THE RELATIVITY THEORIES AND THE SPEED OF LIGHT
David W. Talmage1 and Ronald R Hatch2
1. University of Colorado Health Sciences Center, 290 S. Fairfax St.,
Denver, CO 80246.
2. NavCom Technology, Inc., 123 West
Torrance Blvd., Suite 101, Redondo
Beach, CA 90277
Abbreviations and Key Words: STR, Special Theory of Relativity; GTR;
General Theory of Relativity; GPS, Global Positioning System; ILSF, Isotropic
Light Speed Frame
ABSTRACT
From a positivist
perspective, Einstein’s two relativity theories (the Special, STR and the
General, GTR) have made very accurate predictions of observations. But from a realist point of view they have
not provided satisfactory explanations of many phenomena or successfully
related the two theories with each other or with quantum mechanics. It is our contention that practical
experience with accurate clocks has provided a realistic interpretation and
unification of the two relativity theories.
In this interpretation the observed predictions of Einstein’s two
relativity theories lead logically to the conclusion that the primary effect of
a gravitational field is a gradient in the speed of light and that all other
observed effects of a gradient in the gravitational potential, including
the curvature of light, the slowing of clocks and the force of gravity, result
either directly or indirectly from the gradient in the speed of light.
We
start with the confirmed predictions of relativity (1-3) for which there is
general agreement. Secondly we describe
the quantitative relations between these observations, and lastly we draw what
we consider some logical conclusions and construct realistic models of both
gravity and inertia.
2. The speed of light is independent of the motion of its source (5).
3. Matter particles in to and fro or circular motion relative to any inertial frame contain more energy than the same particles at rest in that frame. The increase in energy is a function of the speed of their motion relative to that frame.
4. Atomic clocks in to and fro motion run more slowly than clocks which are at rest in their inertial frame (6, 7)
5. Matter particles that fall in a gravitational gradient release energy. The source of that energy has never been clarified (8).
6. Atomic clocks at rest in a gravitational gradient run more slowly than those at rest at a higher altitude, i.e. at a higher gravitational potential (3).
7. Mass and energy are interchangeable according to the equation E = mc2 (9).
8. Light passing the rim of the sun travels more slowly than it does away from the sun and bends at an angle of 1.75”, which is its least time path (10, 11).
9. As matter particles are accelerated close to the speed of light, they demonstrate resistance to acceleration and an increase in inertial mass, which approaches infinity as the particle’s speed approaches the speed of light (9, 12).
In addition to the above confirmed predictions of Relativity, we assume the conservation of both energy and momentum.
Quantitative Relations
Between the Above Observations.
Energy and Clocks: There is a striking correlation between the energy content of particles and their clock rate, i.e. the fractional change in energy content is equal to the fractional change in clock rate. However, the correlation is in opposite directions in the cases of gravity and motion.
Thus, in the case of gravity, matter particles have a lower energy content and a slower clock rate at a low altitude than they do at a high altitude and
E/E0 = f/f0 = (1 – 2GM/rc2)1/2 (1)
where G is the gravitational constant, M is the mass of a body, r is the distance from the body’s center, E and f are the energy content and frequency of a matter particle at r, and E0 and f0 are the energy and frequency of the same particle at infinite altitude.
In the case of motion clock rate decreases as the particle’s energy increases and
E/E0 = f0/f = 1/(1 – v2/c2)1/2 (2)
where E0 and f0 are the energy and frequency of the particle at rest in the frame of measurement, E, f. and v are the particle’s energy, frequency and velocity in that frame and c is the speed of light in empty space.
With both gravity and motion, the correlation between energy and clock rate is exact. This can be illustrated by recasting equations (1) and (2) into the change in clock rate, Df, caused by either a change in velocity (v0 to v) or a change in gravitational potential (r0 to r).
Δfv = (1 – v2/c2)1/2 - (1 – v02/c2)1/2 (3)
Δfg = (1 – 2GM/rc2)1/2 - (1 – 2GM/roc2)1/2 (4)
Equations (3) and (4) hold when the earth distorts into an ellipsoidal shape due to its spin. Mean sea level becomes a surface of equal energy. Clocks at the equator should run more slowly than at the poles because of the motion caused by the rotation of the earth (STR). Clocks at the poles should run more slowly than those at the equator because they are closer to the center of the earth (GTR). The two exactly cancel and clocks at sea level run at the same rate all over the earth (13). Thus, on the earth’s surface equations (3) and (4) sum to zero. The increased kinetic energy of motion at the equator is exactly matched by the increased gravitational energy and the two effects cancel because they have equal but opposite effects upon the clock rate.
