I told her she did not need to memorize each equation, as only ten essential numbers are added, subtracted, divided and multiplied. For instance, subtracting 60 from 80 is nothing more than subtracting 6 from 8 and 0 from 0 to get 20 as two tens.

The mental block had already taken effect. When I gave her a small calculator to help her with her math it became apparent that she was confused as to which way to read numbers. For instance, she would read 56 as 65. She did not have dyslexia, at least as of yet; she had developed instead an inferiority complex in belief that she was expected to know everything grownups know. I told her it is difficult to learn anything if you already know everything and life is a learning process even for grownups. I also pointed out to her that she did learn, as when she correctly answered 11 plus 4 as 15. The praise was to encourage her not to give up in the face of defeat but to confidently know she can find the simple steps to learn. Mistakes can unfortunately be fatal, but I ensured her that those of us who learn from them are more likely to achieve success.

Life is also a learning process for us all, as evident with the historical evolution of theoretical knowledge. However, although scientific theory evolves as a step by step process, a complete knowledge of these steps is generally missing for most of us. An understanding of the tensor calculus of general relativity theory, for instance, is a complex undertaking that only a few of us are willing to commit to. As a result, most of us are inclined to either accept or deny a theory according to faith.

Some of us are more faithful than others. Some of us prefer instead a rationally complete understanding of the world in which we live. Generally we are stuck somewhere between faith and understanding, but the internet now promotes experts on any subject to more easily contribute to a world wide web of knowledge.

Physicists have said a supercomputer is needed to solve Einstein’s general field equations, but computer programming is based on a binary code, a simple two number system. It is thus possible to relate Einstein’s general field equations to a step by step process for it to be more easily comprehended, but the steps in this case is numerous enough to fill volumes of books.

The math allows us to accurately describe specific aspects of nature. The math complexity also simplifies the task for experts in the field, but it is not needed for a fundamental understanding of theory.

A fundamental understanding of theory can also be undertaken in accordance with its history as a step by step progression providing a convenient reference to which everyone can relate. However, the history of physics has a mystical side to it. For instance, in view of Aristotelian physics this mystical element included light as the means from which the divine source of all creation supplied the material world with motion and energy. Nowadays relativity of space and time, and of mass and energy, is now described according to how light moves and interacts with matter. Moreover, the whole universe is now assumed to be finite whereby all of its enormous matter and energy expanded, and still expands, from a singularity, a space so tiny that it cannot be defined. Adding to this theory are concepts of dark matter, dark energy, black holes, worm holes, other dimensions, other universes and so forth.

The expanding universe cosmology struggled for a decade or more to become accepted by the majority of mainstream physicists. This difficulty of acceptance is typical of a new theory attempting to overcome the dogmatic view of the establishment. Copernicus, for instance, struggled to establish the heliocentric theory of Earth and the other planets in the solar system, as the Aristotelian doctrine of Earth at rest in the center of the universe had become the official position of the Catholic Church for its interpretation of reality.

Big bang theory of an expanding universe is now part of the establishment, but throughout history the establishment has been revolutionized by new theory for its ability to better explain new discoveries. It also is questionable whether big bang theory will remain in the distant future as established as it is now. It does have a determined challenge of an “electric universe” theory explaining the cause of light distortion as due to its encounter with the existence of a plasmatic state of matter in intergalactic space instead of as due to an expansion between galaxies.

The electric universe and expanding universe are both theories with historical origins. Even though the expanding universe theory is now the more popular of the two, in time it could possibly be superseded by the other one. As to whether such speculation of dark energy and worm holes are retained as part of an all embracing new theory or are eventually regarded as having a mystical outlook could very well depend on a general step by step interpretation of the history of theory.

A complete understanding of all this seems out of reach for the simple minded. However, Einstein once suggested an understanding of relativity theory could more easily be understood by way of the Pythagorean Theorem. An effort has thus been made to simplify all the mathematics in this book for it not to be any more difficult to understand than the Pythagorean Theorem is for a sixth grade student.

INTRODUCTION

Rene Descartes philosophized, “I think, therefore I am . . . . If I am deceived of my existence, then I must at least be the Deceiver.” He therefore confirmed his existence by way of his own awareness of himself.

Am I alone?

Resistance to thought and action testifies there is an objective world extending beyond my control. I am not alone. We therefore exist.

I witness existence but do not seem to know how either existence or a state of consciousness is possible. I therefore merely assume we are parts of creation, as by a Supreme Being or from what already exist.

Can something exist without our awareness of it? No matter. Never mind. The mind-matter duality is of no concern, as this book is about the physical world inasmuch as our material existence is comprised of a substance of some sort that varies in shape, size and so forth. In this regard philosophers have attempted to explain everything that exists in the physical world as part of a primary substance that became referred to as æther.

Suppose all physical reality is indeed comprised of æther. What, then, are its properties? How does it, for instance, separate from and recombine with itself in creating all the effects of reality? A substance being primary implies it has no internal mechanism to bond to itself other than by pushing against other primary substance. It must thus be intrinsically elastic in order to maintain a force of action by way of motion, as all action between itself would otherwise result in a loss of relative motion.

Another likely condition for primary substance is that it needs to be of infinite content, even to partially fill infinite space if not all of it, in order that it is able to change direction by way of elastic collision instead of spreading apart without a way to reverse direction to again interact with itself. The question then comes to mind as to whether space is a plenum of æther or a partial vacuum and æther.

Descartes along with other philosophers assumed space consists of a plenum.

How, then, do various densities of matter exist if the æther is everywhere identical in composition?

A plenum does not even have wiggle room for a wave action to occur in the manner sound propagates through air as compressed states of air molecules. The æther as a plenum is thus contrary to the air medium for sound.

It is no wonder that early Greeks deep in thought regarded our world as illusionary. As for the plenum, they considered circular motion in it as possible. In a roundabout way motion is allowed by the complexity of circular paths.

Descartes also assumed all stuff moves circularly. He described it as evolving into a complex system of vortices of various sizes and rotational speeds. Total motion is conserved, as allowed by the movement of other æther. As for the complexity of motion, endless possibilities exist by way of the movement of vortices inside other vortices in creating various relationships. A number of like vortices in one region of space can thus be relatively denser than those in another region of space. However, since the density of this primary substance is everywhere the same, the world comes about by the exchange of motion between vortices.

The source of all creation is thus already created out of what already exists ad infinitum.

In Light of Physics

Some things seem unexplainable; other things we can explain we seem unable to prove. We cannot, for instance, explain the existence of the æther if there is indeed this primary substance from which all things form, but we can use it to explain how constant light speed is possible. A mathematical explanation of it, in fact, was given at the turn of the late 19th century by Hendrik Antoon Lorentz. His equations indicate there is a cancellation of effects whereby the absolute state of rest through which the æther moves is invisible to us.

As an alternative to explaining the null results of experiment Albert Einstein merely postulated instead the constant nature of light speed as an experimental fact and he made no reference to the æther. He stated the concept of the æther is not necessary to formulate theory; all that is needed for describing the observable world in its functional manner is to formulate laws of nature mathematically.

Einstein did formulate special relativity as a self consistent theory in agreement with observation, but physicists were still speculating on the true natures of light and matter. Max Planck had proposed in 1900 a quantum condition for explaining particular effects of thermal radiation. Albert Einstein, in support of this quantum condition, explained the photoelectric effect as particles of electrons recoiling from the impacts of particle-like radiation instead of wave-like properties, as had previously been discovered of light.

Leading into the twentieth century was thus two revolutionary ideas with regard to the relativistic and quantum nature of light. For the most part these two revolutionary ideas were not at odds with each other. A similar effect to the photoelectric one, for instance, is the Compton Effect whereby Compton formulated quantum effects in a manner consistent with relativity theory. Similarly, in 1924 Louis de Broglie discovered wave-like properties of matter and he also formulated them quantitatively according to relativity theory.

Initially the quantum was nothing more than an added condition of relativity theory, but eventually it developed into a contrary means of explaining nature. Whereas relativity theory is deterministic with regard to cause and effect, quantum mechanics interprets the quantum as conditional to probability.

This condition of probability pertains to the wave effects of nature. Erwin Schrodinger provided a wave equation to formulate de Broglie’s ideas according to Wave Mechanics whereby an electron cloud produces quantum effects. However, subsequent analysis of the particle-wave duality by such physicists as Bohr, Born and Heisenberg led to the principle of uncertainty, as stated by Heisenberg. The world on the atomic scale is thus indeterminate with regard to direct cause and effect.

In 1927 the top physicists of the time convened in Copenhagen, Germany to conclude a yearlong debate ending with the Copenhagen Doctrine. Schrodinger’s wave equations had been shown to be successful for predicting events, but Max Born, Werner Heisenberg and Niels Bohr argued there is an impossibility aspect of determining exact position and exact momentum of a particle, as the means of observing them (such as by light) necessarily influences the outcome of the event. Schrodinger’s wave mechanics was thus accepted as a means of predicting outcomes, but only with its wave equations reinterpreted as probability equations.

Along with indeterminism and the particle-wave duality was the demise of the æther as a valid means of explaining nature. Since the primary aim of science is to describe nature in accordance with observation, and since experiment indicates the æther is invisible if it does exist, it is thus non-existent as far as science is concerned.

Although Einstein stated the æther is superfluous for the formulation of theory, he did suggest that it is useful for understanding theory by way of a historical perspective. There is as there should be, for instance, experiments attempting to determine the simultaneity of events, as contrary to SRT, but they could easily be misleading if they are without historical reference to the invisible æther at absolute rest. If the simultaneity of events is absolute instead of relative, for instance, it is then possible to determine the speed of light with respect to absolute rest, which is what really needs to be proven. Premature claims contrary to the history of special relativity therefore tend to confuse rather than benefit our understanding of theory.

Even though Einstein was highly respected for his opinion, his suggestion was trumped by other leading physicists of the time. They decreed the concept of the æther is beyond objective science. As far as science is concerned what is unobservable does not exist. Since the æther had been determined to be invisible at best, it was therefore proven not to exist in the real world.

Criteria of Theory

The general criteria of a theory of science are that they describe, explain and predict phenomena. Space, time and motion, for instance, are described as units of distance, units of time and the amount of distance something moves per unit of time. Explaining motion according to theory is according to laws of motion. If mathematically described, then the theoretical laws of motion predict places and times for events to occur.

If a theory does not predict anything, then it is of no use to science. The ability to predict results is thus what establishes theory. General relativity theory, for instance, was established after astronomers confirmed its prediction that the path of light close to a massive body such as the sun is curved.

Another establishment according to prediction is the big bang theory. It was established by a discovery of a cosmic background radiation whose temperature at present agrees with theory in that the expansion of the universe from creation has cooled it. The original prediction was 5 degrees Kelvin by Ralf Asher Alpher (1921-2007), as in accordance with his explanation of how heavier elements formed from the cooling of the universe from its expansion. At the time, however, an exact rate of the expansion was not accurately known, leading to such other predictions as 50 degrees Kelvin by Gamow and 10 degrees Kelvin by Peebles. It was eventually determined as 2.7 degrees Kelvin although the range in the Hubble Constant has varied over the years from about 50 to 80 kilometers per second for a distance of one million parsecs.

Olaf Kristian Bernhard Birkeland (1867-1917) also proposed a theory as early as 1896 that did not receive acceptance until confirmed by a space probe in 1967. After providing a general solution to the equations of the theory of electromagnetism given by James Clerk Maxwell (1831-1879), Birkeland applied the theory to explain the auroras of northern and southern lights as disturbances from the sun’s radiant energy interfering with a magnetic field above Earth’s atmosphere. Since he described the magnetic field as an ionized gas, and because Lord Kelvin had stated all space between the Sun and above Earth’s atmosphere is void of matter, Birkeland’s theory was discarded until the magnetic field of plasma was discovered by a military probe in 1967. Overwhelming evidence in support of it in the 1970s occurred by way of satellites in orbit. It is now estimated that more than 99 percent of the mass in the universe is in the ionized state now called plasma.

Consistency of Theory

History is not only useful for an understanding of theory; it can help maintain and restore consistency of theory. As a theory evolves it adapts to explain more phenomena. Sometimes inconsistency results because of incorrectly adapting to new discoveries. Sometimes further correction of past theory is needed.

Big bang theory is a prime example of theoretical evolution. It has been modified repeatedly in order to be consistent with new discoveries and it most likely will require further modification if not replaced with new theory altogether.

Big bang theory has been challenged with internal inconsistencies, as with problems regarding flatness, fine-tuning, a monopole, the nature of a horizon, etc. Alan Guth was able to resolved most of them with the concept of inflation predicting lumpiness during early expansion, but this success is countered with another problem.

The other problem is the expansion rate appears to have increased instead of decreased by gravity. The existence of dark energy is assumed its cause, as by a cosmological constant provided by Einstein’s general field equations. The cosmological constant is a natural result of the calculus, but any value, including zero, is possible. It is thus allowed but not required and there is counter reason that it does not apply.

One reason why the cosmological constant might not apply could be a Cosmic Coincidence that the big bang theory does not explain, as of yet. Gravity is an extremely weak force compared to an electromagnetic one, as indicated by the equation

G is the gravitational constant of proportionality that determines the gravitational potential at any distance r from any mass m in the manner Gm/r. In contrast, e is an electronic unit of charge relating electromagnetic potential in the manner e^2/mr. The above equation is obtained by dividing the gravitational potential of say the proton mass mp by the electromagnetic potential at the same distance of the electron mass me.

A numerical equivalent to this ratio is obtainable in relation to the Hubble Constant. Its value according to the data obtained by the WMAP space probe is H_0 = 70.5 ± 1.5 kilometers per second from a light source one hundred million parsecs from us. At a distance of 2rn = 5.76 X 10-12 centimeters, which is the diameter of the nucleus of the hydrogen atom, the velocity of the Hubble Constant is much smaller. Since one hundred million parsecs is 3.09 X 10^19 kilometers, dividing 70.9 km per second by 3.09 X 10^19 km and multiplying by 5.76 X 10-12 centimeters is 1.32 X 10-29 cm per second. This velocity per light speed of 3 X 10^10 cm per second is also 4.4 X 10-40. Because 70.9 km per second is well within the range of 70.5 ± 1.5 km per second:

The speed of the Hubble Constant at a distance equal to the diameter of the hydrogen nucleus thus appears equal to the ratio of electromagnetic and gravitational potentials between the proton and electron masses.

Big bang cosmology provides no explanation for the Cosmic Coincidence as of yet. The reason for this lack of explanation is the constant rate of expansion is actually variable. If the universe does expand, the rate of expansion is only constant with regard to distance. It is not constant with regard to time. It decreases by the increasing distance between galaxies. The Cosmic Coincidence, in theory, is thus just a coincidence.

A remarkable coincidence it is and one that might be explained by either another modification of the big bang theory or another theory altogether. There is no lack of candidates, which include the electric universe of plasma cosmology, a new tired light theory, and an application of Zero Point Energy (ZPE).

Another asset of history is discarded ideas due to lack of development and verification might still prove to be useful. Birkeland’s plasma is one example; ZPE might be another.

Plank proposed the concept of ZPE as an attempt to explain the quantum according to classical laws of nature. It means that if you remove all mass and heat energy from a system, there is still motion of energy in space. Although it was proposed by Plank in 1811 before Heisenberg proposed his uncertainty principle, ZPE is consistent with the principle, which predicts events exactly according to their uncertainty, such as the existence of a virtual field of particles. There is too the condition of probability that motion must exist at a temperature of absolute zero.

Another requirement of theory is that it needs to be consistent with other theory. Einstein, for instance, attempted for several years to unify his field theory of gravity with that of electromagnetism. Here, too, the concepts of ZPE and electric plasma cosmology could be relevant. Plasma is of an electrical origin and ZPE could be the means of explaining both quantum and relativity aspects of reality.

Big bang theory requires an underlying source of energy to explain an increase in the rate of expansion. ZPE might well be the mysterious dark energy that is hypothesized. However, this assumption implies big bang theory is indeed correct.

Another possibility is a New Tired Light Theory proposed by Lyndon Ashmore. It explains the Hubble Constant not as a red shift due to galactic recession; it is instead a red shift caused by the absorption of light energy as it moves through the plasma in intergalactic space. Some evidence in favor of it is the discoveries by Tift and other astronomers that there appears to be a red shift in correlation with the plasmatic density of galaxies and their clustering.

The Objective

As for the objective of this book, it is to review the history of theory for a more simple understanding of its development. The history of theory, as considered here, reaches as far back as Aristotelian physics and it includes quantum physics, relativity and cosmology.

Although the æther is now regarded scientifically invalid, it is here used for an understanding of theory. The æther not only provides the means to explain the constant nature of light speed; an explanation of how it is possible matter can emit gravitational energy in a way it continues on gravitating all mass the same and not violate conservation of momentum is provided as well. How the continuous creation of gravity does not overfill space with it is also explained. Moreover, the underlying nature of mass is explained along with the equivalence of inertial and gravitational mass.

Electrodynamic effects are also explained. Electric charges of opposite polarity attract each other; electric charges of the same polarity repel. However, electric currents that move in the same direction contract each other; they repel if they move in opposite directions. Light reflects to maintain the same speed, but matter reflects to move at various speeds. Different light can occupy the same space; different mass cannot.

Explanations of all these effects are in accordance with a plenum and consistent with a tired light theory and recycling universe that is without limit except for being divided into finite parts limiting observation to within a particular one.

Further significance of the consistency of all these explanations is that they allow for unification of field theory with regard to gravity of general relativity and a virtual field of quantum electrodynamics according to probability.

THEORIES OF MOTION

Circular motion was conceived in ancient times as divine, as seemed evident of stars orbiting high up in the heavenly sky where they are above earthly chaos. Earthly substance is thus at the center of the universe below the heavenly stars.

As to explain the primary source of motion itself, Aristotle (384-322 BC) proposed an Unmoved Mover is its provider. What evolved from this proposal was a theory of emanation. Robert Grosseteste (1168-1253) and Saint Bonaventure (1217-1274) later, for instance, advocated God first created lux, a corporeal form of a substance that duplicates itself indefinitely. Motion is thus the duplication of form moving as energy waves in all directions. Lux constitutes the material form of substance by reflecting lumen, which is light. Light is also how God mediates between souls and bodies. As nature takes its course, it is not alienated from God, as He intervenes by emanating light from within.

Light, as according to Aristotelian physics, is thus the essential source of motion, as distinguished from earthly substance having no inclination whatsoever to move without assistance. This theory was challenged by John Philoponus (about 490—570 AD) inasmuch as he asserted material substance is inclined to remain in motion without assistance.

This idea identifies, in part, with inertia: whereby a state of non acceleration, as mass in relative motion or at rest, maintains unless it is changed by means of an external force, such as gravity or the collision from other mass in relative motion. However, even though it was an insightful idea for advancing theory, it was instead rejected by theologians with more influence in favor of the Aristotelian doctrine.

In modern physics light is still an essential part of mass. By the equation E = mc^2 the energy E of mass m is per light speed c squared. The main difference of it apart from Aristotelian physics is that the inert aspect of mass allows relative motion to continue wherefore light becomes a primary source of change with regard to the internal composition of matter. However, there is still a distinction between light and matter. Matter varies in speed here and there whereas light speed is a constant except in combination with matter. Matter neither reaches nor exceeds light speed, but to claim light is massless could be misleading, as conservation laws such as of energy and momentum apply to mass interacting with light as well as mass interacting with mass.

Impetus and Inertia

The modification of Aristotelian physics did not fall on deaf ears outside of Europe. In the golden age of Muslim academic culture in Persia, Avicenna (980–1037) concluded motion is an inclination transferred from the thrower that does not cease in a vacuum but requires a resistance such as air. This reiteration of the Philoponus position identifies with modern concepts of inertia and momentum if in the context of an actual existence of empty space through which to move, but still embedded in general thought was the idea of the plenum. Both Philoponus and Avicenna conceded the power of motion given to an object to move through a medium would eventually be used up.

Saint Thomas Aquinas (1223-1274) and Francis de Marchia (b. around 1285—d. after 1344) also accepted the position that motion is maintained until impeded by the position of another object, or by a force such as gravity, but an ability of an object to propel forward indefinitely with no additional assistance was granted by Jean Buridan (1295-1358).

Buridan proposed motion given to an object from another object is sustained by the object until passed on to another object. He named this inherent property of motion impetus. He did not identify impetus with the energy of light, but he offered biblical justification in interpreting Genesis literally as stating God rested on the Sabbath after He created the world in six days. Because God rests, He allows His creation to sustain motion such that no longer is there any need for Him to replenish it.

Impetus theory is identical to the modern concept of relative motion except that Buridan referred to rest as distinct from motion, as to allow for an underlying medium such as the æther for a state of absolute rest distinguishable from the relative motion of all matter moving through it. Otherwise the theory is consistent with a modern mechanical interpretation inasmuch as Buridan even stated impetus is proportional to weight times speed. A heavier object or a faster one thus has more impetus, which is similar to more momentum in modern terminology. Since gravity provides impetus to increase motion towards earthly mass, and earthly mass gives up impetus to escape from earthly mass, a cannonball falling through a hole in Earth is increased in impetus on the way down to the center of Earth the same as the cannonball gives up impetus to move up an equal distance to the surface at the other end. Such analysis later exemplified such periodic motion as the free swing of the pendulum and oscillatory motion in general, as theoretically developed in the 17th century. As for the 14th century, impetus was to be interpreted otherwise.

Nicole Oresme (1320-1382) maintained impetus is a temporal quality used up in motion by the inertness of earthly substance tending toward its natural place of rest, the Earth, as Aristotle had contended, and as evident of how objects falling to the ground lose their motion. He also distinguished between impetus given to the motion of the heavenly stars and impetus given to the violent and accidental motion of earthly events. However, because impetus is spent during motion, he argued contrary to Aristotle it cannot cause an object to accelerate to an infinite speed even in the vacuum of space.

Oresme also considered Archimedes’ principle of the lever in developing a cosmology. The position of the heavier object is nearer to the fulcrum to maintain balance. In interpreting this principle as applying to the cosmos, Oresme referred to the Aristotelian idea that earthly substance tends toward the center of the world where Earth comes to rest. However, the moon, sun and other celestial bodies moving about indicated to him the center of gravity could shift, as in changing the potential for matter to acquire impetus. It is thus possible Earth can slightly shift in position as well. He further reasoned, however, that Earth’s movement is not provable one way or the other. He also proposed the criteria two equal hypotheses should be the merit of simplicity, as Copernicus would later advocate, but Oresme accepted a stationary earth in support of the common interpretation of the Bible at the time.

The Copernican Revolution

While impetus theory developed at Paris, France, more eloquent ways of describing nature developed at Merton College in Oxford, England. Such scholars as John Dumbleton, Richard Swinehead and Thomas Bradwardine proposed an abstract system of degrees and latitudes for analyzing such qualities of nature as hot and cold, and various forms of motion according to quantity.

The intent of the Oxford scholars was to provide a mathematical description of processes, as not to claim their abstract calculations were actual laws of nature. They nonetheless provided a quantitative means for mathematically analyzing the results of experiment in arriving at such concepts as constant acceleration and instantaneous velocity. This is particularly true with regard to Domingo deSoto (1494/5-1460) applying the calculating technique with impetus theories that were developed at Paris to refine the earlier calculations of Oresme for uniform acceleration of falling objects due to a constant increase in impetus.

Following this development, Nicholas Copernicus (1473-1543) proposed a heliocentric scheme of the sun at the center of the solar system whereby the planets, including Earth, revolve around. This scheme was to be advanced by Johannes Kepler (1571-1630).

Aristarchus of Samos (around 310 BC–about 230 BC) had advocated the heliocentric system of planets, including Earth, revolving around the sun. However, his scheme was overcome by the greater influence of Aristotle, who failed to recognize the great distance of stars and thus made an incorrect conclusion based on the condition of parallax.

Parallax is the apparent change in position of an object caused by the observer moving about here and there. The positional change appears greater for closer objects. Nearby scenery, for instance, changes rapidly for passengers looking out the window while inside a moving automobile, whereas a more gradual change in relative position occurs of more distant mountains. The change in the relative position of the sun appears not to change at all even though Earth rotates for day and night to occur and it revolves around the sun for seasonal changes.

Being unable to observe parallax of more distant stars, and believing their distances are relatively close enough for parallax to occur (although they are not) if Earth moves around the sun, Aristotle concluded the yearly constancy in the relative positions of the stars in the sky indicate a stationary Earth.

Copernicus did not consider parallax. Apart from it, observations provided astronomers with more and more data on the relatively closer positions of planets in our own solar system such that a scheme of circles within circles for motion around Earth became more and more complicated. Copernicus thus proposed the much simpler scheme of Earth circling the sun.

Along with suggesting the heliocentric scheme is less complicated, Copernicus asserted that no internal effects of Earth moving through space is detectable if all relative parts are moving uniformly, which implies the principle of relative motion.

Publication of Copernicus’s book De Revolutionbus occurred the same year of his death, but authorities outlawed the book and later works by Kepler, Galileo and any other of its defenders. Giordino Bruno (1548-1600), advocated an entire world full of solar systems, and he further speculated stars move relative to each other but are too distant from us for detection of their relative motion. However, he was burned at the stake for his outspokenness. Galileo was merely sentenced to confinement for his defiance of the order.

Copernicus had nonetheless set forth a revolution in thought. Readers in Italy and elsewhere in Europe accepted De Revolutionbus. Simon Steven (1548-1620) of the Netherlands supported the heliocentric system in his book De Hemelop he published as early as 1608.

The Copernican system was not faultless. Indeed calculation of celestial data compiled by astronomers indicated planetary motion was not of true circles. As Copernicus revered the circle as a divine principle, his scheme included thirty-four epicycles. This weakened his argument of simplicity. A Copernican revolution had nonetheless begun. Ironically, a so-called mystic, Johannes Kepler, who claimed to have listened with a sensitive ear to the musical harmony of the planets in motion, including Earth, would defend it.

Kepler’s Celestial Scheme

Kepler (1571-1630) was proficient in mathematics. The skill enabled him to become Tycho Brahe’s (1546-1601) assistant in plotting data of celestial movement. Brahe had rejected the heliocentric system in favor of a stationary Earth mainly because he could not detect parallax of the stars. He thus regarded the material of Earth as an inert condition of nature. However, he did accept a heliocentric system for all planets other than Earth revolving about the sun. As he maintained the sun and moon only revolve about Earth it would only be another step to describe Earth as revolving around the sun.

Kepler studied the data compiled by Brahe and in 1609 proposed three empirical laws to describe it.

The first law is the planets, including Earth, move in elliptical instead of exact circular orbits around the sun. A circle transforms into an ellipse by separating its center into two foci, as a particular property of the ellipse is the total distance between two straight lines connecting the two foci to anywhere on the perimeter of the ellipse is always the same, as illustrated below.

The second law refers to the distance between the sun and a particular planet: equal area in equal time is swept between the sun and planet by the product of the distance of the planet from the sun and the speed of the planet being constant. Planets thus move faster when closer to the sun in order to maintain the same amount of area per time: rv = r’v’ = r(r/t) = r’(r’/t’) such that r^2/t = r’2/t’.

The ellipses are not the same for each planet, but Kepler determined a common property. The third law is the square of the period of a planet’s elliptical orbit is equal to the cube of the mean distance of the planet from the sun. The ratio of Earth’s time around the sun squared to the cube of its mean distance from the sun is thus the same for other planets in the solar system.

Say Mars is four times more distant from the sun than is Mercury. Since their orbits are nearly circular, the ratio of orbital radii cubed is about 64. The orbital distance of Mars is also about four times greater than that of Mercury. If the orbital speed of Mars is about half the orbital speed of Mercury, then orbital periods of Mars are about 8 times longer in time than those of Mercury, which squared is also a ratio of about 64.

Although Kepler’s scheme describes the planetary motion of our solar system, a generalized description for all orbital motion is lacking. It does not predict, for instance, orbital speeds for a more massive sun.

It is possible Kepler could have had some insight of the laws of nature, but they were to be developed by Galileo, Newton and others.

Terrestrial Mechanics

Physics refers to the laws of motion as mechanics. Complementing the celestial mechanics of the planets is terrestrial mechanics. Its development also connects with gravity, as with determining the nature of bodies falling to Earth.