Equations (3) and (4) also apply to the energy relationships of satellites in orbit. The escape velocity of a mass in orbit is such that the kinetic energy is equal to the negative of the potential energy. Thus, the clock is affected equally by the kinetic and gravitational energies and the escape velocity can be obtained by setting equations (3) and (4) equal. Approximating the square roots and solving for the escape velocity gives: Ve =(2GM/r)1/2 (5) Recognizing that the kinetic energy of a mass in circular orbit is given by one-half of the kinetic energy of escape gives a circular velocity of: Vc =(GM/α)1/2 (6) where a is the circular radius.
A satellite in eccentric orbit has an oscillation between the kinetic and potential energy around the nominal values. The two energy changes have exactly the same effect on the clock in both magnitude and sign. Thus, we can solve for the changing velocity in an eccentric orbit by setting equations (3) and (4) equal and using equation (6) to replace the initial circular velocity. V =(2GM/r - GM/α)1/2 (7)
A demonstration of the equality of the fractional changes in energy and clock rate is the behavior of Global Positioning System (GPS) clocks in orbit around the earth.. These clocks run faster at apogee than they do at perigee for two reasons: they move more slowly in their orbit and they contain more gravitational energy. In this case the two effects upon the clock are equal and additive (14). This results from the fact that the clocks in a free fall orbit maintain constant total energy as they exchange kinetic and gravitational energy.
The speed of light and clock rate: The time delay of the return of a light beam bounced off of Venus when the path of that beam passes near the sun is usually explained as due to the curvature of space time (15). It can also be explained as a reduction in the speed of light near the sun. In our opinion the two explanations are equivalent but we believe that it is the change in the speed of light that causes the appearance of a curvature in space time rather than the reverse. We also prefer to think of the speed of light as the primary effect because it provides a simple causal explanation of the effect of the gravitational gradient on the clock rate of matter particles. This is provided by the strict two fold difference between the fractional changes. Thus,
f/f0 = (c/c0)1/2 (8)
The following quotation from Einstein (16), written in 1916, indicates that in his first analysis of GTR he thought that the change in the speed of light was the cause of the curvature of light path, “…our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.” Our current understanding of quantum electrodynamics is that light always follows the least time path, which has been shown to be the path predicted by GTR (11).
The slower speed of light is not observable along the path followed because of the combined clock slowing and length contraction of material particles, each of which accounts for one-half of the total effect. We accept the interpretation of GTR that material particles contract in a strong gravitational field and also the prediction of STR that matter particles contract in the axis of motion, although neither contraction can be demonstrated by direct observation. The fact that the fractional change in the speed of light is twice the fractional change in clock rate will be important in the conclusions discussed below.
The isotropic light speed frame (ILSF): The special theory of relativity is based on the fact that from laboratory experiments it is impossible to distinguish between inertial frames or to detect motion relative to a preferred frame. However, this absence of evidence does not prove that a preferred frame does not exist (17, 18). And the observed asymmetry of the background cosmic radiation has made it possible to measure the speed and direction of the motion of the solar system with respect to that background which is presumed to be a remnant of the big bang (19). The failure to detect the preferred frame by measuring the difference in the round trip speed of light in different directions was explained by Lorenz by postulating a contraction of matter in the direction of motion that exactly canceled the difference that would be expected if the earth were moving through a preferred frame. The amount of this Lorenz contraction is exactly the same as that predicted by STR for motion relative to the observer. Since this contraction is too small to detect the question of who is right, Einstein or Lorenz, has never been settled. Experiments attempting to measure the one way speed of light with accurate clocks that have been synchronized and moved apart have also failed to detect the motion of the earth through space (20). But the situation here is a little different from the Lorenz contraction correction because the effect of round trip motion on clock rate can be detected (3, 21). The amount of the observed change in clock rate is exactly that predicted by Einstein and is also the amount required to exactly cancel any difference in the two one-way speeds of light. Although there are different interpretations of this paradox, we believe that the exact cancellation is strong indirect evidence for the existence of a preferred frame.
There are other observations that provide convergent evidence of a unique ILSF. These include the independence of light speed from motion of its source, the aberration of starlight (22) and the obvious effects of rotation of the earth and other objects. While different explanations of all these effects exist, the presence of a unique isotropic light speed frame provides a simple explanation of all of them.
Experience with the Global Positioning System. The Global Positioning System currently has 28 satellites, each of which has an atomic clock, in orbit around the earth at a radius of approximately 25,500 kilometers (23) These clocks send out radio signals which allow receivers on the earth to triangulate their position with great accuracy. The clocks, however, have to be corrected for changes in their speed of motion and gravitational potential. Typically, the message transmitted from the satellites is updated every two hours. A polynomial correction is transmitted in the message giving a clock bias correction, a clock frequency correction and a clock drift rate. Often the drift rate is zero. Generally there is very little change from one upload to the next.