An experiment on gravity was performed as early as the third century BC by Strato. He determined that the sound of a body falling to the ground differs for a different height of fall. He thus surmised an increase in speed occurs during the fall. An experiment in the thirteenth century was also attempted by Jordanus de Nemore (1225-1260) in a laboring effort to distinguish weight according to an angle of descent.

Leonardo da Vinci (1452-1519), whose work was unable to survive except for his notes, experimented to determine if the direction of fall is towards Earth’s center. He dropped two heavy objects from a tower in an attempt to find a decreased distance of separation, but the attempt failed.

Da Vinci failed to determine the direction of fall, as the change in distance is too minute to detect with the instruments with which he had to work, but what he discovered instead is the increased speed of fall is pyramidal, as increasing uniformly in equal intervals of time in analogy to counting stairs. However, from his notes, which might not necessarily reflect what he actually concluded, he incorrectly stated the distance of fall is proportional to the time of fall.

Oresme, Galileo and others correctly deduced the distance of fall is proportional to time squared, but da Vinci might have only erred in his taking notes of his findings. In any case, to his credit, da Vinci seems to have been wise to the ways of nature. In anticipating Newton’s third law of motion, for instance, whereby force and resistance to force are mutually the same, he claimed air and water use the same amount of force to resist movement.

In 1553 Giovani Bellaso of Brescia asked in a book he wrote why balls made of either iron or wood fall at the same rate. His question seems to refer to the result of experiment and also to imply there was an attempt to formulate theory.

Demonstratio by Giovani Battista Benedetti (1530-1590) published in 1552 was a book that attempted to determine the nature of falling bodies analytically.

Benedetti also might have considered the plenum, as in applying Archimedes’ principle of buoyancy to the condition of bodies falling through a medium. He first assumed bodies of the same material and density fall at the same rate, as contrary to Aristotle’s doctrine of heavier bodies falling faster than lighter ones. In a revised edition published in 1554, Benedetti changed his position to that of bodies of the same material but of different size do not fall exactly at the same rate.

Perhaps critics influenced Benedetti to reverse his position, or perhaps geometrical considerations were in play. If an object divides into two or more parts, for instance, more inside becomes part of the outside and hence more exposed to atmospheric conditions. Since only the surface area changes, not the total volume of all parts, this means the mathematical proportions of volume and surface area are relatively dependent on size. Smaller objects thus encounter more friction per surface area to volume or weight, which causes them to move more slowly through a medium, as is true of smaller particles falling through the atmosphere.

Different size bodies falling at different rates are indicative of a medium. They fall at different rates in a medium but fall at the same rate in vacuum space. However, this is only true of such media as water and air. A medium with infinitesimally fine parts great in number could saturate between material parts. Thus, if atoms or their internal components are relatively of the same proportional size and density relative to the medium (as would be consistent with modern theory) then the medium would affect all of them in the same manner.

As it were, not knowing the true nature of atomic particles, Galileo Galilei (1564-1642) theorized that all bodies (regardless of size, weight or material they are comprised of) still fall, in vacuum, at the same rate.

The abstract analysis of motion at Merton College likely guided Galileo rather than such work as that of Benedetti. In any case, the hypothesis Galileo had put forth provided a means of testing whether the laws of motion are typical of objects moving through empty space, as would seem necessary for the planets in the Copernican system to move unopposed by a medium.

Galileo experimented with objects moving along planes and took note of the free swing of pendulums to discover an appreciable amount of reduced friction tends to allow motion to maintain. He thus postulated the law of inertia with regard to continual motion and acceleration that Newton would later formulate in his system of mechanics.

As to test the equality of fall between masses, it is likely Galileo performed experiments, as is alleged of his dropping objects off the leaning tower of Pisa, but this claim is uncertain. Nicole Cabeo (1585-1650) had made experiments in 1641 in claiming to confirm that objects do not fall at the same rate. When informed of the experimental results, Galileo replied how difficult it is to attain accurate results from such experiments.

Galileo seemed to take other results of experiment for granted. For instance, Pierre Gassendi (1592-1665) directed an experiment to be performed on a moving ship at sea, as to find out if an object follows a straight course of the ship while falling to the foot of the mast. His own experiment having already verified his laws of motion, Galileo confidently asserted it would.

To his credit, Galileo truly deserves the acclaim of pioneering the modern approach of establishing laws of nature according to observational facts rather than by ontology or abstract concepts of intuition.

Weighing the Debate

The idea all of space is filled with an undetectable medium is contrary to the empirical approach, but the new discoveries do not prove there is empty space in which to move; it only affirms objects move as though empty space is before them, not that it actually exists before them. Moreover, the new mechanics is far from a complete explanation of reality. It does not explain, for instance, how it is possible for corporeal matter to attain and maintain form in the manner it does. How, for instance, are elastic collisions possible without an internal force to maintain material form?

Such questions were still pondered. Francis Bacon (1561-1626), for instance, questioned such concepts as a vacuum state with regard to the nature of matter. If matter consists of individual atoms, what keeps them intact? He concluded atoms need to somehow attain inner qualities by means of some intangible spirits of a medium of some sort to have cohesion and form. He also advocated a primary role of science is to describe nature according to how it is observed.

Another philosopher who did uphold the atomic theory as a sort of internal mechanism was Gassendi. He offered an atomic theory not of inherent forces but of inertia in view of the principles of relative motion and inertia. He contended inertia is necessary to resist penetration and to change the motion of other atoms by direct contact.

He further assumed atoms sometimes combine to produce various effects of nature, but the observable world, including the atoms, is essentially comprised of secondary effects that arise from a primary source producing form and cohesion. The primary source is indeterminable by us even though it gives rise to the secondary effects, such that secondary effects actually constitute the natural world of observation.

One philosopher who went so far as to advocate a plenum in view of the concepts of relative motion and inertia was Rene Descartes (1596-1650). Descartes was well aware of the implications of these new concepts, but he opposed the vacuum state. He thus undertook the task of explaining relative motion and such effects as gravity in view of the plenum.

Since motion in a plenum is by reason necessarily circular, the Cartesian universe contains vortexes that differ in size and rotational speed whereby exchanges occur. Smaller invisible vortexes accelerate to greater speeds in determining the weight of heavier ones, and the visibility of the world is determined by the size of our nerves extending from our brains.

Descartes also postulated conservation of motion, which is similar to conservation of momentum in that in a collision between two masses the change in speed of the greater mass is less than the change in speed of the lesser mass, but more change in motion occurs to the lesser mass. In view of inelastic collision, relative motion ceases altogether unless the event of inelastic collision involves such other influence as the creation of radiant heat. In this case motion is conserved in the observable world in the form of a potential, as to the motion of a world detectable by way of our senses in contrast to its underlying mechanism. This condition seems evident of the Cartesian philosophy inasmuch as Descartes stated the speed of an iron ball transfers by collision to the end ball of the row.

Modern theory has similar issues with regard to a concept of dark energy that somehow increases for it to increase the rate the universe expands at. There are also virtual particles according to probability, with no determinable causal effect in sight.

An underlying mechanism to explain phenomena is thus provided by way of a virtual field. It could be used to explain gravity, for instance, by way of virtual particles moving undetected away from matter in the way of creating a vacuum for both real particles and other virtual particles to fill the vacuum. In so doing, more virtual particles are converted for rejection, thus creating a gravitational potential for conservation of energy and momentum of our observable world.

In a later chapter this vacuum effect of a plenum is elaborated on to explain electrodynamics as well as the gravitational effect.

NEWTON’S MECHANICS

Although Isaac Newton (1629-1695) is recognized for founding Classical Newtonian Mechanics, there is nearly no part of it, if any, that had not been thought of by someone else. His first two laws of motion, with regard to momentum and force, are attributable to the works of Buridan and Galileo. John Wallis (1616-1703) explicitly stated the second law in 1603. The third law of motion, regarding mutual action and reaction, was offered by Leonardo da Vinci (1457-1515) in claiming air and water resist each other equally. Robert Hooke (1635-1703) claimed to have suggested to Newton the inverse square law of gravity.

Newton stands out nonetheless as outstanding for his contribution to the advancement of theory. It was essentially a comprehensive formulation of ideas that resulted in unification of Kepler’s heliocentric scheme of the solar system in accordance with relative motion and gravity as forces of nature.

Newton essentially formulated the foundation of mechanics for other theorists to expand on. Lacking in his theory, for instance, was a clear concept of energy. Although Huygens proved in 1669 that a living force mv^2, called Vis viva, is conserved in elastic collision, it was not shown to be conserved in inelastic collision, as is momentum. Newton thus argued momentum is more fundamental to theory.

A conservation of energy law was not formulated until the 19th century and kinetic energy ½mv^2, or Vis viva mv^2, is conserved in inelastic collision according to Einstein’s modification of Newtonian Mechanics in replacing Newton’s absolute space and absolute time with relative space-time instead.

Newtonian Mechanics is nonetheless an integral part of modern theory along with its understanding.

Laws of Motion

In addition to absolute space and absolute time as self-evident concepts allowing a comparison of events according to standard units of measure, Newton also believed the material content of the universe always stays the same. It does not change by being in relative motion, under the influence of gravity, or by anything whatsoever. He then postulated three laws of motion in view of conservation of mass:

1. Law of inertia: objects in a non accelerating state of relative motion or rest remain as such until acted on by an external force, such as gravity or collision with other mass

2. Force is the product of mass m and acceleration a, as per time t with regard to acceleration

3. An equal and opposite reaction occurs with every action between masses.

The law of inertia is also expressed as the product of mass m and its velocity v as momentum P. Hence, the first law is according to the equation

By this law, the momentum remains unchanged until acted on by another mass or external force.

The amount of force F that changes momentum is defined as the product of mass m and acceleration a, such that the second law is according to the equation

A change in velocity per time determines acceleration a such that it is possible that a quick enough fly exerts more force from changing speed from at rest to fifteen miles an hour than would someone throwing a heavy brick twenty miles per hour. However, since the brick has far more mass than the fly, more force is generally applied to it than the acceleration of the fly.

More definitively force is per time and per mass. The change in speed of twice as much mass at half the rate in twice the time is the same amount of force:

The Greek delta letter Δ denotes change, as change in velocity from v_0 = 0 to v_1 and change in time from t_0 = 0 to t_1.

Since velocity refers to both direction and speed, the change in velocity can either be a change in speed or a change in direction, or a change in both direction and speed. A rocket moving in a circle, for instance, is in a constant state of acceleration due to the constant application of force. The rocket could also constantly increase in speed by the same force. Additional force could also increase the rate of circular acceleration.

Galileo had previously established these first two laws. Newton added the third one: the law of mutual force. Hence, if a force acts on a mass, the mass reacts with equal and opposite force. This means the change in momentum of the rocket caused by the rocket fuel results in a change in momentum of the rocket fuel, as the rocket fuel would otherwise be inexhaustible.

What is therefore implied from mutual action and reaction between mass is conservation of momentum. Conservation, in physics, means staying the same and conservation of momentum means total momentum of all mass in any particular direction never changes by the action of one mass on another. The action can either be a collision of two or more masses or a force such as gravity. If a greater mass collides with a lesser mass, conservation of total momentum of the action is maintained by a change in velocity of a greater mass in one direction being relatively small and the change in velocity of the lesser mass in the opposite direction being relatively large. Mutual changes in momentums of both masses is according to the equation

A change in velocity v of the greater mass M moving at a slower velocity v thus equals a change in velocity V of smaller mass m moving at faster velocity V.

Consider the moon orbiting Earth as an example of equal changes in momentums of masses caused by their mutual gravitational influence on each other. In this case, a relatively slower moving Earth being more massive than its moon results in a change in direction of the moon being a greater change in velocity while still having greater speed. In effect, the moon moves in a relatively large circular path around Earth while Earth moves in a relatively small circular path within the larger. As to why Earth never makes it around the moon is because Earth is too slow with its changing of direction relative to each new position of the moon.

Centripetal Acceleration

A constant change in direction in a circular path is centripetal acceleration. In 1666 Newton formulated it mathematically, but he delayed the publication of his work for many years. Christian Huygens formulated it independently and published his work in 1673, but it was Newton who used centripetal acceleration for the unification of celestial and terrestrial mechanics.

Consider by Newton’s first two laws of motion a particle tends to move in a straight line, but it actually moves peripherally instead from a fixed point due to a centripetal force constantly acting on the particle to change its direction. The centripetal force is any agent preventing the particle from escaping its orbit, such as gravity or whatever. The mathematical expression is

The letters a, r, and v represent respectively the rate of acceleration, orbital radius and orbital speed.

Since centripetal acceleration is a particular form of acceleration, it equates to any form of acceleration generally expressed by the equation

Acceleration is thus generally a change in velocity (as speed or direction or both) per change in time.

A system moves along the arc at constant speed v in time T from initial velocity vi to final velocity vf, in relation to triangles. Radius r_1, an extended tangent of r_1 to the right, and radius r_2 extended to the tangent of r_1 form a right triangle. Another right triangle forms from the extension of the tangent of r_2 to the tangent of r_1. Because of the common vertex at the right, it is a smaller-upside down-right triangle similar to the first one. All ratios of corresponding parts thus equate.

Because distance is the product of time and speed the vector directions vi and vf represent both distance and velocity. The other leg of the triangle with legs vi and vf is the vector direction towards the center of the circle and is representative of the change in velocity, and it is therefore denoted as Δv. The ratio of r_2 + Δv and x + vi of the larger right triangle is the same ratio of Δv and vf of the smaller one such that

The values x, vi and vf are interpreted as either speed or distance for x + vi and vf to relate respectively as v and vT, where T is the time of acceleration.

These relations are according to smaller distance and less time of acceleration. The arc between r_1 and r_2, and the line segments s and vf converge at the limit for shortest time of acceleration to equate in manner

Centripetal acceleration thus equals a constant change in direction towards the center of the circle.

Kepler’s Scheme

Centripetal acceleration further relates to force, as with regard to centripetal force. Since force is defined as F = ma, centripetal force similarly equates as

Note: Fc increases for smaller r, as for faster change in direction.

Another nature of force is gravitational, which is also centripetal with regard to its maintaining orbital motion. This connection was the means that enabled Newton to unify Kepler’s celestial scheme with forces of nature in the formulation of a theory of gravity.

Newton used Kepler’s planetary laws of motion to derive the inverse square law for gravity. Kepler’s third law, in particular, relates the planetary orbits in the solar system. By it, the square of the period of any elliptical orbit equals the cube of the mean distance of the planet from the sun. The ratio of the time squared of Earth’s revolution around the sun to the cube of its distance from the sun (as from Earth’s center of mass to the sun’s center of mass) is thus the same as that of Mars or any other planet in the solar system.

Kepler’s third law in mathematical terms is

The letter k is a constant of proportionality equating the proportionality between the period of revolution A squared and the mean radius r cubed of semi-major axis of an elliptical orbit.

If the ellipse is a circle, which it can be, then r is a radius of a circle. As for simplicity, let the distance of orbit be that along the circumference of a circle such that the orbital distance is π times twice the radius of the circle.

The time or period of revolution of the planet can also be express in terms of distance divided by speed, as in the manner

Squaring and combining equations gives

Solving for centripetal acceleration by multiplying the last two sides of the equation by the velocity-squared and dividing them by k and by r to the fourth power gives

Centripetal acceleration according to Kepler’s scheme is thus proportional to 4π^2/kr^3.

Further multiplying both sides of the equation by mass m relates it to centripetal force in the manner

In accordance with Newton’s third law of motion the gravitational force between two bodies of mass is the same. Since radius r is a common distance separating the combined forces of masses m_1 and m_2, the product of their centripetal forces equates as

This equation expresses Newton’s general form of the inverse square law of gravity, with G as a constant of proportionality in place of 16π^4/k^2. It is determined as 6.67428(27) x 10-8 cubic centimeters divided by grams and seconds squared.

A Galilean Interpretation

A simpler explanation of Newton’s law of gravity is according to the discovery by Galileo that all bodies of mass fall at the same rate. It is more analytical and less mathematical.

Galileo’s findings indicates the gravitational force from and to each mass is proportionally the same. For instance, twice as much mass requires twice as much gravitational force such that the force distributed per mass is the same. The rate of fall toward a particular mass is thus the same for all mass. However, the rate of fall still depends on the amount of mass doing the gravitating. Another Earth with twice the mass of our Earth, for instance, has twice as much force to double the rate of acceleration. Moreover, another moon with twice the mass of our moon has twice the force of our moon. Together the other Earth and moon have four times as much force to attract each other, as according to the amount of arrows below.

Consider an Earth and moon with thrice as much mass and so on, or simply divide any Earth and moon each into any equal number of parts. Count the total number of mutual attractions between an Earth and a moon part. This is simple multiplication, as the total force of attraction between the Earth and its moon is the number of moon-part-actions times the number of Earth-part-actions according to the above illustration. However, since the result differs as to the number of parts calculated, there is a constant of proportionality included for consistency, as for specifying the unit of measure of a part, such as a gram, centimeter, second and so forth.

The total force of each mass is thus the product of the two forces of each mass. It includes the product of each mass dividing by their mean distance squared.

The mean distance squared is also an aspect of the equation known as the inverse square law. The law is consistent with how radiation spreads from its source of emission, as illustrated above.

If gravitational force spreads in the manner say of light from its source, then the intensity at each equal distance of an imaginary spherical surface expanding from the source of emission decreases in accordance with an increase in surface area, as 4πr^2 for a distance of r. Newton inverse square law formula for gravity is thus again of the form Fg = Gm_1m_2/r^2.

The Escape Velocity

The gravitational influence of mass is supposedly extended from a closed orbit, but the mass only needs to move at a rate faster than its gravitational binding energy to escape the orbit.

The speed needed to escape an orbit is calculated according to the kinetic energy K = ½mv^2 of mass m moving at speed v in comparison to centripetal force, which is the gravitational binding energy. Its orbital speed in a circular orbit is the square root of GMm/r = mv^2 of mass M say at Earth’s surface if Earth’s mass and radius are M and r. Since the centripetal force is twice the kinetic energy in direct proportion to speed, the orbital speed times the square root of two is thus the needed velocity of escape. At Earth’s surface, for example, it is approximately 175,000 miles per hour.

Explaining Gravity

Newton was not content with his inverse square law for gravity only explaining action of one mass on another as occurring at a distance. He considered it as casually absurd and thus attempted to explain gravity more completely in the manner of a contiguous action of masses somehow affecting the space between them and thus indirectly affecting the other mass.

Newton attempted to explain gravity according to an agent acting between mass for contiguous action to occur, but he was reluctant to recognize the æther as a plenum or a medium for wave action. He regarded it as an obstacle to the free movement of planets and the natural motion of mass in general unless it could be rare in content. He thus considered it is extremely fast moving particles of minute mass for internal elasticity of containment. He reasoned a teeny nearly massless particle with a greater speed can move with the same momentum as a slow moving massive particle, but a containment of the former can allow less resistance to movement of other mass than would a containment of the latter.

Newton’s description of the æther has merit and possible truth inasmuch as gravity could very well be the result of a vacuum effect caused by the interaction of æther with mass. A more inert mass accelerates the speeds of lesser inert æther particles. A vacuum effect occurs because of the increased speed of æther nearer to and between mass, as where the interaction is more intense in expanding its containment and to even out farther away from the vicinity of mass. This effect can occur if more massive material particles increase the speeds of the æther particles for them to increase their containment range. The less massive but more elastic and vibrant æther vortices expand outward in leaving a vacuum in their wake. If less vibrant æther replaces them, then the two must not interfere with each other to negate the process. Perhaps the more vibrant æther splits to be less massive than the less vibrant æther it is replaced with. As mass splits and rejects the vibrant æther, the less vibrant æther pushes forward to fill the otherwise vacuum. A partial interaction of æther with mass further constitutes the gravitational effect.

Kinematics

Newton’s concept of the rarefied æther compares favorably with the kinetic theory of gases. He did not, however, define energy in his mechanics other than as a force in relation to conservation of momentum and conservation of mass.

Although Newton unified celestial and terrestrial mechanics, the development of terrestrial mechanics was not completed by him. Lacking, for instance, was the concept of kinetic energy, which he did not use to derive the numerical value of the escape velocity.

Kinetic derives from the Greek word kinesis that means motion, but it was applied much later, as about 1850 by Lord Kelvin.

Gottfried Leibniz (1646-1716) called the energy of motion “vis viva”, meaning the living force. Willem’s Jacob Gravesande (1688-1742) found the penetration of clay from weights dropped from different heights is in proportion to the difference in the square of their speeds. Emilie du Chatelet (1706-1749) explained this result as work energy of the change in speed of mass used to move a mass quantity a distance proportional to the inertial resistance causing the change in speed.

With calculus, Joseph Lagrange (1736-1813) found in 1811 there is an additional difference between Vis viva mv^2 and potential energy of momentum mv by a factor of 2. The factor ½ for kinetic energy K = ½mv^2 came from Gustave Coriolis (1782-1843) in 1829, even though a kinetic theory of gases had been developed earlier by Johann Bernoulli (1667-1748) in accordance with Newton’s laws of motion.

Consider a moveable partition that separates two gases into equal volumes of cubic space. Each gas has the same number of molecules, but molecules of one gas have fourth the mass moving twice the speed, on the average, than do the more massive molecules of the other gas. Since ½m(2v)2 = ½(4m)v^2 the gases have the same kinetic energy and since one fourth the mass at twice the speed strikes the partition twice as often, the momentum of action on both sides of the partition per time of action is the same, such that the partition does not move. This condition of the kinetic theory of gases is thus the same as Newton’s condition for the æther.

Another condition is that of elasticity. In contrast to elastic collision where mass reverse momenta is an inelastic collision where masses combine as one in the manner

Let M = 2m. Hence

Kinetic energy is therefore not conserved in inelastic collision according to Newtonian Mechanics.

Conservation of kinetic energy of elastic collision is proven with three equations according to Newton’s laws of motion:

(1a)

(2a)

(3a)

Accordingly, n denotes any positive real number such that the product nm denotes any mass quantity that is proportional to m. The left sides of equations (1a) and (2a) represent the momentums and kinetic energies of the masses before collision, and the right sides of the equations represent the same after collision: v_1 and v_2 are the velocities before elastic collision and v_3 and v_4 are the velocities after collision. Equation (3a) defines a condition of elastic collision where the difference in relative speed between masses remains the same after collision as before collision, but reversed in direction.

To simplify, both sides of equations (1a) and (2a) are divided by m, and both sides of equation (2a) are multiplied by 2, obtaining

(1b)

(2b)

(3b)

To prove elastic collision conserves kinetic energy, the task is to derive equation (2b) from equations (1b) and (3b).

Equation (1b) is first rearrange by subtracting v_2 and nv_3 from both sides of it to obtain

By dividing both sides of the resulting equation by (v_1 – v_3) a solution of n is obtained as

Rearranging equation (3b) by adding v_2 and v_3 to both sides of it obtains

Dividing both sides of it by (v_1 + v_3) obtains

The product of the two solutions n and (1) gives

By taking the first and last equalities of this equation and multiplying them by (v_1^2 – v_3^2) obtains

Adding nv_3^2 + v_2^2 to both sides of this result obtains

Multiplying both sides by m obtains

(2a) is thereby derived from (1a) and (3a) in proving conservation of kinetic energy in elastic collision from conservation of momentum and from conservation of the difference in relative speeds after collision.

The proof also assumes conservation of mass and that no exchange of mass occurs between masses. The exchange of mass between masses due to their elastic collision is conditional to Einstein’s special theory of relativity as part of its Newtonian Classical Mechanics modification. Energy of motion, according to special relativity theory, is conserved in inelastic collision by it converting into another form, such as heat. Energy and momentum are conserved in elastic collision with the exchange of mass of masses in collision.

NATURE FROM WITHIN

Sometime in the thirteenth century Giles of Rome (b. before 1247 – d. 1316) proposed an atomic theory according to the principle no form of matter can exist smaller than a certain minimal quantity of substance. He tried to support his theory with the investigation of a vacuum state by way of a cupping glass or siphon producing a suction force. He was unable to prove the atomic nature of his theory, but similar investigations of the vacuum state continued, eventually leading to Boyle’s Law relating pressure and volume of gas at a certain temperature.

From Boyle’s Law along with the development of chemistry the laws of thermodynamics along with the classical theory of the atom were established. History brings to light a more detailed step by step process of this development.

The Kinetic Theory of Gases

Giovanni Batiste Beliani (1582-1666) debated with Galileo on how to explain vacuum effects. In the year 1620 the debate focused on the effect of air weight. It was known water could flow from a vessel through a siphoned tube placed over a hill. However, if the top of the vessel was sealed, a partial vacuum occurred at the top of the vessel from the leakage of water at the bottom, as to restrict the water from flowing through the tube.

Galileo suggested attractive forces exist between the water and the vessel whereas Beliani believed the air outside exerts pressure on the water attempting to come out the tube at its other end. Beliani was correct, as further investigation of the vacuum state led to the invention of the mercury barometer, as by Evangelista Torricelli (1600-1647), and also the air pump by Otto von Gueriche (1602-1686) of Germany.

Torricelli used the barometer to compare pressure of air at sea level to it high in the mountains. Not only did he find a difference; he further discovered that air pressure changes with a change in the weather.

Gueriche invented the air pump to produce more vacuum in order to increase the work capacity of air. The outcome was him using the barometer in 1660 for forecasting the weather.

In England Henry Power (1623-1670) and Richard Townely (1629-1707) together experimented with air below atmospheric pressure and found the product of pressure and volume stayed constant. Robert Hooke (1625-1703) experimented with air above atmospheric pressure and obtained the same result. Robert Boyle (1627-1691) and Hooke further investigated the nature of gas pressure in general to discover the same result. Boyle then proposed in 1662 the law that the product of volume V and pressure p of gas is constant at fixed temperature T, as expressed by the equation pV = k. (Edme Mariotte (d. 1684) of France also proposed the law independently later in 1676.)

Boyle derived his law according to Newton’s laws of motion whereby the constancy of volume-pressure is geometrically determined. Another volume of twice radius, for instance, is eight times larger with surface area four times larger. Molecules thus have four times as much surface with which to collide. However, the average distance for a particle to reach the surface is doubled for it to collide half as often. The intensity of collision is thus one-eighth as much for one-eighth as much pressure at eight times more volume.

To understand Boyle’s law in terms of kinematics first consider pressure p in terms of force per area, as pounds per square inch where weight is synonymous with the force of gravity. The latter further equates in terms of centripetal force mv^2/r, as according to mass times velocity-squared per distance of orbit. Pressure per area thus equates as mass times velocity-squared per radius of orbit r and per containment area d^2. The product of radius and area is dimensionally the same as volume: V = rd^2. Hence, pV = (rd^2)(mv^2/rd^2) = mv^2, which is twice the kinetic energy K = ½mv^2.

What followed from Boyle’s law was a relation of heat and temperature. Although generally attributed to the motion of atoms or molecules of matter, all that physicists essentially knew about them is the former is a quantity contained of the mass and the latter is a measure of how much a particular substance such as mercury expands in relation to heat absorbed. Now, with Boyle’s law, it appeared they could be resolved in mechanical terms of substance and relative motion.

Daniel Bernoulli (1700-1782) initiated the kinetic theory of gases along with his study of hydrostatics. Bernoulli advocated a mechanical theory in analyzing the kinematics of molecular interaction in analogy to the collisions of billiard balls. Such a process had been regarded at the time as being too simple for resolving the complex nature of reality, but it was a consistent way of explaining Boyle’s law nonetheless.

It remained questionable as to whether or not k is the same for all temperatures T. Guillaume Amontons (1663-1705) foresaw the ideal gas law pV = nkT before it became established, as stating in a 1702 paper that a product of pressure and volume equals a product of temperature and a constant. He also considered a zero temperature in equating zero temperature with zero pressure, which anticipated an absolute temperature scale established about a century and a half later.

Another form of the law is the law of volumes, or Charles’ law, whereby there is an increase in volume, instead of an increase in pressure, with an increase in temperature. The law was proposed by Jacques A. C. Charles (1746-1823) in 1787, which, with Archimedes’ principle of buoyancy, led to the invention of the hot air balloon.

Joseph Louis Guy-Lussac (1779-1850) established the law quantitatively, as published in 1892, whereby from each degree centigrade in temperature change a corresponding change in volume occurs of one part in 273 parts volume of gas, as of the same pressure.

As an ideal gas law was hinted at by Amontons in 1702, it was explicitly stated by Paul Emile Claypeyon in 1834 in relation to Boyle’s and Charle’s laws. It was derived in 1856 by August Karl Kronig (1822-1879) in accordance with the kinetic theory of gases, and also in 1857 by Rudolf Clausius. Johannes van der Waals (1837-1923), however, showed in 1873 that the law is not ideal because electrical attractions and molecular orientations are of further influence.

A criticism of the kinetic theory of gases itself was that the violent internal motion of matter would cause it to explode every which way. No counter argument came forth until the middle of the 19th century when Clausius explained minute particles great in number obstruct each others’ mean free paths of escape. Their constant collisions keep reversing direction such that the total distance moved is much longer than outward distance itself. The mean free path of escape relates to a Van der Waal’s Force, as well, in that the molecular size of molecules in collision can affect impulse time of response and thus the time at which force reaches the walls of the container.

The kinetic energy of gases was to be revived in a statistical form by Clausius, Maxwell, Boltzmann and others in the later part of the 19th century according to conditions of probability. Further modification would be required with the discovery of the quantum and a probability interpretation of quantum physics.

The Substance of Heat

Heat as molecular motion had many proponents, including Boyle and Hooke, but until the later part of the nineteenth century a theory of heat as a substance was more accepted. The reason is somewhat complex, but the idea of relatively stable matter with its violent, inner molecular motion causing it, to the contrary, to explode in all directions was influential. In any case, instead of explaining heat as “internal movement” of the internal components of matter, the more popular idea was heat results from absorption and emission of a particular substance by matter.

Both Boyle and Newton proposed fire consists of material substance, as the residue caused to burn and produce heat. Boyle experimented to find a number of substances that did not decompose. He defined such a substance as an element.

Etienne Francois Geoffrey (1672-1731) advanced in 1718 the known fact that a particular substance of a compound (such as carbon of carbon monoxide) can be replaced by another (say hydrogen to form water molecules from the oxygen of the carbon monoxide). He then derived a table of 16 columns demonstrating the order of replacement of some known substances. This effort evolved into a table of affinities wherefrom the element A instead of the element B combines with the element C because elements A and B have more of an attraction for each other.

Henry Cavendish (1731-1812), Joseph Black (1728 – 1799) and Joseph Cavendish (1731 -1810) made use of the table of affinities for discovering nearly all the elements of permanent gases. The discoveries further enabled an explanation of the oddity of weights from combustion and calcinations of different materials, as resulting from the combination of different elements to produce various combinations of exchange.

Newton had considered an inert matter contained by elastic forces of some kind of æther and offered an explanation of heat as a repulsive force decreasing in inverse proportion to the distance between molecules. He argued particles of light excited the æther, which conveyed the excitement onto matter to produce heat and other effect. He even supported the connection of æther with heat and light by experimentation on the bases a vacuum did not prevent a transfer of heat (as radiant heat requires no material medium).

Attraction and Repulsion

Newton was also influential to future theory for advocating a dualistic principle of both attractive and repulsive forces of nature: one of gravity and another of heat. Stephen Hales (1677-1761) developed the idea both attractive and repulsive forces consisting of two kinds of matter tend to become balanced in a state of equilibrium. This was to have profound influence on Benjamin Franklin (1706-1790) and others with regard to two fluid theories of electricity and magnetism.

Theorists generally inclined to relate all forces as substance determining the internal nature of matter. In the 1740s, for instance, Franklin proposed electrical phenomenon is an elastic fluid of mutually repulsive particles. Matter is electrically neutral if it contains the right amount of particle fluid, repulsive if it contains an excessive amount, and attractive if it is deficient of it. Gowin Knight (1703–1772) also proposed a fluid for magnetism and the propagation of light as the vibrant motion set up in the fluid.

William Cullen (1710-1790) advanced the idea the forces of matter result as various modifications of the æther pervading matter. He proposed that electricity, light, heat, gravity, magnetism and so forth emanate as various forms of æther that is itself gravitationally weightless and distinct from matter.

Latent Heat

Cullen’s student Joseph Black considered the idea heat, light and so forth are modifications of the æther. He followed it through with a systematic study of the effects of combustion and calcination that established the science of calorimetry.

Black’s main study pertained to temperature and heat. Newton had defined the quantity of heat as the amount of time it takes to lower its substance to room temperature. Black took this to mean that heat can be measured as the time that is required to drop or raise its temperature a certain amount. He thus measured a certain quantity of water according to the time it takes to raise the temperature one degree. The temperature, however, did not change in such cases as involving a change from water to ice or vice versa, and from this find Black proposed the concept of latent heat.

This latent form of heat had also been noticed by Daniel Gabriel Fahrenheit (1686-1736). He discovered water remained in the liquid state while cooling at the freezing point (as now 32 degrees Fahrenheit) but also congealed into the solid state above this temperature by way of shaking the container. This find that Black also verified on his own in 1761 suggested heat could be stored as a latent form of energy without a rise in temperature. A mixture of ice and water, for instance, need not change in temperature with change in heat.

From Phlogiston to Caloric

In consideration at this time for an explanation of the latent form of heat could have been with regard to a theory of phlogiston as an inner substance of matter that converts to heat and the flame of fire. However, it was to be surpassed by a theory of caloric.

In aiming to disprove a theory that phlogiston is a primary substance of fire, Antoine-Laurent Lavoisier (1743-1794) could have introduced caloric in naming the substance of heat. George Ernst Stahl (1660-1724) had proposed phlogiston is a substance whose violent motion produces heat and flame when passed into the air from the dispersing of matter. Plants then absorb and recycle it. There is truth to this idea if we identify phlogiston with carbon, which Stahl did, but he also claimed phlogiston is the only element that can exist by itself not as a compound, and is the catalyst for all processes of combustion.

This generalization was open to dispute, as some substances lose weight during calcinations but others gain weight. Thus, in some cases, phlogiston needs to be of positive weight; in other cases, it needs to be of negative weight.

A key to resolving this quandary was the table of affinities first presented by Geoffrey; wherefore came many chemical discoveries. Particularly pertinent was that of oxygen whereby physicists no longer needed a phlogiston to explain a changed state of matter. Calx plus phlogiston producing metal, for instance, could more easily be explained as calx giving up oxygen to become metal; or, conversely, metal absorbing oxygen becomes calx. More experiments by Lavoisier showed the conversion of sulfur, phosphorus and arsenic into oxides results in their gain in weight because there is a decrease in the weight of air.

In disclosing the inadequacy of phlogiston theory Lavoisier held the general belief of Cullen and others that æther acts as a weightless elastic fluid that is not influenced by gravity and is primary responsible for such effects as light, heat, electric-static repulsion and so on. He followed up experimental results of Cullen on cooling effects of such volatile liquids as alcohol by vaporization and found the temperature of ice did not increase while changing to a liquid state. In replacing phlogiston with caloric he proposed an element such as oxygen has more affinity for absorbing caloric than does another, and by vaporizing into the atmosphere leaves the base material cooler than before. This, too, more consistently explains the change in weight of the substance, as caloric is only a catalyst.

From Caloric to Atomic Theory

It had also become evident substances combine in definite proportions. For instance, a precise amount of oxygen combines with a precise amount of hydrogen. Joseph Proust (1754-1826) thus stated this result as the Law of Definite Proportions.

A similar law is the Law of Multiple Proportions proposed by John Dalton (1746-1844). According to it the chemical elements consist of tiny particles called atoms. The atoms of a particular element are all of the same size, weight, mass, etc. that differ from those of other elements, but that different elements combine in ratios of simple whole numbers in forming chemical compounds. Dalton even published a table of atomic weights of six elements: hydrogen, oxygen, nitrogen, carbon, sulfur and phosphorous. The lightest of these elements, hydrogen, was, as by convention, assigned the number one.

A similar law is the law of combining proportions of various gases, as proposed by Gay-Lussac. He and Alexander von Humboldt (1769-1859) discovered that two volumes of hydrogen combine with one volume of oxygen to become two volumes of vaporized water with the same temperature and pressure. Gay-Lussac further considered data collected by Humphrey Davy (1778-1829) with regard to the volume ratios obtained by combining nitrogen with oxygen. He further found by experimentation a half gaseous volume of nitrous oxide is obtained by combining a volume of nitrogen with a half volume of oxygen of the same temperature and pressure.

Similar finds encouraged Gay-Lussac to conclude that gases combine in simple ratios of whole numbers, as they also do according to weight. However, he did not explain the nature of these whole number combos as to why some differ from others. Why, for instance, does water vapor squeeze one volume of oxygen and two volumes of hydrogen into two volumes total?

The whole number ratio combo was explained by Amedeo Avogadro (1776-1856) with the hypothesis a gas with the same volume, pressure and temperature of another contains the same number of molecules. As to why two volumes water vapor is the result of two volumes of hydrogen gas and one volume of oxygen gas he assumed molecules are formed from “solitary elementary molecules”, or atoms. Since a molecule (or two atoms) of hydrogen gas combines with an oxygen molecule (or one atom) to form the molecule of water, the number of molecules per volume stays the same, as by two hydrogen atoms as two separate molecules converting into a single molecule.

Avogadro’s Law, as it became, was at odds with Dalton’s atomic theory that assumed the compounds of elements are the result of like atoms repelling each other in allowing atoms of different weight to occupy the space instead. Dalton and his followers thus could not accept the concept that identical atoms combine to become a molecule. As it were, Avogadro’s law failed acceptance until a fellow Italian, Stanislao Cannizzaro (1826-1920), pointed out in 1861 that the law could be used for a convenient table of atoms in simple ratios of whole numbers.

Rudolf Clausius (1822-1888) then helped promote the kinetic theory of gasses in explaining the vibrant motion of atoms is stable by being great in number, as each encounter between numerous atoms acts to slow the mean free path of escape by constantly reversing their directions, which is consistent with the Cartesian near interpretation of gravity by Newton according to vibrant æther cells or vortices, but which also implies that space is indeed filled with an enormous number of miniature cells as a medium of interaction.

The Fate of the Caloric

A role of caloric in the development of theory was to replace the phlogiston of fire to explain latent heat. The properties ascribed to the caloric were it consists of individual particles repelling each other, as flowing from hot to cold matter, as gravitationally attracted to matter, and as conserved. Thus Nicolas Leonard Sadi Carnot (1796-1832) used the caloric theory in deriving theorems for a more efficient steam engine.

Postulating conservation of heat as caloric Carnot theorized it flows from the hottest to the coldest parts of the mechanism performing work, as caused by the viscous flow of caloric. Since caloric is conserved, the process compares to a waterwheel turning by the flow of water that forever recycles. Similarly, since systems are unable to exchange caloric to perform work if they are of the same temperature, the recycling of caloric is required. Adding more fuel, for instance, allows a hot steam engine to continually release caloric to perform work.

Carnot’s conditions for efficiency were correct for the most part, but the conservation aspect of caloric is inconsistent with energy as conserved by converting from one form of energy to another.

Neither physicist nor chemist had yet established the modern law of conservation of energy, but Count Rumford (1753-1814) had demonstrated an enormous quantity of heat is generated by boring cannon holes. Humphrey Davy (1778-1829) rubbed two plates of ice together to demonstrate heat can be produced even if the surrounding temperature is below freezing where no caloric should be available. No appreciable change in weight or mass occurred in either case.

In demonstrating the enormous amount of caloric needed to be released as heat is unavailable, Rumford proposed vibrant motion causes heat instead whereas Davy offered heat results from the absorption of light. Davy also suggested a novel idea: that light combines with oxygen to become “phosoxygen”.

Conserving Energy

A difference between conservation of caloric and conservation of energy is caloric does not convert into another form of energy whereas all energy does, as in view of its modern concept. This modern concept was stated in 1841 by Julius Robert Mayer (1814-1878) as a force (then regarded as a varying form of energy) that merely changes from one form to another such that it is not created or destroyed. He argued kinetic energy lost by inelastic collision between masses transforms into heat.

James Prescott Joule (1818-1889) verified Mayer’s argument in relation to friction. Heat that results from stopping motion by friction was common knowledge. Joule measured it quantitatively to conclude lost heat is due to work being used to overcome friction.

It was known that the flow of electricity through a highly resistant wire heats the wire. Joule established this effect quantitatively in 1841 in confirming current transforms into heat in mechanical units of work.

Hermann von Helmholtz (1821-1894) lectured in 1847 before the scientific community that there is no such thing as a perpetual motion machine performing work without compensation for it in return.

Simply put, given an isolated system, the internal energy of the system comprises, as stated in modern terms, the total of kinetic and potential energies of the molecules, which remain constant unless acted on by some external influence. Where the systems interact, a change in internal energy is according to the quantity of heat absorbed and the amount of work performed on the system, as according to the equation

H denotes a quantity of heat, W denotes the amount of work performed and the letter E proceeded by the Greek delta letter Δ denotes the change in energy.

Note that one form of energy is related in terms of its potential. A ball at some height, for instance, has a gravitational potential. If it rolls off the table and falls, then its potential energy converts to kinetic energy of free fall. By the friction of the ball falling through the air and colliding with the floor, kinetic energy further converts into heat. Potential energy thus links to force with regard to such circumstances as mass position. If the path of mass is circular, for instance, then change in force and change in its potential are zero in regard to a conservative field of force. However, contrary to potential energy is the concept of entropy whereby a portion of energy is lost for useable work.

Entropy

Clausius, in 1850, and William Thompson (1824-1907)—renamed Lord Kelvin—in 1851, independently reformulated the theorem put forth by Carnot for it to comply with conservation of energy.

In view of conservation of energy the condition of adding fuel to sustain a difference in temperature for doing work is maintained, but in place of the concept of caloric is the distinction between useful energy and non-useful energy. Useful energy is that which can be used to create change; non-useful energy is energy in a state of equilibrium that does not change except by outside influence. Two bricks in thermal equilibrium at the same temperature, for instance, are incapable of doing work by way of an exchange of heat from one brick to the other.

It is therefore possible to have a certain amount of energy in the form of heat at absolute temperature say T_1. In theory, we can only harness all the energy of the temperature if it reduces to absolute zero, as by some remarkably efficient machine capable of harnessing it, but since systems tend toward an equilibrium state, as somewhere between T_1 and absolute zero, the energy can only be harnessed by lowering it from T_1 to T_2, as according to the relation

Applicable to this relation is an absolute temperature scale, which Kelvin introduced after Joule suggested in a letter to Kelvin that it was possible to measure the difference from absolute zero. All heat energy is thus available if T_2 = 0; none is available if T_2 = T_1.

The relation here does not include latent or stored energy, as that of atomic energy. Clausius had already considered this aspect of the principle and went on to generalize the process in the form of an empirical law he named entropy, which has been defined in various ways. Its general conditions are: entropy is a measure of the energy of an isolated system unable to do work on the system; entropy of a system does not decrease other than by increasing entropy of another system. A proportional amount of energy within the universe is thus never available to produce change. Whether this total proportion of non useable energy itself increases further depends on what is the ultimate capability of the universe.

For an example of increasing entropy consider a laboratory having no outside influence except for the pull of gravity. Inside the laboratory a string keeps a rubber ball from falling. Eventually the string breaks to allow the ball to fall in converting potential energy into kinetic energy. Assuming the ball and floor to be nearly elastic, the two forms of energy, potential and kinetic, alternate as the ball bounces, but the ball also encounters the friction, or viscosity, of the air while in motion, and the process tends to be inelastic. Even if there is no air, it is inelastic due to heat generated by the ball’s impact with the floor. As the ball eventually comes to rest on the floor, kinetic energy converts into heat energy, as given to increase the relative speed of air molecules or heat up the outside area. The process thus ends in a state of equilibrium that is irreversible except for outside influence, such that the entropy of the laboratory is increased to maximum until another part of the universe intervenes.

A quantity of heat, Q, is thus a determining factor of entropy in ratio to the absolute temperatures of the internal bodies of an isolated system, as the difference in temperatures of the bodies determines the amount of heat available for useful work. Thus, when a body at temperature T_1 surrenders an amount of heat Q to another body at temperature T_2, a change in entropy, ΔS, of the two bodies is

If the system performs work, then the amount of heat Q_1 lost at temperature T_1 will generally differ from an amount of heat Q_2 gained at temperature T_2, such that the change in entropy is according to the equation

The result ΔS = 0 is called an adiabatic process that is efficient enough for entropy to be conserved.

Generally the action between systems is such that energy is conserved but its entropy is not conserved. An adiabatic process is thus a special case of nature. If the universe is infinite in extent, for instance, it could decrease entropy by way of the condensation of mass by gravity creating pressure and higher temperature to counterbalance the increase in entropy from work of individual systems. The finite expanding universe allows an increase in entropy, as for an eventual heat death of thermal equilibrium. However, since the rate of expansion is now interpreted as increasing due to increase in so-called dark energy, an adiabatic process of conserving entropy could still be in effect.

The adiabatic process, as given in a later chapter, was an integral part of the derivation of the quantum aspect of nature. The derivation related to an analysis of the temperature and pressure of a blackbody. Part of this analysis is a so-called Stefan-Boltzmann fourth power law in accordance with thermodynamics and the adiabatic process. Although it pertains specifically to blackbody radiation, there is a similarity regarding mass-energy density of the atomic structure. A proton is about 1836 times more massive than an electron, for instance, but is contained within a volume of space, as inside the nucleus of the hydrogen atom, that is about 1836 times less in radius than the rest of the volume of the atom containing the electron. The 1836 times more mass inside a volume of space about 1836 cubed times smaller is a ratio of mass densities about 1836 to 1 to the fourth power.

A more down to earth example of entropy is with regard to environmental concerns. Potential energy is stored within Earth as oil. Using it increases entropy, but this increase is countered by a decrease in entropy in the atmosphere, as the spent energy in the form of carbon monoxide results in greater absorbing of heat from the sun. However, the atmospheric work energy is less controllable, causing such havoc as hurricanes, draught and so forth. As potential energy inside Earth is used up, resulting in more hazardous conditions of the atmosphere, rational solutions are needed to find out how to use solar energy in place of fossil fuels.

FROM WAVE THEORY TO RELATIVITY

Theories of nature evolved from opposing views pertaining to how space is filled. By the viewpoint of Newton, the internal nature of matter is comprised of tiny, indestructible atoms moving by way of a partial vacuum, but according to the viewpoints of Aristotle and Descartes a substance fills all space to comprise a plenum.

Belief in the plenum was popular from the time of Aristotle until the development of the laws of motion. After Copernicus put forth his heliocentric view of the solar system and Galileo and Newton put forth their mechanics, it became apparent Earth moves freely as though the space before it is empty. It was thus only natural to assume tiny, indestructible atoms partially fill space. However, Descartes and others proposed to the contrary the atoms are tiny vortices swimming in a sea of æther such as only to seem as though moving in a partially empty space.

Nowadays the majority of physicists consider the æther either as non-existent or as invalid. It does not empirically exist and is therefore invalid if the world of physics confines itself only to observational effects. The æther nonetheless has a long history contributing to the development and understanding of theory and wave action is an integral part of modern physics, as illustrated by the chain reaction below.

The illustration above illustrates how momentum continues by either a medium or empty space before it. As by the medium, the momentum transfers to and from each iron ball by way of impulse. There is thus an impulse of momentum carried from one end of the row to the other when the former is struck by another ball. In this case the ball at the other end continues the momentum as seemingly relative motion.

The impulse action is typical of wave action. Since our perceptions of reality are subjective, it is possible that relative motion of particles is discrete wavelets of energy, as transferred by impulse and only perceived as particles moving by way of an empty space before them. However, the momentum of the action forward needs to somehow be conserved by the reaction of the medium if the waves spread in various directions, as contrary to the straight action of the irons balls. Such originators of wave theory as Huygens were aware of the iron balls as pendulum action of them hanging on strings, but the momentum aspect seems to have been ignored. At best, it developed gradually along with a periodicity of waves and their circular nature.

The particle description is simpler, but the wave action is useful for understanding the true complexity of nature. Newton, for instance, was unable to explain the cause of gravity by way of a contiguous action. He thus described it according to an “action at a distance principle”. Although there were countless attempts to provide a causal explanation by other theorists, none were successful for centuries to come. Wave theory on the other hand can be more extensive in its approach. Waves, for instance, can superimpose to negate their relative effects, as to explain gravitational action at a distance in analogy to the illustration of the iron balls.

Wave action, however, is extremely complex with regard to the various ways it can occur, as depending on the nature of the wave producing medium. Sound waves, for instance, propagate by longitudinal action whereas transverse action is a typical wave property of light. Most waves have a periodic nature, such that any periodic motion of a particle can be described in accordance with a wave equation, but surface waves of the ocean vary in their periodicity with regard to a change in water depth.

Wave action is insightful for anyone willing and able to grasp its complexity, but such complexity here is avoided in favor of restricting it to a history of light.

Light and Wave Theory

Waves are obvious events, such as surface ripples on a pond that are known to be created by some sort of disturbance. As for a more extensive application of the wave concept to the nature of our world, Aristotle proposed light occurs from a wave-like disturbance of air. Descartes also advocated a wave-like disturbance of the plenum was the cause of light. However, as far as is known, there was no constructive wave theory of light until 1678 when Christian Huygens (1629-1695) proposed his.

Huygens offered a principle that wave envelopes are created anew at every point in space that a wave impinges. Each envelope spreads in all directions, but supposedly (as without any explanation by Huygens) those that reverse back towards the center where the original disturbance occurred are obliterated by wave envelops continually created, as to counter each other in restoring a state of equilibrium, whereas the outer envelopes continue to spread from the center with the support of the behind action as secondary waves.

The theory has been criticized for not explaining the obliteration effect, but it is likely Huygens had in mind that the wave action was in compliance with the law of conservation of momentum. He formulated the second law of motion regarding force and centripetal force before Newton reformulated them according to his more complete theory of the laws of motion. The inner obliteration could thus have been perceived by Huygens as a mutual cancellation of equal momenta in opposite directions whereas the advancing waves merely carry momenta forward.

Huygens was able to explain double refraction in accordance with his theory. However, reflection and refraction were more simply explained in accordance with a particle theory of light.

The law of refraction was accurately detailed in a manuscript by Ibn Sahl (940-1000) of Bagdad as early as 984. It was promoted in 1021 in a treatise on optics by Alhazen (965-1014) who viewed light as consisting of rays of particles. The law of refraction was further formulated by Willebrord Snellius (1560-1626) and by Descartes in introducing the sine function for the ratio of angles. It is known as Snell’s Law.

As a stick submerges into water it appears that its direction changes, but it is an optical illusion caused by the refraction of light, as changing direction when entering the denser medium of water. The reflection of light is simple: The angle of incidence Ө_1 equals the angle of reflection Өr. Refraction involves a change in speed of a wave that maintains constant frequency for entering a medium from another whereby the ratio of angles of incidence Ө_1 and refraction Ө_2 equate with the ratio of speeds v_1 and v_2 and the inverse ratio of refractive indexes n_1 and n_2 of the two mediums:

Huygens used his wave theory to explain double refraction of light, as discovered by Rasmus Bartholin (1625-1698) in 1669 to occur in a calcite crystal called Iceland spur. In double refraction light rays split into two directions, an ordinary one and an extraordinary one. The ordinary direction is in compliance with the law of refraction whereas the extraordinary direction is in non-compliance with the law. An explanation of this non-compliance by Huygens’ theory is allowable insofar as the ripple of the medium spreads waves in all directions. However, a more complete explanation was still forthcoming with the development of wave theory, as to include the properties of interference and transverse vibrations.

The corpuscular theory of light remained in favor up until around the beginning of the 19th century after Thomas Young (1773-1829) proposed the principle of interference. Leonardo da Vinci (1452-1529) observed water waves can cross paths without obstructing each others’ movements. Young applied this phenomenon to light waves in further surmising waves combine to either increase or decrease their effect depending on the degree they are either in or out of phase. If waves overlap in phase, then the intensity of light appearing on a smooth surface is enhanced. If waves overlap in opposite phase, then their effect is canceled for a dark spot to appear. Thus, in some cases, the overlapping creates more light; in others, it annihilates light.

Young introduced the principle of interference to explain light and dark fringes in diffraction patterns. Francesco Maria Grimaldi (1618-1663) had discovered sunlight spreads abnormally when it passes through a small hole. Young drilled two holes for an experiment and found light and dark fringes occurred when they otherwise would not if only one hole was drilled. The fringe pattern is explained as the diffraction patterns of two rays of light overlapping in and out of phase. Where they overlap in phase, light intensity increases more than the sum intensities of each ray before they overlapped; where they overlap in opposite phase, no light appears.

Some experiments produce no interference. This is now explained as light emitted from a source being relatively incoherent. Since light waves are extremely rapid, and since trains of them are relatively short, it is possible to detect two or more rays superimposing only in particular circumstances. It occurs in Young’s experiment by drilling holes close together. Another method is to split a light ray into two components, as by partial reflection. The split parts further reflect in different paths of slightly different distances for them not to rejoin in their original state; they superimpose instead into a slightly different state.

Transverse Waves

Young was able to explain nearly all light effects except polarization, the condition whereby transverse motion determines a particular direction for either the reflection or refraction of waves. Etienne Louis Malus (1775-1812) discovered in 1808 that either reflection or refraction produces polarization. Young was not able to explain it because his medium for light waves was compared to the propagation of sound through air as longitudinal waves of rarefaction and condensation of the air medium moving to-and-fro in the direction of propagation. This process does not explain a varying intensity by which light is either absorbed or reflected according to the angle of incidence.

Young suggested in 1817 that the waves need to contain transverse components in order to account for the polarization effect. Augustin Fresnel (1788-1827) was unaware of this suggestion when he formulated in 1818 his theory of optics explaining polarization in regard to transverse waves. His theory includes both Young’s principle of interference and the principle set forth by Huygens of the continuous waves spreading from each point source of contact. However, Fresnel’s transverse wave added another enigma inasmuch as transverse waves do not normally occur in non-solid states except for surface waves of a liquid.

In one-dimensional cases transverse waves move only along a rope but they do not spread laterally. A taut and elastic medium for three-dimensional space seemed to be too much of an obstacle to explain how the planets and other mass objects can move as freely through it as they appear to do.

The Elastic Medium

In investigating properties of the elastic medium, it was assumed by Claude-Louis-Marie-Henri Navier (1785-1836) objects are comprised of extremely minute and compact particles in relating to a caloric theory of heat whereby an attractive force and a repulsive force counteract each other as a restoring force in a state of equilibrium. If the restoring force is in a liquid state it reacts according to the relative speeds of the particles. In the solid state it reacts according to the distance of separation between particles.

Navier’s theory was elaborated on by Augustive-Louis Cauchy (1789-1857) with a law of elasticity that Robert Hook (1635-1703) had proposed. According to it the stretching of an elastic body is proportional to a force applied to it.

Cauchy interpreted Navier’s theory as setting up a condition of strain. Physicists call the mathematical formulation of this condition a tensor in relation to a more complex vector quantity in applying to variable forces of higher order. A vector pertains to a quantity having both particular magnitude and direction. The speed of a current, for instance, displaces the path of a boat crossing a river at a given speed. A vector speed and direction is the boat moving in one direction and the current moving in another. A tensor could include an increase in the speed of the current, say, due to the reservoir of water into which it falls increasing speed and decreasing height as it nears a waterfall.

Cauchy’s results were mathematically the same as Navier’s for homogeneous media, but more than one elastic proportionality constant is needed for isotropic media. Whereas a homogeneous medium is relatively the same everywhere, an isotropic one is relatively the same only in all directions and can vary with distance and other aspects. The media is necessarily isotropic in the case of Cauchy’s results in allowing more than one kind of wave (as transverse and longitudinal) to propagate through it.

The equations of elastic solids were incompatible with optics insofar as they allowed for a longitudinal vibration in addition to transverse ones (which might ultimately relate to the relative movement of matter). Cauchy overcame this incompatibility by considering the æther as labile, as able to change in some ways to a negative compressibility. This negative compression allows the æther to react differently to different kinds of waves and even to allow the longitudinal velocity to be zero.

George Green (1793-1841) investigated Cauchy’s results further and found them to be inconsistent with conservation of kinetic energy. They were also shown by Simeon Denis Poisson (1781-1840) and Franz Ernst Neumann (1798-1893) to be inconsistent with a wave theory developed more completely by Green.

Electromagnetic Rotation

As to how the planets and other objects move so easily through æther of such solidity, Gabriel Stokes (1819-1903) suggested the effect is relative: the æther relates to the slow moving planets as a rarefied fluid, or jelly, but to the extremely rapid vibrations of light as a solid.

James Mac Cullagh (1809-1847) proposed another solution. By it ethereal vortices, or atoms, do not resist a displacement resulting in distortion of the medium, but to a change in their relative rotations instead. This process is of a transverse nature that allows ethereal atoms to move freely through the æther, as only their rotations are subject to luminous effect.

As with these two ideas combined, matter moves through æther without resistance, as if sinking into a jelly, whereas light occurs as changes in the rotational states of atomic and ethereal vortices.

As rotation allows movement in a plenum, there are infinitely complex variations of rotation to allow unlimited effects of light, electricity and magnetism.

Hans Christian Oersted (1777-1851) tested in 1820 the effect of a magnetic needle near an electric current induced in a wire from a battery to discover the wire deflected the needle. A connection between electricity and magnetism was thus experimentally established.

Francois Arago (1786-1853) then demonstrated an electric current could magnetize iron. Soon thereafter Andre-Marie Ampere (1775-1836) demonstrated that electric currents affected each other similar to that of magnetic poles. The electric currents repel each other when flowing in opposite directions and attract each other when flowing in the same direction.

In 1831 Michael Faraday (1791-1867) discovered a change in a magnetic field induces an electric current in a wire. The aid of mechanical energy in rotating the poles of a magnet thus produces an electric current in a coiled wire that produces additional magnetic effect in turn. As electric current produces an electromagnet that produces additional current, as by alternating the poles of the electromagnet near to the wire, the result is electromagnetic induction as the basic principle of electric generators transforming mechanical work into electricity.

A law to equate an electrical current to a magnetic field was developed by Baptiste Biot (1774-1862) and Felix Savart (1791-1841), and by Pierre Simon Laplace (1749-1827). A significant part of the law is a constant of proportionality c for equating a unit of electricity e per time t passing through a unit length d of a section of a wire in proportion to the magnetic pole strength p, as p = ed/ct or cp/e = d/t. The pole strength of the magnetic field is of the same dimensions as the unit of charge of the electric field. They thus cancel out in the equation for c to be identified as a velocity: v = d/t.

Wilhelm Eduard Weber (1804-1891) and Rudolph H. A. Kohlrausch (1809-1858) ascertained in 1836 the value of c is the same as light speed, namely about 3 x 10^10 centimeters per second.

The constant of proportionality c having the same dimensions as velocity was significant for formulating an electromagnetic field theory. Ampere had believed magnets are really electromagnets induced by electric currents within the molecules of matter instead of in wires. However, Faraday believed magnetic currents, or, as in his way of thinking, “lines of force” exist in a seemingly empty space whereby changes occurring in electromagnetic fields take time and the propagation of their effect is the propagation of light.

Faraday did not formulate a mathematical theory. That was left up to James Clerk Maxwell (1831-1879) to formulate a theory of electromagnetism. According to it, electricity need not conduct through either wire or molecules of matter, but can propagate through the continuum of space as provided by the presence of an electromagnetic field. Simply put, the displacement of electric current produces an electric field that induces a magnetic field that, in turn, induces another electric field, etc., such that the open field creation progresses at light speed as the electromagnetic spectrum.

Advancing Theory

Verification of Maxwell’s electromagnetic theory came in 1888 when Henrock Rudolf Hertz (1857-1894) produced electromagnetic waves in showing that they interfere with themselves and he even measured their wavelengths as fringes produced on a screen.

The next task became to determine the state of the æther in relation to matter. For instance, if the speed c is constant through the æther, it is also consequential if æther itself is in motion, as either existing in a state independent of matter or influenced by the presence of matter.

Three possibilities were considered: 1) no æther is carried by matter; 2) matter only partly carries æther; and 3) matter carries all æther within the confinement of its path.

Hertz adopted the third hypothesis, which Stokes had already presented in 1845, but it was inconsistent with experimental results. Somewhat more consistent with the facts was the partial drag hypothesis, which had been proposed by Fresnel. Even closer to a theory consistent with all facts was one offered by Hendrick Antoon Lorentz (1853-1928), which assumes æther is a constant state independent of matter such that it can be designated as a particular state of absolute rest.

The assumption is incorrect, but its rebuttal led to the special relativity principle, which can explain all experimental results by assuming properties of matter are altered when moving through the æther. Clocks, for instance, are slower and the length of matter in the direction of motion is shorter.

A particular experiment of significance at the time was one suggested by Francis Arago (1786-1856) that indicated matter drags æther, as illustrated above. As a light ray splits into two of them by a partially coated silver mirror, other mirrors direct the two rays to pass in opposite directions through a glass tube of running water. In result, the ray moving in the same direction as the water arrives back sooner than the ray moving to the contrary. However, the increased speed of light and its decreased speed are only equal to a fraction of the water speed as in agreement with Fresnel’s partial drag hypothesis.

But Fresnel’s partial drag hypothesis was not able to explain a similar experiment carried out in 1881 by Albert Abraham Michelson (1852-1931) and Edward Williams Morley (1838-1923). It excluded the running water. If æther is either dragged or partially dragged by matter, then the slight shift in fringes of the wave pattern on a screen by this similar experiment should indicate a change in direction of Earth as it rotates on its axis and revolves around the sun. To the contrary, however, no change was observed to occur.

Explaining Experiment

The result of one experiment was consistent with Fresnel’s partial drag hypothesis. Another experiment favored Stokes’ complete drag hypothesis. What was needed was a theory able to explain the results of all experiments in consistent manner. A near candidate at the time was Lorentz’s electron theory.

Lorentz had theorized that electromagnetic fields consist of minute particles that bond together by their mutual attraction from having opposite charge. They are thus in a mutual state of vibrant equilibrium. This state affects light propagating through it. Since light is a product of the electromagnetic field, the state of the field is changed as well. As the electromagnetic waves of light interfere with the equilibrium state of charged particles, the field reacts to change the vibrant state of the charged particles. The resulting effect is that there is an increase in inertia of matter as it moves through the æther, as to vibrate at a slower rate and as having more external momentum.

The vibrations of matter also replace the æther as a light medium, as typical of water or glass changing the direction and speed of light, but light propagating through the material medium of the electronic state differs from that of the ethereal medium. The material medium varies in its relation to variable light whereas the ethereal medium is the same for all light. Different size light waves move at different rates depending on the relative density of the material medium. The light moving in the same direction as the water is therefore faster than if moving contrary to it. Matter becoming the medium of light propagation instead of dragging it thus explains the result of the Arago experiment. It did not, however, explain the Michelson-Morley null results.

In order to explain the null results of experiment Lorentz further assumed that matter moving through æther is squashed in the direction of relative motion as well as retarded in time.

The arm of the apparatus in the relative direction of motion being contracted results in light moving the same relative distance, as part of the apparatus, in any direction regardless of how they move relative to the æther. It alone is sufficient to explain the null results of the Michelson-Morley experiment.

Lorentz went a step further to define “local” time in assuming clocks in relative motion with the æther are likewise affected. Hence, the time of propagation is the same as if the apparatus is at absolute rest with the æther, suggesting the state of absolute rest in the æther is not ascertainable by means of the Michelson-Morley experiment.

Jules Henri Poincare (1854-1912) urged Lorentz in 1900 to generalize his theory for it to comply with the principle of relativity wherefore one motion of mass is merely relative to that of another mass. Lorentz did provide transformation equations to this effect, but he maintained it might still be possible to detect absolute rest. Meanwhile, Einstein independently derived the same Lorentz transformations in a manner free of all preconceived notions pertaining to the æther.

Lorentz and Einstein’s Explanations

The same transformation equations were derived in 1887 by Woldemar Voight (1850-1919) to describe the rigid medium of light as a non-compressible fluid. Voight considered the theories of Cauchy, Neumann and others in view of the Doppler Effect propounded by Christian Doppler (1803-1853). By it sound waves or light waves either extend or contract depending on the relative direction of motion between the observer and the source of emission. However, neither Lorentz nor Voight applied, in general, the transformations to the laws of mechanics. Einstein did, however, and, in consequence, physics abandoned the æther as a vital part of scientific theory.

In reformulating the principle of relative motion Einstein emphasized the æther is superfluous for the formulation of theory. He demonstrated this assertion in 1905 establishing the theory of special relativity as a unification of electrodynamics and mechanics. In so doing, he only postulated the constant speed of light as an empirical fact of nature, as with no reference to the æther or anything else for a possible explanation.

Einstein did suggest the æther could be retained for the purpose of understanding theory, just not for its formulation, but other physicists did not agree the æther should be retained. After physicists discovered light and matter both have a dualistic nature, as with particle-like or wave-like characteristics, such leading physicists as Bohr, Born and Heisenberg reinterpreted the so-called wave equations as probability equations, as to determine a probable location, time, energy and momentum for a particle effect to occur.

SPACETIME RELATIVITY

Einstein formulated special relativity according to two postulates: 1) light speed is constant in a vacuum relative to the observer regardless of what the velocity of the observer is relative to any other; 2) the laws of physics are the same in all inertial reference frames.

The second postulate is also called the principle of covariance. Light speed is covariant, but it is unique as well in that its speed in vacuum space is the same whereas the motion of matter varies.

The understanding begins with the mathematical explanation of the Michelson-Morley experiment with regard to its null result. It continues with derivations of Lorentz Transformations and so forth, as explained in view of the modification of Galilean relativity and how observation of absolute rest is nullified.

The Michelson-Morley Experiment

The Michelson-Morley experiment was contrived to measure light speed in relation to the æther. If the æther is representative of a state of absolute rest, if all light waves propagate at the same speed through the æther, then light speed should vary as Earth’s motion varies through the æther in various directions in orbit around the sun. However, no significant variation in light speed has been ascertained in this manner, such as in non compliance with the principle of relativity.

In accordance with the nature of this experiment light speed is measured as a to-there-and-back event. A silver-coated lens is positioned at a 45-degree angle to the incident light to split it into separate rays. One ray passes through a lens in the same direction while the other ray reflects at a right angle. Two more lenses then reflect the light rays back to the silver coated lens to pass through it to superimpose onto a screen.

What physicists expected from this arrangement is the total distance each split ray moves differs due to the perpendicular lengths of the apparatus not being precisely equal. What actually appears on the screen is an interference pattern of light and dark fringes (as predicted of superimposed waves according to wave theory.) A change in this interference pattern is what did not occur to verify a change in the relative speed of light.

To explain the null results, Lorentz first assumed the length of the apparatus contracts in the direction of relative motion by the mathematical factor

The symbol β represents v/c, the relative velocity of matter divided by light speed. Perpendicular lengths sx and sy are by theoretical agreement precisely equal:

Each arm of the apparatus thus compare as equal to a proper length denoted as s such that, if the apparatus is theoretically at absolute rest, the respective times it takes light to propagate respective distances there and back is according to the equations

In these equations, tx1 and ty1 are the respective times there and tx2 and ty2 are the respective times back.

What if the apparatus moves at velocity v in the x direction relative to absolute rest?

According to Galilean relativity and the premise light speed is invariant relative to the æther, the times for light to move respective distances sx and sy vary (if no relativistic contraction of length in the direction of relative motion occurs). Relative speed of light should be c - v towards the direction of relative motion and c + v in the opposite direction of relative motion. Total time of the to-and-from propagation along the x-axis should be

This time is comparable to 2tx = 2s/c, which is as if the apparatus were at absolute rest. If instead the arm of the apparatus contracts in the direction of relative motion, then the difference from that of absolute rest is only by the factor 1/α.

Similarly the total time it takes light to propagate in the perpendicular direction of relative motion, say during time 2t’y, can be determined. The actual path of light is according to two directions: 1) the direction along the arm of the apparatus that is perpendicular to the direction of relative motion; and 2) the direction of relative motion in keeping pace with the apparatus. The actual distance is along a hypotenuse of the right triangle with respect to the distances moved of those two other perpendicular directions. Hence

The comparative time light moves to-and-from in the perpendicular direction of relative motion is thus

It is the same with respect to the direction of relative motion if the arms of the apparatus in the direction of relative motion contract by the factor α.

Because light moves at the same time, speed and distance along both arms of the apparatus, there is no difference observed of a shift in the pattern of fringes. Although this explains the null result of experiment, it only requires the apparatus contract in the direction of relative motion; it does not require clocks to retard as well. However, it is just another step to determine them as relatively retarded according to their relative motion through the æther, as to complete the analysis in view absolute rest is invisibly non-discernable.

If clocks are slower by the factor 1/α, durations of events are shorter by the factor α. Hence

Absolute rest is thus invisible with regard to the there and back measure of light speed.

What remains unexplained is why light speed is constant from here-to-there. It is explainable, but the explanation involves the principles of covariance and simultaneity. It is possible to measure light speed by timing signals from one place to another, for instance, if the clock that determines the time of an emission is synchronous with the clock that determines its time of reception. However, the synchronization of clocks by means of comparing signals invalidates the measure of light speed from signals emitted according to these clocks. To confirm the two clocks are synchronous by direct means requires a transportation of one clock to the location of the other, as to involve relative motion that retards clocks. Since the exact speed of the clock relative to absolute rest is an unknown, the amount of retardation of the clock in relative motion is unknown as well.

Simultaneity

Although Einstein postulated constant light speed without explanation, his principle of simultaneity is a means of explaining it. Because Observer B’s clock in relative motion is slow, it is not simultaneous with the clock of Observer A relatively at rest. By the principle of covariance, however, A and B perceives events the same since B can also be regarded as relatively at rest. The simultaneity of events is thus relatively the same for both observers.

Consider B moves away from A at velocity v to a distance x after time t according to A’s clock. The task is to show B’s perception of time is the same as that of A’s.

At distance x it takes time x/c for light from B to move to A. The time for A to see B move the distance x is thus x/v + x/c. Since the coordinate lengths of B are contracted in the direction of motion by the factor α and since duration of events are also shorter by the factor α, as timed by B’s slower clock, and because the difference in B’s velocity from that of light is c – v in relation to A being relatively at rest, the equality of A and B’s timing of the event is

The relativity of simultaneity is thus covariant.

Lorentz Transformations

Transformation equations transform distance and time coordinates of observers in relative motion to the coordinates of the other observer. Let x, y, z, t be the perpendicular space coordinates x, y, z along with the time coordinate t of Observer A relatively at rest, and let corresponding coordinates of Observer B relatively in motion be x’, y’, z’, t’. At t = t’ = 0 respective origins O and O’ of coordinate systems overlap, such that the time and distance of an event in coordinate system B, as perceived by Observer B, is transformed in view of Observer A’s perception, and vice versa.

With clocks in relative motion slow, the principle of simultaneity comes into play by way of how clocks are synchronized. Let x’2 be midway between x’1 and x’3 with the direction of relative motion being from x’1 towards x’2 and so on. The time of light from x’2 to x’3 is ½(x’3 – x’1)/(c – v), whereas it is ½(x’3 – x’1)/(c + v) from x’2 to x’1. The difference in time relative to A is

Since x’3 – x’1 is contracted in the direction of relative motion by the square root of (1 – v^2/c^2), the equation becomes

The coordinates distances are arbitrary such that they represent any length anywhere in the direction of the x’-axis. Hence, designating t’ as the coordinate time of B relative to A, x_1v as coordinate time t of A, and x_3 as x coordinate distance of A, the equation becomes

This is the Lorentz transformation that transforms the coordinate time t’ of system B in view of system A.

A Lorentz transformation of distance coordinates is similar. Since the difference in simultaneity of time is according to constant light speed, which is the same time for the same distance, the difference in distance equals the difference in time. By using light speed as a conversion factor in the manner ct’ = x’ and t/c = x, it is only needed for the derivation:

Since lengths perpendicular to relative motion are not contracted and no change in distance occurs in the perpendicular direction of motion, coordinate lengths y’ or z’ thus equal coordinate lengths y or z:

Covariance

These transformation equations are here derived in view of how an observer at absolute rest interprets the events perceived by observers in relative motion. They are not yet related to how observers in relative motion determine events. What is not yet explained is a more general application of the equations in view of the principle of covariance.

By covariance the laws of physics are the same for all systems of reference. Constant light speed is thus covariant, but it is a unique property that differs from relative motion of matter whereas covariance applies to all physical events.

Covariance in particular means the perceptions of observers A and B are the same with regard to A or B being relatively at rest and the other moving at speed v. Since relative motion affects lengths and clocks, it is not obvious their speeds are the same relative to each other, but covariance of their relative motion is easily verified mathematically.

Consider Observers A as at absolute rest whereby Observer A sees Observer B move towards Observer A at velocity v the distance from x_1 to x_0 during time t_1 – to. The event includes a difference in time it takes light to move the difference in distance of positions x_1 and xo = 0. The time ta of Observer A seeing Observer B moving the distance x_2 – x_1 is thus

Since the clock of Observer B is slow by the factor 1/α, since Observer B approaches the oncoming light at velocity v, and since coordinate lengths of Observer B are relatively shorter by the factor α, the duration of Observer B seeing Observer A move along the length (x_1 – xo)α according to observer B’s clock is

The task is to show ta = tb:

Since α^2 = (1 – v^2/c^2), the equality ta = tb is confirmed such that observers A and B perceive relative motion the same regardless if either Observer A or Observer B is at absolute rest.

Illustrating covariance more generally is by way of solving for x and t in the Lorentz transformations. Hence

The comparative forms of the transformations are the same except for the direction of motion. The observer moves at velocity v relative to the other and the other moves at velocity -v. All motion is therefore relative.

Adding Velocities

Since the rate of a clock rate in A differs from the clock rate in B, the velocity of C relative to A being v_1 + v_2 is not obvious. In fact, it is not v_1 + v_2. In order to determine the correct velocity calculated by observers of system A requires a theorem for adding velocities.

To derive the addition of velocities theorem first consider inertial systems A, B and C. Consider system A as at absolute rest, system B as moving relative to A at velocity v_1, and system C as moving relative to B at velocity v_2. Given the velocities of C relative to B and B relative to A, the aim is to determine the velocity v_12 of C relative to A along the x-axis.

Consider the velocity of C relative to B as

This velocity is in terms of relating the coordinates of B to those of A. Multiplying the first and last sides of the equation by t – v_1x/c^2 obtains

Adding v_1v_2x/c^2 and v_1t to both sides of the equation obtains

Finally, dividing both sides of the equation by t and 1 + v_1v_2/c^2 obtains

This equality represents the velocity of C in relation to the coordinate system A.

The formula above is for comparing velocities in the same direction of motion. It is further possible to derive a formula for systems moving perpendicular to each other. For the task, consider system A at absolute rest, system B moving along the x-axis at velocity v_1, and D moving along the y’-axis at velocity v_3. What is to be determined is the velocity of D relative to A.

The analysis begins by comparing the coordinates of systems A and B, as in accordance with the Lorentz transformations:

This equality represents the velocity of D along the y’-axis of B in view of the coordinates of B.

Multiplying v_3 along with the far right side of the equation by the square root of (1 – v_1x/tc^2)2(1 – v_1^2/c^2) obtains in reverse order

This equality is the velocity of D relative to A.

The fraction x/t was previously determined to be v_12. However, it can represent any velocity along the x-axis. Let it be B’s y’-axis moving in the direction of the x-axis at velocity v_1. Hence

In result, D moves along the y-axis in a direction only relative to A.

The velocity of D relative to A with respect to the actual direction in the xy-plane is not yet determined. To determine it the Pythagorean Theorem is applied to speeds in perpendicular directions. A comparative length of the y- or y’-axes is the same, but the distance D moves along the y’-axis relative to A is determined by both the velocities of B along the x-axis and of D in the direction of the y-axis. The hypotenuse of a right triangle connecting perpendicular speeds represents the actual distance and speed. The result is

The velocity v_13 is that of system D relative to system A.

Since the derivation of these equations for adding velocities is conditional to the assumption light speed is invariable for all observers, they are to be consistent in showing light speed added to light speed or added to any velocity is light speed. To confirm:

The speed of light is therefore the same in all inertial systems in accordance with the addition of velocities formulas.

The Clock Paradox

In theory, clocks in motion are slow. Since motion is relative and covariant, observers A and B in relative motion time each other’s clock as slow. However, if B moves away from A, reverses direction and returns to A, then B’s clock is found by direct comparison to be the slower one.

This is the well-known clock paradox conditional to covariance inasmuch as there can be no distinction of absolute rest from relative motion. Both clocks are thus slow relative to the other; yet only one is slow by direct comparison.

The paradox is explainable since the event is not symmetrical. The traveling observer changes direction whereas the stay at home observer does not. In order to show the clock paradox does not contradict theory, it is thus only necessary to show Observer A’s clock is slow if Observer A accelerates instead of Observer B. Instead of Observer B changing direction to return to Observer A, A accelerates to twice the velocity of B to catch up with B. Because B changes direction to return with the same speed to A with which B left A, B also accelerates to twice velocity relative to that between A and B such that the two accelerations are symmetrical.

Observer B thus moves along the x-axis relative to Observer A at velocity v and changes direction along the x-axis at time T to move at velocity v instead of at -v. Regarding A as at absolute rest wherefore B moves relative to A, the comparison of time recorded by A’s and B’s clocks during the trip is

This longer time results from B moving an extended distance because of a slower clock.

The determination of time for the previous event is simple. However, for the event of A being relatively at rest and then moving to catch up with B, A’s clock keeps two different rates while B’s clock remains the same. By the addition of velocities theorem a change in velocity is not simply from v to 2v, as it is from v to v_12, which involves a corresponding change in rate of clocks. This condition is thus more complex than the previous one.

The task is nonetheless to determine the total time for A to catch up with B is the same as before, namely 2T/α. In perspective, what is to be determined is

Time T is A’s time while at absolute rest and T” is A’s time while moving at velocity v_12. Time T’ is the time of B’s clock in relation to A’s. A’s time is longer than B’s time by the factor 1/α because the acceleration is that of A instead of B.

Observer B moves relative to Observer A in time T a distance X at velocity v_1. In order to catch up with Observer B, Observer A accelerates from relatively at rest to velocity v12. The time T” it takes A to catch up with B is according to their difference in their speed. According to A this difference is v_12 – v_1, where v_12 is v_2 = v_1 relative to B. Hence

The total time relative to Observer A is

However, relative to Observer B, whose clock is slow by the factor 1/α, the duration of the event is shorter by the factor α. The total time of the event according to Observer B’s clock is thus

This time is also the time Observer A determines the event of Observer B moving the distance 2X’ to there and back as though Observer A is at absolute rest.

Constant Speed Change

According to Newtonian Mechanics, acceleration as change in speed can increase without limit. To the contrary, the addition of velocities theorem indicates light speed is a limit that matter can neither reach nor exceed. A relativistic modification is thus in order.

Applying the addition of velocities theorem for a system in constant acceleration is not a simple task, as the change in speed from two seconds of acceleration is easily determined by adding speeds in accordance with the addition of velocities theorem, as from speed changes after one second and after two seconds, but determining speed change at any time of acceleration entails a lot of calculation.

The task at hand is even more complicated due to the constant change in speed not being truly constant according to non-accelerating observers since the rate of speed change decreases at relatively higher speed, but it is constant according to an observer that is also constantly changing speed. Observer P, for instance, constantly accelerates if the speed of P perceived by P is the same when P is coincident with inertial systems A, B, C, etc. if the change from one inertial system to another occurs in equal time intervals and if the speed and direction of motion of B relative to A is the same as that of C relative to B, D relative to C and so forth.

The arrangement below depicts observers C, P’, B, P and A as coincident at time to = 0, with the speed of C as v_12 forward along the x-axis, acceleration of P’ as constantly changing from v_12 to 0, speed of B as v, the acceleration of P as constantly changing from 0 to v_12, and A as relatively at rest.

Covariance applies with regard to the symmetry of both P and P’ simultaneously meeting with B after simultaneously moving away from A and C to change speeds from 0 to v_12 and from v_12 to 0 according to the clocks of A or C. However, the clock of B is relatively slower for B to determine the event as to occur in less time. B thus perceives the event differently than does A and C, but symmetry with regard to B as relatively at rest is P and P’ simultaneously moving away from and returning to B in opposite directions as if moving away at initial speed v while decelerating to 0 where they reverse direction to accelerate from 0 to v.

Significantly the distance d of acceleration in view of A is vt, the time taking P to catch up with B moving at speed v away from A. Hence

The distance of constant change in speed thus relates as

Significantly, if v_12 is extremely small in comparison to light speed for the relativistic factor to be negligible in effect, then the equation approximates to classical non-relativistic formula in the manner

If the change in v_12 is (.6c – 0) during one second, for instance, then one half v_12 is .3c for u = .3c, whereby it approximates to vt = ct/3 = d/3. A velocity v_12 that is considerably less than c renders a considerably more accurate approximation.

The speed v as approximately ½v_12, such that d = vt, also approximates as an average speed change per time t, as according to classical formula. However, the modified equation only describes a change in speed in accordance with a time interval of A_1’s clock. Because P_1’s clock slows with increasing speed, a decrease in the rate of acceleration relative to A_1 occurs as well. It decreases with time in approaching maximum speed c at a minimum speed change per time c approaching that of zero.

As previously noted, changes in speeds of P or P’ are perceived differently by B than by A and C, as the difference in speeds as perceived by B is v whereas A and C perceive them as v_12. This perceptual difference constitutes another clock paradox also resulting from an asymmetrical condition of acceleration, as depicted below where A sees the event differently than does B.

The depiction is of B approaching A at speed v. P with B constantly decelerates from the speed of B in a second of A’s clock to become momentarily relatively at rest with A. During the one second of deceleration B moves past A and ahead of P. If the acceleration of P from v to 0 is covariant relative to A and B, their perceptions of it should be measured the same even though B is relatively moving away from P and A is relatively moving towards P. Their perceptions differ, however, because of the asymmetry of the event.

Let v = .6c and t = 1 second. Hence

The time of A observing the deceleration of P is TA = t – d_2/c = (2/3) seconds, the time t of one second of the deceleration minus 1/3 second for light to reach A at 1/3 unit distance for A to see the initial deceleration.

The distance of B from A and P at this time is vt – d_1 = 3/5 – 1/3 units = 4/15 units. Because B relatively moves away at speed v from the oncoming light from the event, the time TB it takes B to see the event from departure with P, as according to the slower clock of B, is

A thus sees the time of the event differently than does A. The ratio of times is TA /TB = (2/3)/(4/3) = 1/2. B thus perceives the event to occur in twice the time.

The principle of covariance still applies insofar as B can be considered relatively at rest just as can either A or C, but covariance requires symmetry. Symmetry, for instance, is with regard to Observer A’ relatively at rest with A, but positioned 1/3 unit distance from A where P and B depart from each other. A’ thus sees the event of P meeting A after time t + t/c = (4/3)t, the same as for B in the previous situation.

This last analysis differs from the previous one in explaining the speed change of P as only from B to A whereas the former analysis explained the change in speed from A to past B. Since covariance requires the time of acceleration from A to B by the clock of P to be the same time from B to C to D etc. and since ratios of these times relative to A, B, etc. are the same, it does not appear actual ratios are derived by covariance, as the clock of P in view of the last analysis could be any time slower as perceived by either A or B.

Since B’s clock rate in ratio to A’s is according to the relativistic factor α, and because the same ratio of clock time with respect to A, B, C, D, etc. is perceived the same by P, a change in ratio of P’s clock rate from A’s to B’s is similar to the same relativistic factor. The factor is also a progression, as P’s clock rate relative to C’s in ratio to B’s is in ratio to A’s by a relativistic factor squared. An increase in the relativistic factor by the power of one thus occurs relative to A’s clock rate for P’s clock rate in ratio to B’s, C’s, D’s, etc. However, the progressive change in ratio of P’s time is similar to but not equivalent to that of B, C, D, etc. Since P and P’ equally change speed relative to B, their differences in speed at any time is somewhere between the speed of B relative to either A or B. The clock of P from 0 to v relative to A is thus faster than B’s, but it is slower if either from 0 to v_12 relative to A or from 0 to v relative to B.

How, then, do we determine the time perceived by P?

Relativists generally compare the time of P’s clock by way of an Inverse Hyperbolic Function, which is a graphical means of plotting the time difference as the progressive difference in time with relative motion to determine where specific times and speeds are at on the hyperbolic curve.

The Doppler Effect

The Doppler Effect, proposed in 1842 by Christian Doppler (1803-1853), explains why a whistle of a train is of a lower pitch when the train is receding and of a higher pitch when it is approaching. The explanation is according to the vibration of air molecules forming waves. Lower pitch sound is of stretched out weaker waves whereas higher pitched sound is of compacted more energetic waves, which depends on the speed of the source and the listener of the sound receding from each other. They stretch by either their source moving in the opposite direction in which they move or by the listener moving away in the same direction the waves move. The exact opposite applies for shorter waves.

The effect is also consistent with the dynamics of relative motion for ordinary particles. The impact of a bullet fired from a gun, for instance, is more energetic if the gun firing the bullets moves towards the target rather than away from it.

It also applies to light, whether the light is either particle or wave in effect. Systems approaching each other naturally receive light signals more rapidly than do systems receding from each other. Light, as either waves or particles called photons, thus stretch out in effect when the emitting source is moving away from the observer or the observer is moving away from the source. Furthermore, if the source producing light is in relative motion, then the signals and their relative lengths are less frequent and less energetic because of the clock mechanism of the source being slower, but the principle of covariance still requires all effects to be the same for any difference in velocity between the source of light and the object receiving it.

The Doppler Effect is thus a more specific case of a more general principle. The task is only to illustrate its general covariance by examples of observers firing bullets at each other and then convert it to the specific case of the Doppler effect of light propagation.

Let Observer A be at rest at the origin from where Observer B moves away at velocity v_1. After the time T and the distance X of their separation, as according to A, A fires a bullet at B. Also after time T’ = T/α_1 of their separation, as according to A, B fires a bullet at A. The task is to show the time for receiving a bullet is the same for A as it is for B.

First consider the time Tb for B to receive a bullet from A is T plus the time Tx it takes the bullet moving at velocity v_2 to catch up with B moving away from X at velocity v_1. Hence

This is the time according to the clock of A. Since B’s clock is slow by the factor 1/α_1, B determines the total time as

The task now at hand is to determine the time for A to receive a bullet from B. Since B’s clock is slow by the factor 1/α_1, the time B decides to shoot a bullet at A after B passes A is T’ = T/α_1 at a distance X’ = x/α_1 between A and B. The speed of B’s bullet is according to the addition of velocities theorem:

The velocity –v_12 of the bullet from B’s gun is negative because it moves in the opposite direction. However, the time X’/v_12 that A receives the bullet is additional to the time X’/v_1 and is therefore positive. Hence the time A receives the bullet according to

This time is the same as Tb. Hence Ta = Tb is covariant.

To show a similar event for light signals it is only necessary to substitute c for v_2 and v for v_1 to obtain

This is the time either Observer A or Observer B sees the other observer to move the distance X.

We obtain a similar result for observers A and B approaching each other. In this case the distance X of B approaching A becomes shorter such that the time of X/v is negative instead of additive. Hence

This is the time for either Observer A or Observer B to see the other on arrival from the distances X and X’.

The relation holds for any distance X or X’ and for any time Ta or Tb. It is thus divisible into any number of distances and times. These times and distances can be related to the wave properties of light, wavelength λ and frequency f such that

They thus represent the relativistic Doppler formulae for a light source either relatively approaching toward or receding from an observer at constant velocity.

MASS-ENERGY DYNAMICS

Similar to the clock paradox is one with regard to relative mass. A mass in relative motion is relatively greater than if it is relatively at rest, but total mass is conserved by way of inelastic collision. That is to say, if you change speed by way of inelastic collision with another mass, the total mass you collide with does not change, but other mass apart from the collision does change due to your change in relative motion.

These conditions of relative mass are theoretically consistent and agree with observation. An increase in relative mass with an increase in motion is derived in a manner consistent with the laws of conservation of momentum and conservation of mass. The derivation is generally with regard to inelastic collision between two equal rest masses, but the result is extendable to unequal masses in either inelastic or elastic collision.

The paradox is with regard to how two masses in relative motion collide, stick together and maintain to have the same relative mass while relatively at rest. A resolution of the paradox considers elastic collision as an inelastic one plus its reverse process. Although the reverse process is opposite to inelastic collision, it also differs inasmuch as an exchange of mass occurs from elastic collision.

Relative mass and momentum are also conserved with regard to the reflection, absorption and emission of light by matter. Mass thus accelerates according to Einstein’s mass-energy equation E = mc^2. In addition, the classical concept of kinetic energy is redefined as the difference between relative mass and rest mass in relative motion

Relative Mass

According to SRT a mass m in relative motion at velocity v in ratio to light speed c is relatively greater than the same mass m_0 relatively at rest, as according to the equation

(1)

Also according to SRT mass-energy is conserved after collision. If it is inelastic (as where relative motion is lost from it) and if the total mass is observed from the same reference frame of motion, then the total mass-energy is unchanged.

The total mass-energy is also conserved for elastic collision, but if there is a change in the relative speed of masses, then there is an exchange of relative mass between them. However, all other mass-energy of the universe changing in view of the observer’s changed state of relative motion is not conserved, as it does not apply to the observation of a change that is caused by an observer’s acceleration independent of the action.

Despite this paradox an increase in relative mass along with an increase in relative motion is verifiable mathematically according to conserving mass-energy and momentum. Constant light speed and covariance also apply, as does the addition of velocities theorem.

Relative mass is first distinguished from the rest mass. Let m_0 be the mass relatively at rest with either Observer A or Observer B. Let m be the same quantity mass if moving with Observer B at velocity v_1 relative to the positive direction towards Observer A. Mass m and mass m_0 become one, say M, relative to Observer A by way of inelastic collision. Conservation of mass and conservation of total momentum apply according to equations (2) and (3):

(2)

(3)

Equation (2) shows the total mass is the same before and after inelastic collision. Equation (3) is somewhat more complex in that mo(0) is at rest with Observer A before collision. Total momentum relative to Observer A before the collision is thus only mv_1. Because both masses move at velocity v_2 after inelastic collision, the total momentum relative to Observer A is also Mv_2.

By substituting m and m_0 of equation (2) for M in equation (3) the latter becomes

(4)

The objective is to show

(5)

Showing equation (5) does equate is achieved by first converting v_2 to v_1.

In so doing the addition of velocities theorem and principle of covariance apply. For velocities in either the same or opposite direction of relative motion the addition of velocities theorem is of the form

(6)

In equation (6), βa = va/c and βb = vb/c. The velocity va is that of a second observer as measured by a first observer, vb is a velocity of something as measured by the second observer, and vab is also the other velocity as measured by the first observer.

For inelastic collision let Observer B represent the first observer seeing Observer A move at velocity v_1. Let A then be the second observer seeing the result of inelastic collision for m + mo to move at velocity –v_2. Since the principle of covariance requires the masses are the same relative to each other’s point of view, the velocity –v_2 as perceived by A is v_2 as perceived by B. By substitution, equation (6) becomes

(7)

(8)

Substituting the solution for v_1 into the conservation of momentum formula (3) gets

(9)

(10)

(11)

The denominator on the far right side of equation (11) further equates as

(12)

Applying the result of equation (12) to equation (11) gives

(13)

In view of equation (8) the fraction or last term in the bracket on the far right side of equation (13) is

(14)

Substituting (β_1)2 of equation (14) for 4(β_2)2/[1 + (β_2)2] of equation (13) renders equation (10) as

(15)

Hence

(1)

This verification of relative mass, as in accordance with the conservation laws of mass and momentum, was with regard to an inelastic collision between two equal rest masses. A more general verification is with regard to any collision whether it is inelastic or elastic, and between any two masses equal or not. A general proof is more complicated. The verification here given is only by way of specific examples.

A head on elastic collision is an inelastic one plus its reversal. An event as such of two equal rest masses is thus symmetrical in that the masses merely recede at the same speed in the opposite directions that they approached from. A critical difference between elastic collision and inelastic collision, however, is the elastic one, in theory, involves an exchange of relative mass between masses; the inelastic one does not. Although there is symmetry with regard to mutual exchange of relative mass between two equal rest masses, there is not with collisions between two unequal rest masses.

Consider mass mb moving relative to Observer A at velocity vb = .8c collides with mass mo relatively at rest with A. At an instant of inelastic collision the two masses move at velocity vc = .6c. After elastic collision mass mo moves at velocity

Moving at .6c is also Observer C who perceives A as moving at -.6c. C perceives mb before collision as say moving at velocity vbc, which is calculated according to the addition of velocities formula as

At the instant of inelastic collision the two masses are relatively at rest with C whereby the elastic collision between equal momenta reverses velocities for vbc to become –vbc relative to C. Relative to A it becomes

Relative to C elastic reversal of inelastic collision is symmetrical such that mb and mo are perceived to leave with the same mass they came with. As to show an exchange of mass, it is here in view of A. First, the total mass before and after collision is

Total mass before and after collision is thus 4mo.

Verification of the above result is by showing its consistency with regard to calculating conservation of total momentum:

It is thereby shown by example that both momentum and mass are conserved by exchange of relative mass.

Mass-Energy and Light

Say inelastic collision occurs between two masses for them to become internally the same as they were in relative motion. The law of conservation of energy comes into play. For, if collision is inelastic in nature, then motion stops. For it to continue some other form of energy needs to apply. With inelastic collision the energy could be stored internally as heat or molecular motion. With elastic collision kinetic energy is used to restore the relative motion of the masses in collision. For the collision to remain inelastic and for the masses to have the same content they had in relative motion, the internal energy is surrendered to whatever system causes the collision to be inelastic.

Heat is viewed as the random motion of internal molecules of mass, but conservation of relative mass and momentum should apply to molecular motion as well. The molecules are not able to directly surrender their motion to molecules of another system if the two systems are separated by space. However, there is still the possibility to consider of heat being absorbed and emitted as radiant energy, such as is light.

Since mass conserves energy to exchange it when it collides with other mass, a kinetic energy potential of relative motion maintains in some form or another. Einstein agreed. Mass and energy according to special relativity are equivalent whereby the mass content of a body is only one of many possible forms of energy as convertible from one form to another.

Consider a form of energy as light. Light emitted, absorbed or reflected by mass constitutes pressure, as predicted by the theory of electromagnetism that was derived by Maxwell in the middle of the 19th century and as verified in 1890 by Peter Lebedew (1866-1911) according to experiment. Reflection and absorption of light by two lightweight flags, for instance, can cause them to rotate around a tiny pole if attached opposite to each other and if one side of each flag is white and the other is black. One flag reflects the light; the other flag absorbs it.

In considering the relativistic nature of an internal form of potential motion Einstein equated the internal energy constitutive of a mass to the specific quantity equal to the product of mass and light speed squared. He even derived this relation in manner independent of the theory of relativity.

The relativistic mass and energy are according to the equation

The mass m_0 is the rest mass of m moving at velocity v and m_0c^2 is the “internal energy constitutive of the rest mass.” The rest mass in relative motion increased by m – m_0 is identified as kinetic energy potential for relative motion in approximation of the formula K = ½m_0v^2 for speeds far below that of light.

Einstein explained the relation according to a long tube with two spheres of mass positioned at each end. The two spheres are here denoted as A and B, such as inside a long tube of mass M relatively at rest. Sphere A has an excess amount of energy E_0. When inelastic collision occurs between the sphere and the tube, the kinetic energy of the sphere causes the tube to move at velocity v with momentum Mv. A photon of light with equal energy E_0 recoils in the opposite direction at speed c. Conservation of momentum applies such that the absolute value of E_0 equals the absolute value of Mv. Since E_0 = m_0c^2

(1)

(2)

Equation (2) is to be used to substitute values.

Momentum is negated when sphere B absorbs the light and passes it on to the tube by means of inelastic collision with momentum of the same magnitude but of opposite direction, but a displacement occurs from one sphere to the other during time t as

(3)

Substituting E_0/Mc of equation (2) for v of (3) gives

(4)

To restore the tube to its original position a particle of mass m_0 equal in energy to that surrendered as light by sphere B is transported a distance d back to sphere A. With all other related activity balancing out on the transporter’s return trip, the transportation causes the tube to move back a distance x to its original position.

Work occurring for the tube to move the distance x equals the product dm_0 in regard to the mass m_0 is a measure of weight. Since the particle and light are of the same energy and since the work energy was used by the particle in replacing the light energy back to its original position, which is a process also restoring the original position of the tube, the actions relate as such

5.1

5.2

Combining equations (4) and (5.2) gives

(6)

The last two equalities give

(7)

However, d is the distance of light propagating from sphere A to sphere B in time t. In other words, d/t is the speed of light. Hence

(8)

The last equation is the internal energy constitutive of the rest mass m_0.

Since the mass in relative motion is increased by a factor (1 – v^2/c^2)-1/2, the mass-energy equation is

The energy constitutive of the mass is thus its internal energy plus that of its relative motion.

Conserving Light Energy

Conserving momentum and mass-energy require them to be the same even though mass can convert to another form of energy as light. Since light possesses momentum, its absorption and emission are subject to the same conditions of matter in collision. Verification is with regard to mass m_0 = 1 with momentum mo(0) = 0 relative to Observer A absorbing a photon of light of momentum mxc such that m_0 and the photon move along with Observer B moving at velocity .6c relative to Observer A. The total mass and momentum before and after absorption are according to the equations

The total mass before and after absorption is thus

Total momentum before collision was (3/2)(1) = 3/2 units. After collision it is (3/2 + 1)(3/5) = (5/2)(3/5) = 3/2 units. Total momentum is thus conserved.

Note: The total mass before and after the collision is simply mx + m_0 = 2.5 units, as in accordance with an inelastic collision.

For a reverse process of elastic collision a photon is emitted from mass mx + m_0 in an opposite direction at which it was absorbed and with energy relative to B, who perceives the change in mass and momentum of emission the same as its absorption. According to A the velocity of m_0 after emitting the photon becomes

The relative mass becomes

Its momentum is (17/8)m_0(15/17)c = (15/8)m_0c.

The photon mass in the opposite direction is

Total mass and total momentum relative to A are

Relative mass and momentum are thus conserved of elastic collision between light and matter by way of a transfer of mass-energy between light and matter.

GENERAL RELATIVITY

After modifying Newtonian Mechanics to comply with relative space-time instead of absolute space and absolute time, Einstein focused on Newton’s theory of gravity for it to comply with the conditions of special relativity. He realized gravity is analogous to relative motion by way of equivalence between gravitational and inertial mass. He thus postulated it as a founding principle to formulate his general theory of relativity. By it inertial mass and gravitational mass are one and the same thing.

Another principle he used in relating it is similar to one Copernicus previously invoked to explain our unawareness of Earth’s orbital motion. He noted we are unaware of it because our motion around the sun is uniform along with the motion of Earth. Similarly, Einstein noted that we are not aware of falling freely by gravity because, as determined by Galileo, all mass and its force fall at the same rate.

Einstein thus equates free fall with inertial motion insofar as there is no internal awareness of either one. However, Earth’s free fall with its moon is felt by way of ocean tides, as caused by a stronger pull of the part of Earth closer to the moon. Since light also gravitates toward matter, and since the constancy of light speed is the founding principle of SRT, Einstein relegated it as valid only as a special case, as one where the tidal effects are negligible ones. As an alternative, he opted for a geometrical description of gravity according to a space-time curvature due to the presence of mass.

There are other anomalous effects to consider for distinguishing free fall from relative motion. There is, for instance, a tendency of masses to fall toward their common center instead of in parallel directions.

Spacetime is thus described as curved due to the presence of mass, whereby SRT is valid on insofar as the inhomogeneous nature of gravity is negligible in effect. However, this restriction of SRT does not mean it is not an integral part of describing the properties of nature. Gravity is still a form of energy that should be in compliance with the laws of energy the same as for motion according to the principle of equivalence.

Although Einstein opted to stipulate SRT as valid only as a special case, it is here considered an integral part of GRT inasmuch as the latter is analogous to the former. Analogies are with regard to the retardation of clocks, the contraction of space and so forth by both relative motion and a gravitational field. They relate in accordance with a mathematical invariance of SRT in further accordance with the Schwarzschild Metric, a solution of Einstein’s general field equations by Karl Schwarzschild (1873-1916).

The analogies are also comparable to acceleration in view of space-time curvature. Although observers in free fall perceive it internally as a non-accelerating state of relative motion, it is externally acceleration in that tidal effects are comparable as such.

Invariance

The Pythagorean Theorem is useful in surveying when the line of sight to be measured if obstructed in some way, as by a creek. The right triangle provides a detour in another direction; the hypotenuse being the actual distance to be measured and the two other legs of the triangle the detour. Since the two other legs can extend in any two perpendicular directions from the ends of the hypotenuse, as illustrated below left, it is thus an invariant for all right triangles formed from it.

In this case the invariant is of the form

A^2 and A’2 differ from B^2 and B’2, but the total area C^2 is always the same.

This invariance also applies to higher dimensions, as illustrated by the rectangular box above. Consider distance s is from origin O to point Q in relation to the perpendicular xyz-axes. In relation to it, distance is from origin O to the point P. Length s is determine by two right triangles formed by s and perpendicular lengths. The first right triangle is formed within the xy-plane with the length as the hypotenuse and the perpendicular lengths x and y being the other two sides. Hence

Extending from point P of the xy-plane perpendicular to point Q is length z parallel to the z-axis. The second right triangle thus forms from the lengths , z and s. Hence

Physicists include, among other things, time and motion, and with special relativity as first formulated by Einstein and then given geometrical interpretation by Hermann Minkowski (1864-1909), time becomes a fourth dimension of the space-time interval

The letter s now denotes the interval, as to determine the value of one variable of one coordinate system if other values of two coordinate systems are known.

The formula for invariance of the interval derives from the Lorentz transformations:

For the derivation time coordinates are converted into distance coordinates in the manner

The coordinates are then added and subtracted in the manner

The product (t’ + x’)(t’ – x’) gives

Hence invariance of the interval is of the form

Significantly invariance of the interval provides a simpler and more convenient form by which to relate phenomena. In the same manner of relating spacetime coordinates, for instance, momentum and energy are

Since we may regard one reference frame as relatively at rest wherefore the total momentum in it is zero, the interval s relates as internal energy constitutive of the rest mass m_0 and speed of light as m_0c^2. Letting P = 0, E = m_0c^2 and multiplying by c^2 gives

The total energy of a system thus calculates by simply knowing the velocity and rest mass of the system.

The Schwartzschild Metric

The Schwarzschild metric is a solution of the field equations of GRT interpreting the inverse square law for gravity of Newtonian Mechanics in view of space-time curvature. Although its validity now applies to only the empty space of the gravitational field outside the radius of the gravitating mass, here considered is also an analogical interpretation of gravity according to constant acceleration. It follows from deducing the mathematical form of the Schwarzschild metric to the form of invariance of SRT.

The Schwarzschild metric is of the form

In physics, a metric is an equation relating coordinate lengths as infinitesimal increments ds, as to allow for the calculation of them in terms of an invariant. Time and distance increments in the Schwarzschild metric relate where the gravitational field becomes relatively homogeneous within a volume of infinitesimal space and ds is an equivalent increment of their invariance. The gravity of Earth, for instance, slightly decreases a foot higher from the ground than it does many miles up. At only an inch higher up it is even more slightly the same and it converges to a homogeneous state at an infinitesimal difference.

The increments dr and dt represent distance and time, respectively, and the last two terms with Greek letters are trigonometric quantities referring to polar coordinates in place of the standard coordinates y and z in flat space-time. Flat space-time means a relatively gravitationally free space-time calculable according to the conditions of special relativity.

The letter c represents light speed in a vacuum of gravitational free space, but a relativistic modification of it according to the Schwarzschild metric is in order. As for explaining this modification in its right context, relativists generally refer to the factors (1 – v^2/c^2) and (1 – 2GM/rc^2) as relativistic. Relative is synonymous as comparable to, and relativistic means a comparable effect in relative motion or a gravitational field. In the Schwarzschild metric it distinguishes the difference in something such as mass-energy, distance or time in a gravitational field or gravitational free space.

A particular distinction indicative of modification of SRT is that of slower light speed in a gravitational field, which is derived according to the Schwarzschild metric.

By ignoring polar coordinates, it obtains the form

According to special relativity, light speed determines the simultaneity of events, as seen by an observer. If the particular event is a particle of light, the difference in distance between the displacement of a particle and its observation is zero. Hence the interval becomes ds = 0 for

Thus the relative speed of light in a gravitational field is less than unity.

Significantly in the absence of a gravitational field 2GM = 0 whereby the relativistic factor reduces to the number one such that the right side of the equation is the speed of light in gravitational free space.

SRT and GRT Analogies

According to SRT invariance of the interval is of the form

The Schwarzschild metric is of the form

The form of the Schwarzschild metric can be identical to the former by replacing c with c’ and by assuming a relativistic decrease of M and a relativistic increase of r occur with relativistic decrease of c in the manner

M* and r* are relativistic comparisons with respect to M and r. Note: the ratio c^2/c’2 in the relativistic factor is nullified by the ratios (M*/M) and (r/r*) where the proportional decrease in orbital speed equals that of light speed. The relativistic factor is thus numerically equal to a relativistic increase in the radius of the field and a relativistic decrease in its mass for a relativistic decrease squared in the gravitational potential of the field.

Lorentz transformations indicate an expansion of length. It relates to the retardation of clocks in relative motion whereby relatively longer intervals of distance are marked off in proportion to relatively longer time intervals, as perceived by observers relatively at rest. The longer r of the Schwarzschild metric is analogous.

There is also a contraction of length that deduces from the Lorentz transformations for a consistency of interpretation. Contraction of mass in the direction of relative motion partly explains the perception of light speed as constant. Similarly, contraction of mass in a gravitational field helps explain the constancy of light speed as locally perceived in the field. However, since gravity acts spatially inward, a relativistic contraction in the field is spatially inward as well instead of only in the direction of relative motion. The contraction in the field is also according to the field homogeneity as constitutive of spacetime curvature within spacetime curvature of the field. There is thus greater relativistic contraction between Earth and its moon than between Earth and Mars, or of the more homogeneous nature of the sun’s field as a whole, such that the spacetime of the field is relatively expanded.

Spacetime apart from orbital motion is relatively expanded with regard to an observer inside the field because all distances between systems do not contract in view of Euclidean space. As systems contract, they compete to result instead in homogeneity of the field in nullification of gravitational effect, or of spacetime curvature.

Since the relative size of observers and measuring rods contract locally the same as the orbital radius of mass on which they reside, there is no change in size locally perceived. Orbital speeds are also constitutive of natural clocks such that they and light speed being slower by the relativistic factor squared is nullified by slower clocks and shorter distances. Because a radius and orbital distance are both relatively shorter by the relativistic factor, natural clocks are only slower by a relativistic factor even though motion is slower by the relativistic factor squared.

Light speed c is also maintained as an upper limit with regard to a perceivable spacetime expansion and a non-perceivable decrease in relative mass. The latter relates to thermodynamics. Gravity constitutes work energy. According to thermodynamics work energy is spent energy, as from emitting radiation. With c as an upper limit for the escape velocity, the proportion of mass-energy radiated increases along with a relative increase in gravitational potential.

With respect to local observers of the field, mass-energy is absorbable without limit because mass only measures according to other mass and an observer in the field is decreased in mass as well. Moreover, since spacetime relatively expands to decrease gravitational potential, size and mass are relative.

A relativistic decrease in mass is contrary to that of SRT describing a relativistic increase in mass along with an increase in relative motion, but the decrease is explainable according to how mass-energy of inelastic collision compares with that of elastic collision. Elastic collision conserves momentum and energy by means of exchanging relative mass whereas a change of state occurs of systems in inelastic collision, as with regard to an interaction with other forces instead of directly reciprocating the initial action of the other mass.

The gravitational analogy is with regard to how a change in state occurs within the gravitational field. A change occurs because conversion of mass-energy is needed for expanding spacetime of the gravitational field. The slowing of light speed and relative motion of natural clocks, for instance, is due to them moving in a more energetic spacetime medium that has more mass to contain.

Since all mass in the field is equally decreased, an observer in the field is unaware of it. There is thus no relativistic change in mass in view of observers inside the field. To the contrary, observers outside the field perceive events in the field as relatively retarded. This can be interpreted as a relative decrease in mass with regard to slower orbital motion, but a more consistent interpretation is spacetime is relatively increased such that constancy of light speed is maintained along with orbital speeds. Since mass is determined according to its gravitational potential or force, which is relatively less for longer radii, the mass is relatively increased in order to be the same gravitational potential.

Mass-energy within the gravitational field is thus relatively increased or decreased in view of observers external to the field depending on how it is described, as either according to invariant light speed or variable light speed.

QUANTUM ORIGINS

Blackbody radiation is the origin of the quantum concept. Formula was derived to determine a relation between temperature and intensity of radiation that a body of mass absorbs and emits while in equilibrium. Formula according to classical laws failed, whereas a modified one conditional to the quantum succeeded. Its history is thus with regard to discovering relations between heat and light.

Heat and Light

William Herchel (1738-1822) wore different dark glasses in the year 1800 to peer through a telescope to observe the sun. By using different glasses of various color lenses he discovered that light filtered through some of them felt warmer than light that was filtered through others. He followed up with the implications of this discovery by devising experiments consisting of prisms and thermometers to further discover there is heat associated with light toward the red end of the spectrum and even beyond into a hitherto unknown infrared part of it invisible to the eye.

A heat-light connection was thus established, but it would be another twenty years before Andre-Marie Ampere (1775-1836) suggested light and heat are only different aspects of the same process. In responding to this suggestion, Marcedonio Melloni (1798-1854) was in agreement inasmuch as he believed both are waves propagating through media. He regarded light as the harmonious waves of æther and heat more as radiant waves of caloric, but his experimental findings from 1833 to 1840 indicated no essential difference in wave properties of these two phenomena. Nonetheless, he further discovered the refractive properties of thermal radiation.

More development followed from experiments by Jean Bernard Leon Foucault (1819-1868) and Armond Hippolyte Louis Fizeau (1819-1896) in confirming the wave properties of radiant heat. The experiments split infrared rays to superimpose and produce alternating bands of hot and cold in analogy to the light and dark fringes of ordinary light.

James David Forbes (1809-1861) discovered heat polarizes as does light. He also advanced the concept of a continuous radiation spectrum that later became essential to Maxwell’s theory of electromagnetism.

The next step for unification of electromagnetism and thermodynamics would have been routine except for the predominance of wave theory at the time and the relation between vibrant molecules of matter with the waves of light not being well understood as of yet.

There had been some attempts to unify theory as such. Leonard Euler (1707-1783), for instance, offered the principle a particular substance of mass is able to absorb light of any frequency with which its smallest particle vibrates. He attempted to explain phenomena according to the æther from which matter forms. His theory was not successful, but his absorbing principle did not go unnoticed.

More essential to the development of theory were empirical discoveries of how the interaction between light and matter is determined by the ability of matter to absorb light. In 1802 William Wollaston (1766-1825) discovered, for instance, dark lines appearing in light spectra emitted from matter. Joseph Fraunhofer (1787-1826) made more discoveries along this line in 1814.

Theoretical physicists became more interested in these dark lines. Stokes, for one, used the principle of Euler to explain them as atoms absorbing light waves by a method of resonance.

Pierre Prevost (1751-1839) had provided evidence indicating all bodies radiate heat. Evidence suggested further that poor absorbers of heat are poor emitters of it whereas good absorbers are good emitters, and it became evident that a material in thermal equilibrium emits what it absorbs. In 1858 Balfour Stewart stated the law that the absorptivity of a material in a state of thermal equilibrium is equal to its emissivity. Stewart assumed the absorptive and emissive ability varies in relation to the nature of the material substance, but in 1859 Gustav Kirchhoff (1824-1887) proposed a general condition of “blackbody” radiation as applicable to all bodies regardless of their material composition.

Kirchhoff examined the spectrum of sunlight after it passed through a sodium flame and found the dark D lines of the spectrum, as they are called, change to yellow when the sunlight is of low intensity, but that they were darker with more intense sunlight. He also found the sodium emits the same part of the spectrum absorbed with an appropriate increase in temperature of the sodium flame. Kirchhoff surmised the ability of a substance to absorb and emit a certain color of light depends on its relative states of equilibrium. Further experiments indicated the absorptivity and emissivity for a material is a function of its temperature and the wavelength or frequency of the light alone.

The mathematical formulation of the law assumes a system obtains a state of thermal equilibrium at sub temperature below incandescence. Thus, if A denotes total radiation per surface area on each body of mass, a the fractional amount of radiation actually absorbed by the mass, and E the permissible radiation emitted from it, the relations are mathematically expressed as

For all materials in a state of thermal equilibrium the powers of emissivity (E_1, E_2, E_3, etc.) divided by their respective factors of absorptivity (a_1, a_2, a_3, etc.) equal the same amount of light incident per surface area:

Kirchhoff defined the blackbody as one absorbing and emitting radiation of all frequencies or wavelengths. In this case, the power of emissivity of the blackbody is EB and the fraction of light absorbed is unity, aB = 1, such that the following equation results:

Dividing by EB, multiplying by a, and then reversing order obtains

The symbols α and ε thus denote the absorptivity and emissivity respectively of a material body in ratio to a blackbody. Further relation is in view of the discovery of a fourth power law.

The Stefan-Boltzmann Law

The rate systems change from one temperature to another for obtaining a state of equilibrium with their environment is also significant. Newton had assumed the process is linear inasmuch as the rate of change in temperature is proportional to the difference between that of a system and its environment, but experiment indicated this relation only holds true approximately at relatively normal temperatures, as the data did not appear linear at higher ones.

Another relation superseded Newton’s in the late 19th century. It came from a study of temperature and light intensity by John Tyndall (1820-1893) and Joseph Stefan (1835-1893). Tyndall had run an electric current through a platinum wire in heating the wire to a state of incandescence. On measuring the radiation emitted at different temperatures he found the intensity to be about twelve times as great with the wire being about 1200 degrees centigrade in comparison to it being 525 degrees centigrade.

Stefan calculated

Since zero degrees centigrade are 273 degrees above absolute zero, the ratios are from absolute zero.

This mathematical relation seemed to hold for all substances at all temperatures. Stefan thus concluded that intensity I is proportional to the fourth power of absolute temperature T:

The constant k is named the Boltzmann constant k. Its value is 1.3806503 x 10-23 J/K, which is 1.38065 X 10-16 grams times centimeters squared per seconds squared per one degree Kelvin, which is numerically minute, as for a slight change in the absolute temperature only to cause a slight change in light intensity.

Tyndall’s measurements were not very accurate. Modern results give a ratio of about 18 to 1, but it was based on a general study. Besides, Ludwig Boltzmann (1844-1916) later deduced this fourth power relation according to the second law of thermodynamics and Maxwell’s theory of electromagnetism and stipulated it is valid for a blackbody only.

Entropy is conserved in compliance with the laws of thermodynamics by means of an adiabatic process, as in an extremely slow mechanical way whereby it is mechanically reversible in a complete cycle. Required for this process is the amount of heat Q a system loses during cycle is also gained during it.

Denote the original state as S_1, as with an absolute temperature T_1, a volume V_1 and an energy density u_1 until it changes to state S_2 at absolute temperature T_2, volume V_2 and energy density u_2. The state S_2 can also change, in theory, to state S_3 at new volume V_3 while maintaining its same temperature and energy density by absorbing energy of the same density and absolute temperature, but the original temperature and energy density are restored at volume V_4 of state S_4.

The changes from state S_1 to state S_4 represent the exchange of actual quantities of heat energy. It allows an interpretation of the process in terms of amount of work performed to change from one state to another.

The total work energy W as performed during the adiabatic process is consistent with Boyle’s law. By it the product of pressure p and volume V of a gas at a given temperature is constant:

Pressure also relates in terms of force:

The pressure-volume product is here according to the centripetal force mv^2/r per area r^2 such that twice the kinetic energy is per volume space. With pV constant, and since volume is proportional to a distance cubed, the following relation results:

In view of Boyle’s law and conservation of entropy:

This equality relates the work performed of distance moved by a constant force for each event of a change in volume of a gas.

The energy density u of a proportional amount of radiation absorbed by the gas in thermal equilibrium is calculated as the force per volume. Hence

By substitution the previous equations become

As for converting in terms of volume space the square root of the square root of the cube of the equality is

Relating to the various states S_1 through S_4 gives

These values are for each state with regard to change in energy density per volume.

The following equation expresses the second law of thermodynamics, as with regard to conservation of entropy:

Q_1 denotes a negative amount of heat liberated from a change of state S_4 to state S_2 and Q_2 denotes a positive amount of heat absorbed from a change of state S_2 to state S_3. These changes in heat are proportional to the amount of change in energy per volume that, in terms of energy density and volume, become

By substituting the quantities on the right side of the equations for Q_1 and Q_2 into the previous equation it becomes

However, in relation to Boyle’s law and the constants for volume space, the following equations result

Substituting right-hand sides of these equations into the thermodynamic equation obtains

Hence

Because energy densities and temperatures equal, the adiabatic cyclic change is constant such that

Moreover, u is the energy density of the radiation of intensity I that is absorbed or emitted, as proportional to the intensity of radiation incident on a black body. By substituting I for u the equation I = kT^4 expresses the mathematical interpretation of Stefan-Boltzmann’s law.

Wien’s Displacement Law

The Stefan-Boltzmann law relates temperature to the intensity of radiation, but it does not specify how a particular frequency or wavelength of light applies. Wilhelm Wien (1864-1928) endeavored to determine a more exact mathematical relation for the intensity of a particular range in wavelength or frequency in regard to its temperatures. He discovered hotter objects emit more radiation of a shorter wavelength than do cooler objects. Sunlight, for instance, is more energetic with shorter wavelengths than the radiant energy invisible to the eye emitted from animate life.

For analysis, Wien adopted the adiabatic concept with regard to blackbody radiation. However, a true blackbody is not experimentally available. Although soot is black, for instance, it still emits radiation that is invisible to the eye. Even so, blackbody conditions of equilibrium tend to occur with a slight change in the environment from its interaction with radiation. Wien thus considered a hollow container with a tiny hole at its surface to allow radiation to enter and reflect here and there on the walls of the container before it finally finds its way out. More radiation thus enters into the sphere than escapes until a condition of equilibrium is reached.

In analyzing the data of the graphical illustration above Wien surmised a black body is comprised of an even distribution of thermal radiation with a constant graphical shape that varies only with a displacement of a small range in wavelength of maximum intensity inversely in proportion to temperature. Shorter more frequent waves of maximum intensity thus correlate with higher temperature. Wien’s displacement law is thus λmaxT = b, where b is a constant.

Because a change in the wavelength of maximum intensity is linear with a change in temperature, twice the temperature equates to half as much wavelength, and so forth. However, relating the distribution of all wavelengths is more complex. Total intensity is to the fourth power of temperature. In order to determine it for any particular wavelength at a given temperature a formula is required to include the three variables of wavelength, temperature and intensity, as in relation to the curve of the graph below.

In view of the Stefan-Boltzmann Law it includes the Doppler Effect, which is a change in wavelength and energy perception of light. It can occur by relative motion or by an unequal exchange of energy of light being absorbed and emitted by matter. In blackbody radiation, it is assumed to occur because of molecules (as oscillators, absorbers and emitters) having greater motion, energy and temperature. Because expansion and contraction of the walls increases in rate due to a greater intensity of more light, they in turn change the energy of particular light, as to more frequent, shorter wavelengths. Since the change is linear with a change in temperature, the fourth power law is extended to a fifth power law with regard to radiant wavelengths.

Wien compared F(λ,T) with a distribution law for molecular speeds in a gas, as derived by Maxwell:

Wien associated cavity radiation here with molecular resonance with wave frequencies proportional to the kinetic energies of resonators. Identifying wavelength λ of the radiant energy with kinetic energy, ½mv^2, of the molecules, the exponential function (number e) in Maxwell’s formula is raised to a power in relation to energy, wavelength and temperature. As the function F(λ,T) of wavelength and temperature, Wien derived a formula for the intensity Iλ of a particular range of λ in relation to constants a and b in addition to k (the Boltzmann Constant) as

It fared well with data in relation to high frequencies, but not in relation to low ones.

Plank’s Solution

Wien’s cavity radiation was a thought experiment for the most part, but scientists had been aware from the mid 19th century that light escaping from a hotter oven through a tiny crack was more energetic. In 1900 an experiment from an apparatus that was designed and constructed by Ferdinand Kurlbaum (1857-1927) and Richard Lummer (1860-1925) in 1898 confirmed that Wien’s formula did not predict accurate results in the infrared of weaker light of longer wavelength. The apparatus was a tube of blackened platinum enclosed inside a ceramic tube except for a tiny hole. Kurlbaum and Heinrich Leopold Rubens (1865-1922) used it for measuring wavelengths as long as 50 microns, which is only one twentieth of a millimeter.

When Rubens revealed the experimental result to Max Planck (1858-1947), that same day in 1900 Planck had a solution. He assumed resonators of radiant heat are intermediate between molecules and radiation. A resonator thus absorbs a particular quantity of radiant energy, stores it and releases the whole quantity at the same time. Planck’s solution to the problem was thus to quantize energy as multiples of hf, where h is now known as Planck’s constant and f is light frequency in relation to energy.

The amount of energy of an oscillator is according to the values of each energy level, which are 0, hf, 2hf, etc. Since some are zero, neither the energy level nor the spatial distribution is continuous. The distribution itself is determined according to the Boltzmann factor in the exponential function

To further develop Maxwell’s statistical treatment of the kinetic theory of gases Boltzmann had derived the probabilities in terms of the exponential function and he also applied discrete energy levels to this function before an infinitesimal division among the actions of the molecules. Planck proceeded likewise, but instead of allowing his oscillators to become infinitesimal, he assumed one of the discrete energy levels applies.

A number N of oscillators in an incremental range of frequency near f has various multiples of energy E = hf, including zero, and is the number n times each consecutive level of the probability distribution, as in accordance with

The infinite series in the equation converges to

The total energy of all oscillators is

This infinite series converges to

Dividing E by N obtains

The value of E/N is the average energy per oscillator of incremental frequency range between f and (f + df) inasmuch as n factors out of the equation.

Comparing Formulas

In relation to Wein’s formula for radiant intensity density per c on surface area 4πr per wavelength λ to the fifth power, the formula becomes

The only difference in it and Wein’s formula is Wein’s constants a and b are replaced with hc and a slightly different form of the exponential function. As for the number 2, twice hc is twice the change in speed c with regard to a reverse in direction for total distance.

The constant h relates dimensionally as a product of mass, velocity and distance whereas the constant k is the product mass and velocity squared. Thus, hc is dimensionally the same as λkT such that they are the same ratio no matter what units of mass, distance and time both use for measuring results. The exponential function thus changes only by the ratio of T, which is consistent with Wien’s displacement law.

If c = λf, then replacing each λ with c/f obtains

However, textbooks give the frequency formula as

By using this formula for maximum wavelength and the other for maximum frequency it turns out that c ≠ λf with regard to their determinations.

The reason the variables do not equate is because they relate to different forms of energy. One form is a modification of Wien’s formula and the other is from a formula derived by Sir James Jean (1877-1946) and John William Strutt (1842-1919), who was renamed as Lord Rayleigh. Wien’s distribution formula is in view of his displacement law for a change in temperature; the other formula was derived in accordance with an equipartition theorem derived by Maxwell, Clausius and previously by John James Waterston (1811-1883) for advancing the kinetic theory of gases.

A degree of freedom is according to the number of modes of vibrations. The same volume of space can contain a greater number of smaller modes. Rayleigh assumed there is a tendency for the smaller modes to dominate. However, an ultraviolet catastrophe results from this tendency of energy increasing to infinity, as in violation of conservation of energy, as the formula differs from the Stefan-Boltzmann fourth power law. The formula thus requires modification.

The results of each formula differ because neither relates directly to specific wavelengths or frequencies. They pertain instead to a range in a change from one wavelength or frequency to another. Consider a range as

A change in the range of frequencies and wavelengths thus does not equate specifically as c = fλ.

In one Planck formula, the change in wavelength λ relates in the manner

The change in radiant energy is thus per fourth power of wavelength.

In the other Planck formula, change in frequency f relates in the manner

There is thus change in radiant momentum occurring per wavelength squared.

Conversions of the two formulas are necessary for them to relate specifically to particular frequencies or wavelengths. This is achieved in relation to the curve of the graph. It becomes more of a straight line as its length approaches zero. At the limit of zero length, it is defined by the calculus of differentiation as linear, a straight line. Moreover, at the top of the curve where it peaks the slope of the line is horizontal whereby it equals zero. The two formulas are thus differentiated for zero change in frequency or wavelength where the intensity of radiation peaks.

Which formula is correct for differentiation?

The derivation of the Wien formula is according to the Wien Displacement Law. The change in energy is in relation to change in temperature. The slopes for all peaks at different temperatures are zero. A Jeans-Rayleigh modified formula thus appears more likely to be the correct formula for differentiation in view of the distribution law for variable intensity.

QUANTUM PHYSICS

An early application of the quantum was the Bohr Theory of the atom. It was superseded by a Quantum Wave Mechanics. Wave equations of Quantum Wave Mechanics, in turn, were reinterpreted as probability equations. The interpretation is now established with the evolution of Quantum Electrodynamics, the quark model, string theory, Grand Unified Theories and so forth. This development is complex, but fundamental relations of physical constants can still be understood according to a more simple theory of the Bohr atom.

Following Bohr’s model is the photoelectric effect, the Compton effect, relativistic quantum modification of Wave Mechanics and the Uncertainty Principle.

The Bohr Atom

Applying the quanta to the structure of the atom came from Niehs Henrik David Bohr (1885-1962). He modified the atomic model previously announced by Ernst Rutherford (1871-1937) in 1911. Rutherford had contrived a model of the atom to describe how alpha particles reflect. Accordingly, the bulk of mass doing the scattering is contained within a nuclear radius of about 1836 times smaller than the radius of the atom itself. There is thus a vast region of empty space about the nucleus with electrons orbiting in elliptical paths. Rutherford further assumed atoms continually absorb and emit radiation as the electrons accelerate around the nucleus. However, although his model was able to explain the scattering of alpha particles (particles with two neutrons and two protons), it failed in explaining other phenomena.

One such phenomenon pertains to the spectra of radiation emitted by atoms. The spectral lines of light associated with atoms did not conform to any pattern consistent with a known theory of continuous spectra. Formulae had been provided apart from theory, as in 1885 by Johanne Jakob Balmer (1825-1890), and later by Johannes Robert Rydberg (1854-1919), Carl Runge (1856-1927) and Henrich Kayser (1853-1910). Their ad hoc formulae agreed with certain observations for the most part, but they lacked theoretical foundation until Bohr proposed quantum restrictions for his modified version of Rutherford’s atomic model given in 1913.

For the modification Bohr assumed electrons orbit around a nucleus of an atom in elliptical paths insofar as atoms either emit or absorb radiation only when an electron changes its orbital state, as where its angular momentum is a multiple of h/2π.

Bohr only modified classical formula by applying quantum restrictions to it, as in assuming a force field exists consistent with Coulomb’s inverse square law for electrostatics and magnetism. An electron thus has a negative unit of charge of e whereas a nucleus has a positive unit of charge of e. The force between them is the product of charge per distance r squared:

In comparison, Newton’s second law of motion gives

Equating the right sides of the last two equations and dividing them in half obtains

It thus relates to classical formula for kinetic energy K of the electron.

The potential energy T of the electron, as within a conservative field of force, is

The total energy W is therefore

The last two equalities give

The orbital radius of the electron is the unit of charge squared per twice the kinetic energy of the electron.

Bohr assumed the total energy W becomes zero as r becomes infinite, or when the atom becomes ionized because of it losing an electron. By applying quantum restrictions to the atomic radius by using the relations nħ = nħ/2π = n (mvr) and e^2 = mv^2r, he deduced

The letter m represents the mass of the electron, ħ the Planck constant divided by 2π, and n an integer from one to infinity.

The respective velocity of the electron around the nucleus is derived from the relation

The square root gives

Dividing by c and substituting α for e^2/ħc obtains

The fraction (1/137) is the fine structure constant.

Bohr further recalculated the energy to eliminate r from the equations. Previous equations give

Multiplying both the numerator and denominator by c^2 and substituting α^2 for e^4/ħ^2c^2 obtains

The highest energy level is the hydrogen atom having only one electron, n = 1, such that

Bohr’s next assumption is the atom can obtain a lesser energy level by emitting a photon of energy W – W’, the difference of the energy levels. This energy relates to the frequency f of the photon by the equation

A stipulation applies here for n = 1 and n’ to only be any integer greater than one where an atom decreases or increases from an energy level to another by either absorbing or emitting a photon of energy hf, as where frequency f relates to spectral lines determined from appropriate values of n and n’ of the above equation.

The Photoelectric Effect

Planck interpreted the nature of the quantum as a molecular oscillator whereas Einstein interpreted it as applying to light as well as to the oscillators in order to explain a photoelectric effect that was discovered in 1902 by Phillepps Lenard (1862-1947). He discovered a metal emits more electrons when the intensity of the light shining on it is increased, but it did not result in an increase in velocities of the electrons as well. This find indicated relative energy of each electron emitted from the metal is more dependent on a single entity of light instead of its overall intensity.

Einstein interpreted Lenard’s findings according to Planck’s quantum condition where energy appears in discrete units as multiples of hf. Light quanta (now called photons) thus collide with a metal such that the energy of each photon transfers to an electron for it to break loose its bondage with the metal. This explains the dependence of velocities of the electrons because it is only necessary to associate the greater intensity of light as more photons interacting with more electrons. (However, it is still possible for the single entity to be a wavelet if emission depends on frequency instead of intensity.)

Robert Andrews Millikan (1868-1953) confirmed Einstein’s explanation of the photoelectric effect after he determined a numerical value for the fundamental unit of charge of the electron. His experiment was of a statistical nature of shining light on a metal screen in measuring the electrical voltage produced by electron emissions. It produced a photon to electron relation of the energy needed for freeing electrons of a particular velocity. Furthermore, while controlling experimental conditions, Millikan was able, as in 1915, to interpret the data in a way it not only convincingly established the nature of the photoelectric effect, it independently confirmed the value of Planck’s constant as well.

The Compton Effect

Similar to the photoelectric effect is the Compton Effect, which includes a redirection and loss of energy of photons as well as the ejection of electrons from the atoms. To explain statistical results of this interaction Arthur Holly Compton (1892-1962) assumed that both light and electrons are particle-like. Thus, the laws of conservation of energy and momentum apply for the statistical results to be consistent with a loss of energy and the angle of deflection of photons of light and the gain in energy of the electrons from their recoiling in opposite directions of the deflecting photons.

Compton examined the scattering of x-rays from a block of graphite, related his findings with the wave property of light and discovered scattered waves had become longer. In view of conservation of momentum the change in a photon’s wavelength after it collides with an electron relatively is

With straight ahead collision the cosine angle is unity such that 1 – 1 = 0 for a zero change in wavelength. A reflection at a right angle is a zero degree cosine angle such that the Compton wavelength for the electron is

For a 180° degree reflection the cosine angle is minus unity such that the change in wavelength is twice the Compton wavelength.

The formulation of the Compton Effect is actually a relativistic formulation of the photoelectric effect for equating the particular interactions between electrons and photons, as consistent with a previous example of relating an elastic collision between a photon and unit mass m. The addition of velocities theorem was used in the previous example to show the velocity (3/5)c of Observer C moving relative to Observer B is (15/17)c relative to Observer A if the velocity of Observer B is (3/5)c relative to Observer A. Part of the light reflects in the opposite direction and part of it is absorbed by m, which becomes (17/8)m. The photon mass-energy that reflects in the opposite direction becomes [(17/8) – 1]m = (9/8)m. The total momentum before and after collision equates

The original photon mass-energy is thus (3/2)m.

In comparison, the Compton formula for relating the amount of reduction in photon mass-energy that is added to m, in accordance with , is

The Compton Effect is thus consistent with an elastic collision (not inelastic) in view of an exchange of mass between light and matter: conditional to conservation of momentum and energy in accordance with special relativity theory.

Wave Mechanics

William Rowan Hamilton (1805-1865) formulated wave mechanics to combine wave properties with the dynamics of particle interaction after he had noticed a similarity in form in the mathematical formulation of the principles of least time and least action. Pierre de Fermat (1601-1665) had offered the first principle as a way to describe a path of light according to the law of refraction as a wave phenomena; the second principle was formulated by Pierre Louis Moreau de Maupertis (1698-1759) as another way to describe the dynamics of the interaction of mass as an action principle.

According to wave theory various physical media for light propagation are according to their refractive indices, as defined by the equation

The Greek letter μ denotes the refractive index of the particular medium, c the speed of light in vacuum or æther, and v its velocity through a physical medium such as glass or air. The refractive index for vacuum space or æther is unity and is greater for other media. Since c is constant, and since μv = c, the speed of light is slower in a refractive index greater than one, which is justified by the law of conservation of momentum since the wave increases in mass in a denser medium to compensate for its propagating at a slower speed.

Fermat’s principle of least time is according to the relation where time along the total path from point A to point B at each increment of distance ds through a medium of refractive index u is

A requirement of this integral is that it needs to be an extremum, as either a maximum or a minimum value. The value of least time comes by way of associating u with c/v such that the greater u results in a slower v and more time.

The significance of this integral with regard to the law of refraction is in realizing the total path that light takes through two media of two different indices. The path from A to B through the first medium and from B to C through the second medium need be such that the total time is a minimum. Least time does not need to be the shortest path; rather, it depends on the angle of entry. The shortest path is a straight line from A to C but the time along this path is greater for a medium having a greater refractive index. If the angle of entry is from a shorter path of a medium of a greater index and the path of the other one is relatively longer, then the total time of propagation can still be less. The law of refraction also expresses this result. The least time principle is thus according to the law of refraction in view of wave theory.

The principle of least action is similarly expressed as

The momentum mv replaces the refractive index μ of the medium. An increment of distance ds along some path from A to B thus has momentum mv for action. For the total path from A to C through two media of two different indices of reflections the same condition exists for less action as it does for less time. The least action principle thus determines the path of a particle in a conservative field of force in the same manner the principle of least time determines the path of the light wave. A conservative field of force is one in which the total energy, as potential and kinetic, stays the same.

The Hamiltonian Action is a formulation of Least Action in view of a conservative field of force. By way of a homogeneous medium of constant force the total action is simply the product of a particle’s momentum mv and the distance r of its travel. The total energy at any increment of the distance before, during or after the passing of the particle is the potential energy of a field in association with the particle in addition to its kinetic energy of relative motion. Energy is constant everywhere in the field, but Hamilton distinguished between the action of the particle and the total energy of the field as varying in time from place to place. The Hamiltonian Action A thus takes the form

W denotes total energy, t the time action, and S is the Maupertuisian Action mvr.

Anywhere along the path of the particle or along the crossing of paths of a swarm of particles (before, during or after passing) the action varies with time to allow for a more intricate interpretation of the action. At any place where the action is zero is the relations

Velocity v as the change in position, r, per time of the action is thus its energy per momentum.

The significance of Hamilton’s Wave Mechanics is it describes the evolution of waves from the multiple interactions of particles and also the manifestation of particles in association with a packet of waves.

A mathematical theory of wave packets was later developed by Lord Rayleigh foreshadowing the wave mechanics of de Broglie and Schrodinger.

The discovery of the quantum indicates light has a dualistic nature. It behaves in part as a particle and in part as continuous waves. Louis de Broglie (1892-1987) theorized matter is of a particle-wave duality as well, as formulated according to special relativity and the discovery of the quantum.

As for the formulation, energy W and momentum P of a particle in free space relate to the number σ of waves of frequency f and wavelength λ according to Planck’s constant h:

The arrow indicates the waves and particles move in the same direction, as for momentum but unnecessary for energy.

Capital letter V denotes the velocity of the waves and, as with waves in general, equates to the product of their length and frequency:

Considering this relation with the previous equations in relation to momentum and energy, it equates as

The case of photons moving at speed c gives

In all other cases, where v is less than c, V is greater, and infinitely fast for a particle relatively at rest.

Since special relativity stipulates no information of events can exceed light speed in a vacuum, the de Broglie waves carry no momentum or energy in order for them not to transmit an immediate effect, but they are significant inasmuch as De Broglie interpreted the particle effects as superimposed waves in analogy to the beats of sound produced by the superimposing of airwaves of certain numerical ratios. The waves form into wave packets where slightly faster moving waves overtake slightly slower ones for a particle effect. The velocity of the packet as a whole is that of the particle, which is slower than the waves themselves.

How the packet maintains intact is somewhat of a mystery. The slightly faster moving waves inevitably continue forward in spreading apart from the slower waves. New waves must somehow add to the packet. The superimposing of de Broglie waves, for instance, could further cause new disturbances of the medium for it to generate new waves. However, the creation of new waves needs to be offset with the annihilation of old ones in order for there to be no indefinite increase in the number of waves. As waves continually spread apart, their physical energy dissipates and maintains conservation by means of the new waves generated. This process thus assumes the wave packets maintain a state of equilibrium with the medium.

Schrodinger’s Wave Equations

Erwin Schrodinger (1887-1961) was able to refine the ideas of de Broglie by using them with the theory of wave packets. Although de Broglie had generalized the association of such wave properties as frequency and wavelength with particle effects, he did not offer a wave equation. Whereas he offered no more than a particle-like projection for describing the behavior of waves, Schrodinger formulated de Broglie’s ideas in the form of a wave equation. Such wave properties as diffraction, refraction and polarization could thus be included in the analysis.

Schrodinger aimed to transform such mechanical properties as momentum and energy into a particular wave equation containing the property of the quanta denoted by Planck’s constant h. He commenced with a wave equation that had previously been derived by Jean le Rond d’ Alembert (1717-1783) as

This partial differential equation describes the elastic tendencies of independent variables in homogeneous media. The wave velocity is V in terms of space-time coordinates (x,y,z,t) and the standing sinusoidal wave u is defined as

The part ψ(x,y,z) represents some unknown function of the amplitude, or maximum swing, of vibration of frequency f located at coordinate point x,y,z.

Because x,y,z represents a single coordinate point the wave equation shortens to the form

u represents the three partial differential equations of the second order of coordinate point x,y,z.

The quantities ψ(x,y,z) and u are related according to the last equation in the manner

De Broglie related quantities as W =hf and V = W/P. Hence

In this equation K = ½mv^2 is the kinetic energy of the particle, and Epot(x,y,z) = ½mw is the potential energy of the field at coordinate point x,y,z where the particle is located at that particular moment.

By substituting the right-hand side of the equality in the wave equation it becomes

This is a wave equation interpreting momentum and energy of classical mechanics. A slight modification is thus in order for a relativistic wave equation.

Both de Broglie and Schrodinger had interpreted V according to the refractive index μ of a medium or field of force. Hence

Considering the medium as a field of force generated by the nucleus of the hydrogen atom, the energy W of the orbiting electron at coordinate point x,y,z, gives

The energy W is the energy of the electron. The field W – Epot(x,y,z) is the total energy minus the potential energy at coordinate point x,y,z. By taking the square root of [W – Epot(x,y,z)]2 – m_0^2c^4 (where m_0 is the rest mass of the electron) the kinetic energy according to special relativity theory becomes

Since W = hf, what is further obtained is

Substituting the right hand side of this equality for V^2 in the wave equation obtains a relativistic form of the wave equation for a particle in a conservative field of force.

Schrodinger’s wave equation containing quantum restrictions reinterprets the quantum conditions of the atom previously given by Bohr. Bohr had postulated a correspondence principle in order to include wave conditions where needed. Bohr’s model also describes electrons circling a nucleus of the atom as corpuscular in nature, whereas Schrodinger considered electrons as a diffused cloud where quantum restrictions result as certain nodal points of de Broglie standing waves.

Schrodinger’s interpretation of the electron cloud as its potential energy according to Coulomb’s law of classical electrodynamics is described by the equation

Solutions of the equation at specific coordinate points x,y,z constitutes a discrete set of values corresponding to Bohr’s conditions of the quantum as

E is total energy of the atom at coordinate point x,y,z; n is any positive integer; and m is the electron mass.

Bohr’s theory explains the refractive properties of atomic spectra as arising from an electron’s change of orbit from one closer to the atomic nucleus than from one at the outer shell. Schrodinger’s theory is a wave interpretation wherefrom nuclear attraction is greater within the shell where change in the refractive index μ, as change in field strength compares to distance of the length of the de Broglie waves associated with the electron.

Spin and Antimatter

Schrodinger’s wave equation in relativistic form explains nearly all the conditions of light spectra that Bohr’s theory explained except for one explained with the ad hoc assumption of spin. A particular spectrum is explained by his theory with the assumption of the magnetic moment of the electron being defined by its own spin, as defined as half the value of the quantum constant h. Nowadays it is said the electron has a spin of ½, but the spin is symbolic in concept insofar as it does not compare with the spin of a ball.

George E. Uhlumbeck (1900-1988) and Samuel A. Goudsmit (1902-1978) proposed a spinning electron in order to correct certain inadequacies of Bohr’s theory in failing to describe more fine spectra detected from the hydrogen atom. Although it allows for a spinning electron, there is no reason for it, but Wolfgang Pauli (1900-1958) showed electron spin is consistent with a wave equation presented in the form of a matrix. The matrix allows a splitting of the wave equation for it to represent an electron spin in either of two directions. When this combines with the amplitude function ψ of waves, it further suggests polarization.

Charles Galton Darwin (1887-1962) then derived a wave equation that includes this polarization effect of a spinning electron describing the fine structure of the hydrogen atom by means of a wave equation. Neither Pauli nor Darwin, however, derived wave equations from wave theory. Adrien Maurice Dirac (1902-1984) took on this task in modifying the relativistic form of Schrodinger’s wave equation.

Schrodinger used alternate ways to derive wave equations for both classical and relativistic forms. For the classical form, the kinetic energy for the condition where no field of energy potential exists is

In addition, the momentum is

With regard to x,y,z-axes kinetic energy is of the form

Schrodinger’s theory replaces the momentum-vectors Px,Py,Pz with the respective operators

In addition, it replaces the energy K with the operator

These replacements obtain equivalence in waveform.

The operators are first derivatives, linear and they apply to matrices Dirac formulated, but a relativistic form of the energy equation requires a more complex solution that includes conditions of special relativity, as for combining energy with momentum in the form of the invariant

In the form of vector coordinates the invariant is

Even though the energy W is equal to the square root of Px^2 + Py^2 + Pz^2 + m_0^2c^2, how the equation on its left side individually relates is not obvious. Schrodinger merely replaced W^2 with second derivative operators in the

The result, however, turns out to be inconsistent with matrices Dirac developed, so that he opted instead to split the energy equation in its vector form into two to apply operators of the first derivative for each half.

It is possible to split the equation into two factors by ordinary algebra:

The next step is to operate on each factor individually to obtain first order derivatives for each. However, a problem with partial differentiation arises because Px, Py, Pz and m_0c are independent variables that are not obtainable as a square root of the sum of the squares.

To split the equation and obtain a wave equation of standard form, Dirac applied the non-commutative rule to obtain

The symbols αx,αy,αz,β are coefficients independent of momentum, energy and time coordinates.

Multiplying the factor in the bracket by the factor (W/c + αxPx + αyPy + αzPz + βm_0c) obtains

The following relations apply:

Relations as αxβ = -βαx are defined as non-commuting variables.

The matrixes do not merely describe a mysterious new form of reality. They are unique in describing the complexity of natural phenomena. The square root of the momentum-energy invariant, for instance, is not applicable in its standard form because the quadratic relation is fundamental to energy itself rather than to its separation into coordinate directions. This means different results occur by taking either the square root of A^2 or the square root of (Ax^2 + Ay^2 + Az^2). If A^2 = 16, for instance, then A = ±4. However, if Ax^2 + Ay^2 + Az^2 = 16, and if Ax = Ay = Az, then

Since splitting a quantity into directional components changes the results, the physical nature of it is open to interpretation. For a wave interpretation, for instance, a physical significance of non-commutative variables is waves superimposing in opposite phase can cancel out effects. In reference to particle effects of electrons, the positive and negative factors of the equations both represents opposite directions of counterclockwise or clockwise electron spin, as in explaining polarization. Moreover, overall symmetry of the equation suggests mass-energy can exist in opposite states: positive and negative, as for antimatter to exist as a negative state of matter.

The existence of antimatter is allowed by way of the square root of the relativistic momentum-energy equation squared can be either a positive or negative solution. However, this, in itself, does not necessitate either solution. For instance, if we begin with positive values, square them, and add the squares to calculate the square root of the sum, a positive result occurs.

The form of Dirac’s matrices is of a symmetry that suggests both negative and positive values, and Dirac followed the interpretation of Born, Heisenberg and Bohr wherefore the waveform of the equations merely represents the probabilities of particle action. Dirac’s theory is thus verifiable as a test of both the predictive power of his equations and of their interpretation as probabilities, and the theory has hitherto been a total success in this regard.

Probability Interpretation

Such leading Physicists as Max Born (1882-1970), Werner Karl Heisenberg (1901-1976) and Niehs Bohr opted to reinterpret Schrodinger’s wave equations as probability equations. Born proposed the wave packet associated with the intensity of an action is a probable whereabouts of a particle. Heisenberg and Bohr then associated both wave and particle as representative of the probability function.

Born first interpreted the results of Schrodinger’s theory. What Schrodinger had proposed is a cloud of negative charge in place of Bohr’s original model of a particle circling the nucleus of the atom. For instance, in the hydrogen atom, which consists of one electron, or one unit of charge, the total charge of the electron cloud according to Schrodinger is –e. In addition, he proposed the charge at any point dxdydz of intensity of the de Broglie waves equals the density ρ of a cloud at that point when the energy of the atom is in a stable state of En. Hence

The product is proportional to wave intensity. It is used instead of in order to allow their product to be negative and the total product of to result as positive density ρ.

Representation of total effect over infinite space is by integrating the point-charge-density in accordance with coordinate point dxdydz. However, total charge of the cloud is still only

A proportion of the charged cloud thus condenses at one moment to a specific and stable location dxdydz.

Heisenberg and Bohr interpreted it according to principles of uncertainty and complementarity. They found it difficult in view of the particle-wave paradox to conceive of a single particle obeying interference of two wave patterns after passing through only one of two holes. They preferred instead to view the particle as a sort of diffused cloud capable of interfering with itself or consolidating into a particle-like form in that the nature of the particle-wave effect is neither wave nor corpuscular in the ordinary sense but manifests as certain observable effects of whatever it is that causes them to appear as such. When unobserved, a diffused cloud is representative of the effect; when observed to more accuracy, a smaller, more precise wave packet is representative of the effect.

Although a diffused cloud of negative charge was depicted by Schrodinger as well, the one depicted by Heisenberg and Bohr differed according to their view of the electron, or any other atomic particle, inasmuch as they interpreted the wave equations as probability equations determining probable energy and probable location of the particle effect to be observed.

An explanation of the probability condition could be it is because total energy moving through space is greater than what is actually observed, as reflected on a screen or whatever. Unobservable secondary effects, as Gassendi had philosophized, could give rise to the observable effects of nature. However, without means of verification, the explanation is not science; it is only speculation. Nonetheless, since probability conditions of quantum physics suggest the existence of a virtual field of virtual particles, the philosophy of Gassendi is worthy for a more complete understanding regarding wave-particle duality and physics in general.

Uncertainty

Heisenberg established a principle of uncertainty to determine the probability of finding the location or time of a particle effect from the probable outcome of its momentum or energy, respectively. According to Born’s interpretation of Schrodinger’s equations, the wave packet defines the region where the particle can be located. The probability of the particle’s position is at any particular point within the wave packet where it is proportional to the product of the total volume of the wave packet and its relative intensity. The relative size of the wave packet is dependent on the means by which it is observable, as by the ability of a photon to penetrate a certain level within the wave packet. Thus photons of higher frequency, greater momentum and energy should determine a smaller wave packet and a more precise location of the particle. To the contrary, however, the composition of the wave packet being of various waves slightly differing in their frequencies, speeds and directions is according to the magnitude of the photon’s impact. A more compact wave packet collides with a more energetic photon to spread more rapidly and cause more uncertainty of its location.

Heisenberg’s uncertainty principle follows from how Born viewed the wave packet. According to Born any one of the waves in the packet could represent a probable particle of particular momentum and energy according to the range in energy by which the waves vary. The causes of their spreading apart by impact of the photon and by the difference in energies of waves render the momentum and energy more uncertain. In following this lead, Heisenberg surmised more exact determination of the particle’s position or time by the less energetic photon causes uncertainty of a particle’s momentum and energy. Conversely, a determination of momentum and energy by a more energetic photon causes more change to render exact position and time more uncertain. The total uncertainty is a product of uncertainties. The product of uncertainties of position and momentum, or the product of the uncertainties in time and energy is the total uncertainty.

The relative momentum of a photon in relation to wave parameters and Planck’s constant h is provided in relation to the equation P = h/λ. The uncertainty of a change in momentum ΔP with regard to a photon’s wavelength is opposite the uncertainty of its change in position Δx. Certainty of position is uncertainty of momentum and conversely certainty of momentum is uncertainty of position. A range of positions for each momentum and a range in momenta for each position thus exist. The total uncertainty is the product

The total uncertainty further includes energy and time. The dimensions of h (mass-velocity-distance or mass-distance squared per time) can be interpreted as the product of distance and momentum (mass times distance times velocity) or as the product of time and energy (time times mass times velocity squared):

This uncertainty or probability is not interpreted the same as that of flipping a coin. If you flip a coin, it could come up heads 3 times and tails 7 times after 10 tosses. After a million times the heads-tails ratio is apt to approximate nearly as 1. In contrast, the probability of quantum physics is an exact prediction. If there is a probability of a particle showing up 3 times out of 10, then it does so as predicted. However, it could show 1 time for the first 8 observations, and 1 time for the 9th observation and 1 time for the 10th observation. That is, it is predicted to show 3 times in any combination of 10 observations.

PLENUM COSMOLOGY

Explaining the underlying nature of the universe by means of the æther has been discarded in favor of explaining all natural phenomena in accordance with observation. Still, the constant nature of light speed is explainable as contraction of length in the direction of relative motion and the retarding of clocks by motion through the æther in nullifying the differences of time and distance of measure at absolute rest. Perhaps the æther can also be used for explaining gravity, energy, mass and the physical nature of our world in general.

Any explanation of the cause of gravity that is not observationally verifiable is also deemed invalid, but some of us still prefer to understand reality in a more complete manner. If we could explain the underlying cause of gravity in a way consistent with other theory, for instance, it might provide further insight for more theoretical development. In any case, an explanation of the push-action-cause of gravity is here provided in accordance with the equivalence of gravitational and inertial mass, the probability conditions of quantum physics and so forth. However, it does not support all of established theory. It is more consistent with a tired light theory rather than the big bang.

Explanations are thus given with regard to mass, light, energy, gravity and so on. Gravity is explained as a push action in view of a tired light theory and an infinite universe divided into finite, observable parts. How continuous creation of gravitons does not fill up more of space, as to continue forward and change the momentum of mass time after time without violating conservation of momentum is explained.

An explanation of gravity can be relatively simple inasmuch as gravitational force entails an attraction in proportion to mass and inverse proportion to distance squared. More complex is electric charge. It entails an attraction and repulsion. Electrons repel electrons and protons repel protons, but electrons and protons are attracted to each other by equal amounts of opposite charge, even though the proton is about 1836.15 more massive than the electron. However, electric currents moving through wires in the same parallel directions contract whereas they repel if moving parallel to each other in opposite directions.

Electric currents running through wires looped in parallel circles produce a magnetic field. A change in the magnetic field, as by a change in distance, induces another electric current in another wire and so on for electromagnetic induction resulting in the generation of alternating electrical current.

Similar effects occur in space apart from wires, as according to Alfven’s theory electric currents running through plasma constitute filaments that also attract and repel.

An explanation of the underlying cause of gravity as related to electric charge is thus more complex than merely explaining gravity, but both of them are here explained in similar, consistent manner in reference to an æther filled plenum.

Circular Motion, Change and Reality

In a plenum there is no room for variable density and no place to move to unless motion is circular, and circular motion of various size and speed is possible. It is how various forms of circular motion change that result in our perception of the natural world.

A change in circular motion can occur in various degrees for a transfer of momentum if an underlying structure is in place to allow momentum to propagate as waves of energy not changing in density, but only in size, speed and other aspects of relative rotation.

The possible structure for change is thus standing waves in states of equilibrium momentarily changing for a wavelet to propagate its changed state at a finite rate onto another standing wave in line. The transfer of the deformed wave is thus perceived as a transfer of momentum. This transfer of momentum is how the plenum, in part, is perceivable as the mass-energy of light and matter, whereby the density of mass-energy is the magnitude of observable momentum as change in deformity according to natural laws of motion.

A particular system of rotations is one clockwise and another counterclockwise such that parts of two touching vertices move in the same direction. There is thus less frictional force existing between them than if they both rotate clockwise or counterclockwise.

It is possible to have an infinite plane of opposite rotations whereby all touching parts move parallel in the same direction. However, rotation itself is planar, as is a disk, as contrary to a three dimensional state of spatial equilibrium. More friction is thus inevitable in the three dimensional reality in which we live.

Note: Light is conventionally defined as massless, even though it has momentum and energy, because it can be in the same place and time with other light and because of a relativity condition that matter increases to infinite mass in order to reach light speed. This is a definition that is also inconsistent with the Newtonian one that defines mass m, velocity v, and momentum P in view of the equation P = mv. For consistency, light and matter are here defined as two different forms of perceivable motion according to how they interrelate as secondary plenum effects, such that light has mass convertible to kinetic energy of the spatial medium, as with a gravitational field in which all relative motion as well as light move slower.

Light, Matter and Energy

The plenum condition of rotation has implications with regard to the polarity of matter and antimatter, radiation and electric charge as well as with a simpler non-polarity condition of gravity. Pertinent questions to answer are: How does matter and antimatter differ from the other? How is constant light speed possible? How does light not impede the motion of other light? How is variable speed of matter possible?

For light not to impede the motion of other light it needs a free path for exchange of forms. The elasticity of the æther is such that the superimposing of forms does not change the individual momentum of change in form. Consider a deformed disk for an analogy. Its diameter is twice another with which it interacts for a direct transfer of deformity. The change in deformity of the larger disk occurs at half the rate of the smaller, but a change in deformity occurring in twice time for twice distance is constant speed change. All change is thus communicated at light speed. It is also quantized if the parameters mvr of the Planck constant relate as constant speed v = c of a change-in-form m in inverse proportion to form-length r. The particle effect is also explainable according to conservation of momentum. Because æther is perfectly elastic in maintaining itself, as not compensating for change in direction, then the self-spreading of waves is a violation of conservation of momentum.

Light does not interfere with other light, whereas matter impedes the movement of light and matter. It entails a different process of exchanging form, which is similarly explained as superimposed momenta, but as an implosion of frictional force.

First consider an electron as a rotation of æther as a particle effect. Surrounding filaments of æther tend to follow the direction of rotation, but other filaments tend to follow the rotation of another electron for the kinetic energies of opposing filaments to create a force field of opposing charge.

Consider next the electron is a particular rotation of æther as particle effect of matter and antimatter (as differing in clockwise and counterclockwise rotation). Surrounding filaments align with the rotations of the electron-positron pair, but oppose filaments that align with the rotations of another electron-positron pair. A force field for opposing charge thus exists. Filaments moving parallel in the same direction and having less friction between them result in non-opposing charge, as in allowing the electron-positron pair to be pushed together until they superimpose where their opposite spins oppose to transform into pure light energy.

(In view of a plenum there is no superimposing of mass. The example is thus only symbolic. More to the point, the change in spin alignment is the result of the inevitable condition of frictional asymmetry whereby there is a quantum probability a frictional encounter of opposing spins occurs.)

Three-dimensional space energy thus implodes to convert into a one-dimensional direction of radiation. The process is comparable to electric charge in cloud formation. Energy builds until a path is available for a discharge. However, the path is not totally free. Wind, thunder and lightning occur as frictional resistance.

Electrons generally repel other electrons. How do electric currents flowing in the same direction attract?

Effects of electron charge are more complex with regard to its primary nature. Because the plenum is a dynamic state of equilibrium, the haphazard flow of electrons in opposite directions constitutes an activity greater than an inertial-gravitational equilibrium state of matter. Electrons moving in the same direction are thus less inclined to interfere with each other, which results in less activity for less frictional resistance for a negative inner state of dynamic equilibrium subject to more outside influence.

This explanation refers to a process of matter and antimatter converting into radiation. The distinction between them as here explained is with regard to the manner of rotation, as mass-energy equally composed of both matter and antimatter. The latter is a potential of change that occurs from superimposing it with the former by means of the surrounding pressure.

The implosion of inertial space is similar. It tends towards centers of action. Outside inertia combines to push inward with greater energy density.

The polarity of electric charge is also explainable. Charge of a proton nullifies the charge of the electron, but a displaced electron displaces another electron in an atom and so on in other atoms to propagate effect here and there, as towards a charge that is of opposite polarity.

Equivalence

The emitted radiation further provides a vacuum effect for both gravity and electrical attraction, but it is a manner of how gravitational radiation is emitted that determines the equivalence of gravitational and inertial mass. Radiation emitted by matter is Doppler shifted in maintaining relative motion. Gravitational radiation is emitted in proportion to mass, whereas all radiation reflected or absorbed alters momenta of the matter reflecting or absorbing it in manner consistent with the laws of motion. The inertial and gravitational equivalence of mass is simply this proportionality of mutual emissions of radiation maintained for relative motion according to the Doppler principle.

The emitted radiation for equivalence is identified as a graviton, but it merely communicates a change in gravitational effect. The center of spatial implosion as vacuum effect changes in accordance with the relative distribution of mass. The total momentum of spatial inertia for gravity changes direction accordingly. This ‘change’ in the overall direction of momentum further concurs with changes in deformity of the æther waves propagating at light speed, as previously explained.

Although radiation at light speed communicates changes in the position of gravitational effects, there is no violation of conservation of momentum because the direct action of gravity is from the negative ripple effect of continuous creation and equal annihilation of gravitons of the vacuum effect from the superposing of inertial mass through the æther and not from direct action of the emitted radiation on matter, as the latter is only gradually detected as less repulsive energy per time.

Momentum given to matter by light in its path is partial and proportionally constant, as in accordance with space-time curvature resulting from the presence of mass. The exchange is also long range, part elusive and gradual according to the probability conditions of quantum physics. The escape from the confinement of the gravitational field is thus without detection except for the gravitational effect caused by the faster motion of escape from conversion of slower inertial space.

Critical to this explanation is a recycling process in view of a tired light theory. The emitted radiation is reabsorbed for no additional increase of gravitons to occur. Because the reabsorbing is gradual and long range, it also does not nullify the gravitational effect.

Vacuum Effects

After discovering the quantum, Planck attempted to explain it according to classical electromagnetism, which further relates to plasma and a vacuum field of zero point energy (ZPE). This development is not now part of established physics, but indications are that it could assist in the unification of physics.

The vacuum field of ZPE does not mean space is empty. It is a ground state at equilibrium temperature of absolute zero.

Plank had originally proposed the concept of ZPE in order to explain the nature of the quantum. It was hypothesized by Einstein and Stern with the study of hydrogen gas at low temperatures. The data indicated an oscillatory state of vibrations does exist at absolute zero. Walther Nerst (1864-1961) then interpreted ZPE as a vacuum space filled with electromagnetic energy.

Plank interpreted his formula as pertaining to the energy of an oscillator. At absolute zero temperature it cannot lose energy smaller than hf, thus resulting in the quantum effect. Consider a field of energy similar to one of balls and springs maintaining equilibrium in various states of vibration. The states can be depicted as standing waves of a stable structure underlying the observable world where some energy balances out in an undetectable manner.

Theoretical support for the relation is with regard to Heisenberg’s uncertainty principle. According to it there is an uncertainty of both the exact position and momentum of an atomic particle. Moreover, there is a probability anywhere in space a particle exists. Since these probabilities result in accurate predictions, there is thus a virtual field of particles as a potential source of energy inasmuch as a particle detectable at rest is a contradiction, as precise position of zero momentum or precise time of zero energy.

Experimental evidence was provided by Hendrik B. G. Casimir (1909-2000). In 1947, he and Dirk Polder (1919-2001) experimented with metallic plates for the measure of a van der Waals force between the plates and polarized molecules. An attractive force bringing the plates closer together seemed to occur if they were placed close enough together that radiation of longer wavelengths cannot fit between the plates. The effect is explainable as a medium of energy no longer being in balance to cancel effect; all waves moving in every direction combine to cancel effect except for a lack of longer, less energetic waves that are missing between the plates for more outside force than inside force.

Niels Bohr suggested to Casimir the results of the experiment could relate to zero point energy. Casimir complied with the suggestion by formulating a theory in 1948. Experimental evidence as accurate to within fifteen percent of the predicted value of theory came much later in 1997 by Steve K. Lamoreaux. Even more accurate results followed, but Robert Jaffe explained in 2005 the Casimir force as the relativistic retardation of the van der Waals force between the metal plates. The evidence for ZPE was thus explained away.

There are various ways of explaining phenomena, as depending on what and how they relate. Since ZPE attempts to explain the underlying mechanism of the quantum and the Casimir force is explainable by both ZPE and relativity theory, the ZPE seems a promising candidate for the unification of theory.

ZPE also has implications with regard to plasma. Birkeland theorized the existence of the ionized gas of plasma in manner consistent with Maxwell’s classical theory of electromagnetism. Hannes Alfven founded plasma cosmology in showing the electrical effects of plasma studied in a laboratory computer simulate in accurately describing galaxy creation and behavior, as clustering and so forth according to a pinch effect. It is typical of electrical phenomena in general.

It was known that electric currents flowing in the same direction through a wire attract, and they repel if flowing in opposite directions. This also occurs with a current of electrons through plasma. Currents pinch together between voids as filaments that further twist into rope-like whirlwinds or vertices, as explained in 1950 in detail in a book by Alfven. He explained that electrical resistance, velocity and energy are constant with time scales to size such that a cosmic process of a million times larger than that in the laboratory occurs a million times slower.

Although ZPE directly follows from Heisenberg’s uncertainty principle, an aspect of it is comparable to the ultraviolet catastrophe. Shorter waves have more energy. There is thus an infinite potential energy for plates to stick together by their distance of separation approaching zero. This condition would be consistent with regard to big bang and black hole theories, but it might also have other interpretation, as with regard to how matter attracts and repels other matter.

Electrons generally repel other electrons. How do electric currents flowing in the same direction attract? The composition of electrons could be more complex, as with a more fundamental electron charge behavior. If space between mass contains energy of a sort, then the haphazard flow of electrons in directions that are opposite each other could increase the energy activity apart from matter. If the motion of electrons is in the same direction, as in contrast to equilibrium states of activity whereby gravity manifests, then the electrons could combine to plow through space with more of a mean free path in which to follow, thus negating their otherwise repulsive activity to be pushed together.

In an even more complex way it could explain the Casimir Effect. The space between particles of matter, for instance, could allow a saturation of smaller space energies such that the squeezing out of longer waves results in effects conditional to the density of plates as well as the distance between parallel plates. There is thus no infinite amount of outside energy pushing on the plates because the spacing between the atoms and subatomic particles allows the cancellation of effects in opposite directions.

The quantum nature of atoms might similarly be explained. A shell of the tiny nucleus within the atom, for instance, could squeeze out less energetic waves to contain a more vibrant equilibrium source of energy on the average. However, even though the nucleus of the atom has a relatively great density, relatively free space between its parts still allows energetic waves of relatively shorter length to nullify effect.

Although more energetic, tinier, denser particles theoretically exist, the probability condition of theory demands their detection is less likely per time. Energy can thus combine to produce different effects, but the average energy overall is the same with regard to the reality in which we live.

The relative size of atoms thus limits the infinite energy potential of space. In turn, the relative size of atoms determines how they interact with other atoms.

Neutrino-Light Composites

How does space not overfill because of continual creation of gravitons? It is because they are destroyed and created in creating vacuum effects. The escaping energy is long range, as more gradually detected and more gradually recycled back into its original inertial state of space. The process is explainable according to the probability condition of quantum physics.

A good example of the quantum conditions is the neutrino. In passing through matter only a fraction of the neutrino energy is detectable, similar to how light moves through glass and other transparent materials. The neutrino also appears to have properties distinct from both light and other atomic particles. Originally assumed to have no rest mass and move at the speed of light, it is now believed to be a small mass moving nearly at light speed. However, it is still controversial as to whether it is light or matter.

Pauli proposed in 1930 the neutrino could explain conservation of angular momentum (spin) along with energy and momentum with regard to a decaying of atomic particles. De Broglie had proposed in 1932 that photons of light could be composed of neutrinos and antineutrinos. However, the composite particle theory of light came into disfavor with a discovery neutrinos oscillate, as changing in space from one neutrino form to another. Maurice H. L. Pryce (1913-2003) put forth in 1938 the theorem that neutrino waves are polarized longitudinally and lack rotational invariance, which is in contrast to the wave theory of light.

There are interesting properties of the neutrino to consider nonetheless. Antineutrino-proton interaction results in the production of a neutrino and a positron, the anti-electron, but the positron then reacts with an electron to convert into two gamma rays. Similarly, a neutron in the nucleus of the atom is detectable by the release of a gamma ray. Neutrinos and antineutrinos have no electromagnetic charge, being neutral. Ettore Majorana (1906-1938) proposed that they are the same particle, as distinguishable by the non-superposition of the mirror image of its two chiral forms. It appears to be particularly associated with the three subatomic particles named the tau, muon and electron.

Why the neutrino?

The gravitational effect is explained as a vacuum effect caused by mass emitting electromagnetic waves that gradually decrease in energy in providing inertia to space. The electromagnetic waves of ordinary light, however, are not a continuous process. Although they produce a vacuum effect with the Hubble Constant as evidence of its recycling process, a gravitational effect requires a constant emission of radiation with energy equaling the amount of inertial space matter absorbs with no other evidence of its occurrence except for the gravitational effect. Although tired light is typical of the process, it is an equilibrium condition in relation to electrical attraction and repulsion.

The neutrino is nearly massless and it appears to be electrically neutral. It is partially undetectable such that it is possible it is continuously emitted by matter to gradually become reabsorbed by space. However, a neutrino could also be only a catalyst for change. The cosmic microwave background radiation might play a significant role as well.

Mass and Volume Ratios

It is proposed that mass derives as an implosion of plenum content of no variable density. It is energy of this content changing in form. Such atomic masses as the proton, kaon, pion and muon are typical of this process. Such National Philosophy Alliance members as Carl R. Littmann and Greg Volk have investigated the similarity of volume ratios to mass ratios to find a remarkable similarity.

A kaon (K meson), characterized for strangeness, is about half the mass of a proton and decays into two charged pions. Pions (pi mesons) have masses that are less than a third of a kaon mass and decay into muons and muon neutrinos, and less often into electrons and electron neutrinos. The muon is considered a heavier version of the electron, as not to be comprised of any smaller particles, but it appears unstable.

Littmann’s simplest comparison of volume ratios with mass ratios is those of the pion: If 3 large spheres circumscribe a small sphere in a plane, a large sphere radius is 6.464 times the small sphere radius and the volume of a large sphere is 270.1 times the small one. The average positive, negative and neutral charge of pion mass is 270.13 times the electron mass.

The kaon-electron mass ratio comparison is 3 large spheres circumscribing 3 small ones in the manner

The ratio of a large sphere radius to the small sphere radius is 9.89898 to 1 and the volume ratio is 970 to 1. The average between a kaon mass charged and a kaon mass not charged is 969.98 in ratio to electron mass.

The proton relates in the manner

If the small spheres are packed between the crevasses of the large spheres the ratio of radii relate as with the kaon, but if the small spheres are positioned opposite the crevasses the radii and volume ratios are 13.9282 to 1 and 3672 to 1. The average of 970 + 2702 is 1836, as compared to the mass ratio of 1836.15 to 1 between the proton and electron.

The muon relates in the manner

The large circles compare to that of the proton mass of 1836.15 electron masses. The ratio of radii between 1 of 2 small circles to the large one is ½. The ratio of one of 3 small circles to the large one is 0.4641 to 1. A ratio of volumes is 1/8 and 0.0999619 to 1, respectively. An average of the 2 volume ratios is 0.113 to 1, or 206.53 to 1836.15. The empirical value of the muon has been determined as 206.7682838(24) electron masses.

Greg Volk has also calculated the number 9.89897 according to a tetrahedral pattern of 4 spheres packed around a center one. The center of the smaller one is the origin of 3 perpendicular axes. The centers of the 4 larger spheres are at coordinate points (1 1 1), (1 -1 -1), (-1 1 -1) and (-1 -1 1) where distance D of the radius R from the origin is

The spheres are symmetrical in touching along planes of respective axes such that the radius R of a sphere is

The radius r of the inner sphere is coordinate distance D minus radius R, such that

An outer sphere of radius R’ = D + R circumscribing the 4 spheres is of the ratio

The nearly perfect kaon-electron mass-volume ratio of 3 spheres that circumscribe 3 smaller spheres is thus equal to a large-small sphere ratio of the large sphere circumscribing 4 medium spheres circumscribing the small sphere.

Arthur Stanley Eddington (1882-1944) speculated on the fine structure constant in mathematical manner

Further speculation with regard to a 2/3 nature of the electrostatic charge yields

The problem with this and mass-volume speculations are differences in theoretical and empirical values of the fine structure constant and such atomic particles as muons and protons lack accepted explanation.

One proponent of an æther theory who attempted to explain the difference in empirical and theoretical values was Harold Aspden (1927-2011). A core of his theory is a proton-electron mass ratio that relates to a ubiquitous muon in the manner

The empirical value of mp/me is 1836.1527 compares favorably to Aspden’s 1836.1522, but his mμ/me value of 206.3329 is more off the mark of the empirical value of 206.7683. However, the muon in the above formula is more of a ghostly muon. Aspen had derived a value of 206.768038 as well as predicting accurate values of the proton-electron mass ratio, fine structure constant and the proton magnetic moment.

The number 8.898979486 also equals twice Volk’s R/r. It is derived from Aspden’s formula above in the manner

Aspden had derived it according to a combination of two electrodynamic formulas previously derived by Charles-Augustin de Coulomb (1776-1826) and Joseph John Thomson (1856-1940):

The combo formula is according to an interaction energy between the surface contact of two particles of opposite polarity and different radii x and y such that their centers are separated by a distance of x + y. For equality, there is a minimum force of zero such that

The significance of this combo formula is that Aspden not only relates a minute lifetime of muon-anti-muon annihilation for the creation of the proton; he further uses it in a similar annihilation process in relation to an interaction between different size gravitons so that the factor linking the muon to the proton links matter and gravitons as well. The gravitons are similar to the Higgs boson introduced by Peter Higgs for creation of mass, as the boson absorbs mass-energy of space, but the Higgs boson only explains a fraction of the mass.

It is also noted that Aspden denied the validity of relativity theory whereas relativity is here explained as a modification of the laws of nature in accordance with effects of relative motion through the æther. The effects are according to the Doppler principle insofar as the equivalence of gravitational and inertial mass is determined according to how matter emits radiation in opposite directions in conserving momentum.

Mean Free Path

As with regard to the mass and volume ratios, it has not been explained how inner momentum escapes from its enclosure. There is the inward momentum of three-dimensional space in opposition to the escape of one-dimensional momentum outward. In this regard the enclosing space itself is not a single entity; rather, it is a complex system of vertices aligned in ways that toroids twist and loop into a field structure. Opposite spins of less friction allow passage if smaller vertices exist within larger ones.

How does energy escape confinement?

The matter-antimatter symmetry of opposite spin was a simplification. A plenum cannot superimpose. The symmetry of less frictional resistance only allows change if a response to it is relatively local. If instead the condition of spin is fixed to an infinite structure of space, then change of spin requires infinite energy. To propagate momentum as charge the plenum structure thus needs to allow change to occur in a way that it is local, as for opposite circular paths to cancel momenta where they originated. If resistance to the change also is locally elastic, then the momentum of the cause can continue forward to a finite distance where it, too, is eventually changed.

Three dimensional space allowing asymmetrical conditions in proportion to symmetrical ones allows such finite change to occur as well. The vertices of the plenum are complex. Two vertices with the same spin can, for instance, be separated by smaller vertices that spin themselves and circle the larger vertices as buffer effects.

More detailed structure of the plenum is explored by members of the National Philosophy Alliance. One member, in particular, is Charles Donald Briddell. He proposes vertices as string-like loops twisting around each other to become more energetic as they interact with other loops in exchanging energy. In particular is a condition of evolution from a one dimensionality to a three dimensionality as multiples of 3. He defines fractals as stable structures having a mass as multiple to the electron that is not of any whole number n as a power of 3. For instance, if n is seven, then 3^7 = 2187. The following particles are shown to be stable:

Explanations given here might not seem to have any practical value, but you never know. For instance, consider the concept of mean free path. Clausius used it to explain tiny particles relatively great in number reflect each other back and forth to prevent mass from exploding every which way. A mean free path is also part of explaining gravity as a means of allowing light to escape for vacuum effects to occur. Moreover, the flow of an electric current through a wire encounters frictional resistance in heating up the wire. Amps are current. Voltage is an electrical difference in potential. More amps require more wire per length for the wire to conduct and not overheat, whereas greater voltage encounters less resistance, as in a high voltage power line. Voltage thus relates to a mean free path. Does it relate to gravity? If it does, then it is likely gravity and electricity somehow link in ways that are verifiable by experimentation.

As for more practical significance, the geometrical patterns such as tetrahedrons and icosahedrons have been useful in chemistry and biology. Nanoparticles of crystals are classified by chemists according to their icosahedral and dodecahedron structures, such as for the cluster compound of boron and carbon atoms. In biology, viruses are protected by protein surfaces that contain subunits that best fit the icosahedron.

Practicality is simple solutions in the application of natural laws. Chemical engineers at the University of Washington, for instance, have discovered light can charge a water battery. Why not? Light collides with atoms to displace electrons. Water pH then varies. It thus appears cheep solar batteries of water at the least could support more expensive solar panels of silicon.

THE COSMIC COINCIDENCE

Why an infinite amount of stars does not light up the sky at night is Olber’s Paradox. Aristotle proposed a finite number of stars. Kepler considered the night sky indicates a finite universe. A century later Edmun Halley (1656-1742) argued the dark sky of the night is allowed by means of an uneven distribution of stars. In 1743 Jean Phillippe Loys de Cheseaux (1718-1751) proposed the universe is either finite or something in space is absorbing light. His proposal was reiterated by Heinrich Wilhelm Mauthaus Olbers (1768-1840) in believing the universe is infinite, and he proposed an interstellar dust is the absorbing medium. The debate persisted in honor of his name.

Astronomers nowadays generally believe that an interstellar dust in thermal equilibrium would absorb enough light from infinite stars to heat up and reemit the light. However, the paradox is misleading in that there can still be a balance between light energy and matter in a dynamic state of equilibrium for an even distribution of them in infinite space. As according to a tired light theory, for instance, if the space medium partially absorbs light, the energy can convert to other forms for the creation of new stars and galaxies.

Energy is constantly converting from one form to another. Matter absorbing light to increase in relative motion also increases in relative mass. Mass and light both interrelate with gravitational fields. It is thus not out of the question that a more comprehensive theory of light, matter and gravity could be in order. What is here proposed is a recycling universe where light and gravitational energy emitted from matter are partially absorbed by the space beyond matter in maintaining a process of dynamic equilibrium in consistant manner with the Hubble Constant as well as Olber’s paradox.

The Hubble Constant

Einstein proposed in 1917 a model of the universe as static and finite. In order for it not to collapse by its own weight, he also proposed a repulsive force exists counter to gravity, which was a mathematical option available from integrating his general field equations. Integration requires the addition of a constant, which can be zero, as they are eliminated by differentiation, which is the reverse process of integration. However, a more indepth examination by Alexander Friedmann (1888-1925) determined the model to be unstable, but he suggested to Einstein a stable universe is possible by way of an initial state of expansion. Georges-Hanni Lemaitre (1894-1966) responded to the suggestion in proposing the universe is expanding from what was a singularity, as according to Schwarzschild’s solution of Einstein’s general field equations.

Astronomers also discovered starlight from more distant sources is weaker on the average. Carl Powell Hubble (1889-1953) observed a classification of stars, Cepheid variables by name, and examined the data to discover it indicates a constant redshift with distance, a relation that is now known as the Hubble Constant. In 1924, Carl Wilhelm Wirtz (1876-1939) correlated the faintness of a galaxy to galactical recession.

A counter proposal, with less theoretical support, was made by Fritz Zwicky (1898-1974). He offered the possibility the redshift can result from light losing its energy while moving through space instead of losing it at the start from the recessional speed of the source. His explanation was that the redshift is caused by the gravity from the stars as the source of emission. It did not appear plausible to other physicists, but he might have persuaded Hubble to state that the cause of the redshift as the recessional motion of the stars had not been determined as fact.

Explaining The Cosmic Coincidence

Since in an expanding universe distances between galaxies is increasing, and since the Hubble Constant is a change in light spectrum per distance, the theory that the universe is expanding requires a constant that varies in time. In theory, then, the Hubble Constant is only constant for distances of a particular time, as to decrease as the distance between stars increases.

Dirac in accepting the theory of a finite expanding universe as the cause of the Hubble Constant further speculated on how it relates to the structural nature of the atom. For instance, the electron mass me, Hubble Constant H, light speed c, electronic charge e, and the constant of gravity G approximate in the manner

The gravitational force of the electron per light speed thus approximates to the Hubble Constant. However, since H decreases as the universe expands, another of the above constants besides H needs to vary as well in order to maintain equality. Dirac chose G for gravity to decrease along with H.

At the time of this speculation the value of H was only approximately determined within 100 kilometers per second. An empircal value calculated according to theory has been obtained by a Wilkinson Microwave Anisotropy Probe (WMAP satellite) launched to map fluctuations in temperature of the cosmic background radiation (CMB). The value of H according to the data and theory is 70.5 ± 1.3 kilometers per second per one million parsecs. A parsec is 3.09 X 10^13 kilometers and dividing 70.5 kilometers per second by one million of them gives 2.28 X 10-18 times per second. The value in relation to the electron mass, as proposed by Dirac, is discredited in being nearly a hundred times less than this more accurate determination.

There is still a cosmic coincidence to reckon with in relation to the mass and size of the hydrogen atom, as within the determined accuracy of physical values given below.

Values of Physical Parameters

Gravitational Constant: G = 6.67428(67) x 10-8 cm^3/(gm)(sec)2

Proton mass: mp = 1.672621637(13) x 10-24 gm

Electron mass: me = 9.10938215(45) x 10-28 gm

Light speed: c = 2.99792458 x 10^10 cm/sec

Electron radius: re = 2.8179402894 x 10-13 cm

Neutron radius: rn = 2.881991 x 10-12 cm

Fine Structure Constant: α = 1/137.036

Planck Constant: 2πħ = h = 6.626069 (gm)(cm)2/sec

Electronic unit of charge e squared: e^2 = mec^2re = 23.07 x 10-20 (gm)(cm)/sec^2

The values above are partly a simplification of theory rather than fact. The real value of the electron radius, for instance, could be two thirds re in accordance with the Thomson formula 2e^2/3r = mec^2 instead of e^2/re = mec^2. The simplified formula re/α^2 thus equals a Bohr radius ra of the hydrogen atom, ra(me/mp) = rn and so on.

The proton and electron are fundamental masses of this smallest atom. The electron has about 1836.15 times less mass than the proton and the radius of the nucleus containing the proton is 1836.15 times shorter than the Bohr radius of the atom containing both the electron and the nucleus. The cosmic coincidence is in further relation to H and the ratio between electronic and gravitational forces of the atom.

The Gravitational Interpretation

Dirac proposed a varying gravitational constant to explain The Cosmic Coincidence. Zwicky proposed the red shift in more distant starlight is caused by the gravity of the light source. Neither of these proposals is here accepted. Although gravity is mathematically related to the Hubble Constant, it is not a direct cause. To the contrary, the red shift in the light spectrum is a cause of gravity, as energy of light absorbed by space that, in return, produces the gravitational effect. It can be interpreted as dark energy not pushing space apart but pushing towards matter. It pushes towards matter by matter absorbing and reemitting it as radiation to leave the vacuum effect in its wake.

It is a recycling process. Partial absorption of light by space is a long range, gradual process that adds to space inertia. To the contrary, however, when inertial mass superimposes on inertial space, virtual energy is emitted as virtual photons, creating vacuum effects in their wake. These vacuum effects result in the inertial space to push inward in replacing the virtual energy that was emitted. All inertial mass being in dynamic states of equilibrium with inertial space tends to push along with inertial space in negating vacuum space in a manner consistent with spacetime curvature.

The electromagnetic energy is long range and in part elusive according to the probability conditions of quantum physics in escaping the confinement of the gravitational field without detection except for that of the gravitational effect caused by the faster motion of escape from smaller, less mass-like entities.

Gravity is the rate of conversion, as in proportion to the amount of mass converting. After converted the escaping energy is gradually reabsorbed by the media of space. This absorption is of the energy of both light and gravity. The nature of it is more complex in that it is the relative distribution of mass in the universe that determines effect in accordance with a dynamic state of equilibrium changing in various ways.

A gravitational force and elementary charge ratio of the proton and electron is according to the equation

The fraction v^2/c^2 also indicates a relativistic Doppler effect, as an approximation of 2 divided by the square root of (1 – v^2/c^2).

A numerical equivalent to this ratio is obtainable in relation to the Hubble Constant. Its value according to the data obtained by the WMAP space probe is H = 70.5 ± 1.5 kilometers per second for a light source one hundred million parsecs from us. A value within the margin of error is H_1 = 70.75 km/sec per Mpc, such that

The speed of the Hubble Constant at a distance equal to the diameter of the hydrogen nucleus thus appears equal to the ratio of electromagnetic and gravitational potentials between the proton and electron masses.

The diameter in relation to gravity is interpreted, as depicted above, as the mean distance between two touching spheres of equal size masses.

An approximation for a Bohr ground state radius ra of the hydrogen atom of mass ma (since ma = mp + me) is

The Bohr radius also relates to the Planck Constant in manner h/2π = ħ = mvr = mcrα = e^2/c. Substituting for e^2 with ħc per α obtains

The gravitational force between two hydrogen atoms thus equates to the kinetic energy of one atom as well as to the product of the Hubble and Planck constants per fine structure constant.

Overall indications are that the determined value of H by WMAP is consistent with a gravitational force per average mass of the observable universe and with a relativistic Doppler shift in the spectrum of starlight per distance.

A Non Coincidence

The cosmic coincidence has not been explained by big bang theory, but a similar formula does allow for a variable Hubble Constant. It derives from standard formula in the manner

The Hubble Constant can thus vary for any mass and radius having an escape velocity of the field equal to light speed. However, connecting formulas results in an exact value in mass Mu of our observable universe:

This result indicates either the observable part of the universe is conditional to fundamental parameters of nature or vice versa, as Dirac speculated in proposing a variable gravitational constant or size is relative in accordance with tired light theory.

A Quantum Interpretation

The primary mission of the WMAP probe was to map the microwave background radiation in order to determine its variance according to theory. The only theories considered were big bang variations. Results are thus partly empirical and partly theoretical, as is the value of the Hubble Constant H determined as 70 kilometers per second per million parsecs theoretical rather than fact. Indeed, different measurements over the years have produced various values, as to indicate H varies according to what is measured and how it is, as if mass presence is a factor of space permittivity.

Lyndon Ashmore has proposed a quantum tired light theory consistent with an average determination of H over the years. The only difference of his theory apart from quantum physics, as now established, is a constant k of proportionality exactly one cubic meter:

H_2 is Ashmore’s value of the Hubble Constant, re is a theoretical value of the electron radius, and me is the electron mass.

That k is exactly one cubic meter is a remarkable coincidence. However, there is justification for it with regard to another remarkable coincidence: the density of the universe in ratio to the density of the nucleus in the hydrogen atom is equal to the ratio of electrostatic and gravitational forces of the electron and proton in the hydrogen atom.

The average density ρc of the universe in relation to H_2, as according to Einstein’s relativistic formula, is

H_2 squared in the equation is converted to light speed c squared per critical radius Ru squared wherefrom it equates as the gravitational escape velocity squared: c^2 = 2GM/Ru.

The density of the universe in ratio to the density of an atomic nucleus of the hydrogen atom equates as

Why does H_2 differ from H_1?

It is because H_2 connects with an average density of mass-energy whereas H_1 connects as a distance per light speed. H_1 is thus according to a permeability of æther for all radiation; H_2 is according to an average density whereby the permeability of plasma varies for different light similar to how its speed varies in such media as water and air. Different values for a Hubble Constant are thus according to relative density of the environment pertinent to their determination.

If plasma is denser where closer to planets, stars, galaxies, clusters of galaxies and so forth, then the red shift of starlight would be greater in accordance with Ashmore’s tired light theory depending on the mean free path through the cosmos. A more distant galaxy of a cluster should be red shifted more than a nearer one, but if plasma is thicker in the galaxy than in the cluster, or thicker between the stars than between the galaxies, it could verify theory by way of correlating a degree of red shift with the distance moved through plasma. If density of intergalactic plasma is consistent with the size and formation of the cluster of galaxies, for instance, then periodicity of red shift is expected.

The discovery of periodicity, or quantization as it was interpreted, was announced in 1966 and in 1967 by William G. Tifft. Other astronomers have reported similar finds up until the new millennium. However, they have been discarded by mainstream astronomers or explained away as coincidental, due to geometrical effect, or due to lumpiness of the big bang during its early beginning.

The Ashmore formula relates to a plasmatic state of matter. Plasma is now believed to be 99% of visible matter. The difference between it and ordinary matter is the electrons in the plasma are less tightly bounded to atoms to allow more electrical activity and motion between the atoms. Atoms in the plasma state, when absorbing and emitting photons, are Doppler shifted in acquiring some of the photon energy. According to Ashmore, it converts to the CMBR, but if the average Doppler shift is to the red end of the spectrum, CMBR needs to somehow recycle in order not to continually increase. It could, for instance, contribute to the push cause of gravity as it is reabsorbed and reemitted by matter as ordinary light.

Matter can reabsorb the CMBR in various ways. It could be absorbed by virtual particles conditional to probability of quantum physics. Some stars evaporate as others form. The CMBR moving every which way can also energize the space inertia and be attached to the emitted light of matter. As the gravitational effect is an equilibrium state, variations of the equilibrium state can also occur as electrodynamic effects.

Why is H_2 less than H_1 if the plasma increases the magnitude of the redshift?

It is because a relatively local quantization of the redshift tends to nullify the distance parameter of H_2. The Milky Way plasma, for instance, increases H, but the local contribution of plasma being greater than the overall average change per distance decreases redshift comparisons per distance.

Cosmic implications are with regard to the virtual field of quantum probabilities and relativistic effects as complements. Although general relativity allows a mass of any size to not exceed an escaped velocity of c as its upper limit, plasma could be more restrictive, as for a smaller universe of matter and plasma slowing relative motion, but with its perception nullified do to atoms also being smaller. Size is thus relative.

Nullification is a consistent relativistic effect. The presence of mass curves spacetime; in turn, spacetime curvature determines the presence of mass. If mass is evenly distributed everywhere, then all gravitational effect is nullified along with its complementary aspect of the plasma condition whereby sized is relative.

Unity

Special relativity theory unified electrodynamics and classical mechanics. The principle of equivalence equates relative motion with gravity. Why has not the pursuit of a unified field theory regarding gravity and quantum electrodynamics (QED) been successful?

An answer from an anonymous expert of physics is quantum electrodynamics uses renormalization to overcome infinities; general relativity does not allow a minimum distance of spacetime for the application of renormalization. If mass-energy is able to condense into a singularity, which is an assumption conditional to big bang theory as a particular interpretation of the Schwartzschild Metric from which all mass-energy in the universe is capable of condensing into a point-like volume of space, and able to expand from one as well, then renormalization is indeed an impediment for the unification of theory. However, the singularity is here proposed as the fault.

In a chapter of this book titled General Relativity the Schwarzschild Metric was analyzed in a way that a relativistic contraction of mass-energy within a field of gravity results in a relativistic spacetime expansion of the field. If true, then the singularity preventing the unification of QED with gravity does not exist and a possible resolution to the unity problem could thus be the relegation of relativity theory as a modification of the fundamental laws of nature. The primary field is thus the virtual field of QED whereby relative motion and gravity further determine probabilities as to how they are perceived.

The interrelation of QED and relativity theory is also conditional to the existence of a multiverse, as to how relativistic expansion and relativistic contraction of spacetime both occur.

The Schwartzschild Metric is Lorentz Invariant if the retardation of light speed and relative motion by a relativistic factor is nullified by a decrease in radius of the field and increase in its gravitational mass by the same relativistic factor. The relativistic effects are not the same as that of adding velocities or gravitational potentials as they relate to a specific magnitude of the field at a particular location of the field, as similar to a relativistic increase in mass for any speed of constant speed change. A somewhat intuitive analogy applies, however, such that a relativistic contraction of Earth’s radius is also conditional to a relativistic contraction between Earth and the sun. In view of the multiverse the analogy is with regard to adding the velocity v to the speed of light c calculated in the manner

Since c is maximum escape velocity of the multiverse, any mass added to it results in the same gravitational potential.

In SRT the contraction of length in the direction of relative motion allows light speed to be perceived as constant. The spacetime coordinates of an observer in relative motion are perceived as extended because the clock in relative motion is slow. Within a gravitational field natural clocks are also relatively slow. They are slow because all relative motion, which includes light speed, is slow by the relativistic factor squared. If the orbital radius between masses contract in proportion to the relativistic factor, and the mass itself is likewise contracted such that no contraction is perceived by a local observer, then the natural clock of orbital motion moves a shorter distance to be timed slow only by the relativistic factor. Any spacetime of the field that does not contract is thus perceived as relatively expanded.

How does part of the field contract while another part remains the same? The answer to this question is explained according to the inhomogeneous nature of gravity.

Einstein explained there is no internal awareness of free fall if everything else in free fall is affected the same way. However, not everything is affected in the same way. Tidal effects are due to the inhomogeneous nature of gravity. Ocean tides, for instance, occur as a result of greater attraction between the moon and the closer part of Earth. Gravity is thus a result of matter and energy following spacetime curvature due to the presence of mass, as according to the inhomogeneity of the field. Earth’s gravity, for instance, cancels itself at its center where it is the same in all directions.

Relativistic contraction of matter is conditional to non-homogeneity of the gravitational field, the virtual field of QED, relative motion, conservation of energy and the multiverse. As with regard to relative motion, energy is conserved in collisions of masses in view of observers apart from them. An observer that changes in relative motion by means of collision perceives all other mass-energy as changed unless the probability condition of the virtual field changes accordingly. The observer thus perceives different virtual particles by means of relative motion, as to nullify Doppler Effect by obtaining a new equilibrium state reflecting in all directions the same amount of virtual energy. This is how push-cause gravity is explainable in accordance with the principle of equivalence.

That the mass-energy itself remains relatively the same is because gravity constitutes work energy and the laws of thermodynamics require it to be spent. An equal amount of work energy is spent as required by the addition of gravitational potentials theorem at the limit of the escape velocity c. However, gravitational work energy spent of a multiverse is everywhere the same to be received from everywhere the same as an adiabatic state of equilibrium.

The size of the multiverse also stays relatively the same. Size is relative because a relativistic decrease in the size of matter and a relativistic increase in size of the field converge along with whatever virtual energy becomes detectable according to probability. If Earth’s mass is increased into a multiverse, for instances, then a person on Earth’s surface is changed along with the transformation of matter with the virtual field.

What if mass in free fall conglomerates towards a common center to form into a multiverse? Inasmuch as each portion of mass falls freely in a homogeneous field of gravity no internal awareness of change is to be perceived. However, as matter relatively inside the Schwartzschild limit contracts, relative expansion and closing of spacetime occurs wherefrom each position becomes the center it multiverse.

A unified field theory thus becomes evident with the interrelating of GRT and QED in a manner that all mass-energy is conserved.

ACKNOWLEDGEMENTS

Being self-educated does not mean independence from experts in the field. I am grateful for all sources of knowledge and support available. One support in particular is the National Philosophy Alliance (NPA) and its editor Greg Volk allowing a liberal foundation to explore and develop. The World Wide Web of the Internet and Wikipedia and its expert contributors in particular has provided an invaluable cross reference. In addition, listed below is a source of printed books from which I have, in part, learned my knowledge of physics and its history.

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Aspden, Haraold, http://haroldaspden.com

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Born, M., Einstein’s Theory of Relativity. New York: Dover (1965).

Briddell, Don, ‘The Neutron Modeled as a Field Structure’. Proceedings of the Natural Philosophy Alliance (18th Annual Conference, July 1920) pp. 75-84.

d’ Abro, A., The Rise of the New Physics. New York: Dover (1951).

Davies P., & Brown, J., Superstrings. Cambridge (1988).

Decandole, James, ‘Charge and the Shape of the Proton’. Proceedings of the NPA, Albuquerque, NM 2012.

Feyman, R.P., QED—The Strange Theory of Light and Matter. Princeton: Princeton University Press (1985).

Fritzch, H., Quarks. New York: Basic Books (1983).

Harrison, E., Modern Cosmology in Retrospect (In B. Balvinot & B. Messina Eds.). Cambridge (1990).

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Hohenberger, William R., ‘Aethereal Fracture Structures for the Electron & the Proton’. Porceedings of the NPA, Albuquerque, NM 2012.

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Kaku, M., Hyperspace. London: Oxford (1994).

Lightman, A., Ancient Light. Cambridge: Harvard (1991).

Lilly, S., Discovering Relativity for Yourself. Cambridge (1981).

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Littmann, Carl R., ‘Sphere Volume Ratios in Tetrahedral and Triangular Patters, and some Implications’. Proceedings of the Natural Philosophy Alliance (18th Annual Conference, July 1920) pp. 351-354.

Lucas, Charles Williams, ‘Electrodynamic Origins of Gravitational Forces’ & ‘The Universal Electrodynamic Force’. Proceedings of the Natural Philosophy Alliance (18th Annual Conference, July 1920) pp. 375-397.

Mallove, E.F., The Quickening Universe. New York: St. Martin Press (1987).

Michio, K., Hyperspace—A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. New York: Doubleday (1994).

Setterfield, Barry John. ‘A Plasma Universe with Changing Zero Point Energy’. Proceedings of the Natural Philosophy Alliance (18th Annual Conference, July 1920) pp. 535-545.

Tombe, Frederick David. ‘The Double Helix and the Compound Centrifugal Force’. Proceedings of the NPA, Albuquerque, NM 2012.

Thorne, Kip S., Black Holes and Time Warps – Einstein’s Outrages Legacy. W.W. Norton & Co (1994).

Weinberg, S., Gravitation and Cosmology—Principles and Applications of the General Theory of Relativity. New York: John Wiley & Sons, Inc. (1972).

Wolff, Milo, Schrodinger’s Universe – Einstein, Waves & the Origin of the Natural Laws. Outskirts Press (2008)

Volk, Greg, ‘Toroids, Vortices, Knots, Topology and Quanta: Part I’. Proceedings of the Natural Philosophy Alliance (18th Annual Conference, July 2011), V8. pp. 675-681.

Pollack, Gerald H., ‘Batteries Made From Water’. Proceedings of the NPA in Albuquerque, New Mexico (2012).