The main effect of the gravitational potential arises from the changing distance of the clock from the earth, but there are also effects produced by the sun and the moon. It has been noted that motion can be calculated as relative to the inertial frame of the sun or to the frame of the non-rotating earth (18). Presumably, one could in theory also use the frame of the isotropic light speed frame of the cosmic radiation. When the sun’s inertial frame is used the varying distance of the clocks from the sun needs to be included in the calculation, but when the non-rotating earth is used the varying distance of the clock from the sun is not included (24). This last observation is explained by the fact that the change in the sun’s gravitational potential is included in the transformation from the frame of the universe’s ILSF to that of the non-rotating earth (25).
1. The source of gravitational energy is a change in the energy content of matter particles. It is clear from work with particle accelerators that the energy content of matter particles changes with motion. Thus the similarity of the effects of motion and gravity on the correlation between energy content and clock rate is strong evidence that gravitational energy is also derived from a change in the energy content of matter particles.
2. The reduction in the speed of light is perhaps the most important effect of the gravitational potential. The curvature of light path around the sun is the result of the reduction of light speed in the gravitational potential of the sun because the amount of the observed curvature is the least time path calculated from the reduction in light speed required by the observed time delay of light passing by the rim of the sun. That light follows the least time path was first proposed by Fermat (26) and has been observed in the laboratory and predicted by Quantum Electrodynamics (27).
3. There is an exact correlation between the fractional change in light speed, the fractional change in energy, the fractional change in length, the fractional change in clock rate and the implied fractional change in mass with a change in the gravitational potential. This indicates that either the gradient in the speed of light is the primary cause of the other phenomena or that a common factor, e.g. a gradient in ether density, is the common cause. As the gravitational potential is reduced (closer to the center of the gravitational source), there is a fractional decrease in the clock rate. Each unit of fractional decrease in the clock rate corresponds to two units of fractional decrease in the speed of light. Clearly, this implies that the wavelength of the light released from matter particles must also decrease by a corresponding single unit of fractional change.
On the basis of the above conclusions we propose the following model of gravity. The background gravitational potential is produced by an underlying background isotropic light speed frame, which is created by an effect of the matter and energy from the entire universe. Superimposed on this background, local concentrations of matter produce local regions of increased density of whatever it is that forms the background (e.g. an ether or the virtual particles derived from the energy of the vacuum) and occupies all space. The increase in local density is proportional to the mass (or structural energy) concentrated locally and this increase is approximately inversely proportional to the distance from the center of that mass. It follows that the speed of light is inversely proportional to the density of whatever it is that occupies space. The fact that the kinetic energy produced, the wavelength of radiation emitted from an atom and the clock rate of atomic clocks are all reduced by the same fraction when the gravitational potential is reduced, clearly indicates that the internal energy of an atom must be reduced and that this decrease in internal energy is associated with the decrease in the speed of light. This strongly suggests that the source of the energy made available when a particle falls in a gravitational field is derived from the decrease in the energy of the particle.
Because of the striking similarities between the effects of gravity and motion on clock rate and energy, any model of gravity would be incomplete if it did not also provide for a concordant model of inertia. The central problem with inertia is to provide an explanation of the observation that every change in the direction or velocity of motion of a matter particle requires an exchange of energy. Even at low velocities matter particles in to and fro motion demonstrate a reduction in clock rate and contain a form of recoverable energy known as heat. These observations fit most easily into a model that postulates that the energy content of matter particles is determined by their motion relative to a preferred frame, which in this model is the unique background ILSF. We assume that matter particles are made up of vibrating energy that moves in this field at the same speed as free energy (c). The motion of the particle with respect to the preferred frame creates an asymmetry in the speed of the vibrating energy with respect to the moving particle. If the particle remained spherical, the asymmetry of energy vibration would increase the time of vibration, t, by 1/(1 – v2/c2) in the axis of motion and by 1/(1 – v2/c2)1/2 in any direction perpendicular to the axis of motion (28), where v is the velocity of the particle relative to the preferred frame. Since the wavelength of the radiation from matter particles is the same in every direction, the vibration time, t, of the particle must remain the same in all directions. But this time can only be the same and the clock rate affected appropriately if a contraction proportional to (1 – v2/c2)1/2, occurs in the axis of motion. Thus, the postulation of a background ILSF permits the derivation in a logical manner of the clock rate reduction and contraction postulated by STR.
Arguments between the two authors over explanations of the fact that energy and clock rate are exactly correlated but in opposite directions in the cases of gravity and motion were the background for writing this article together. Although we could never agree on this and the explanations of many other phenomena, we discovered that there was a great deal on which we did agree. The cause of the different correlations between energy and clock rate has not been settled, but we take here the liberty of presenting the opinions of the two authors on this important but controversial subject.
It is obvious from the difference between gravity and motion that the clock rate cannot be determined by the total energy of matter particles. One of us (RRH) has proposed that the clock rate is determined by the structural energy of the particle, which in his model is reduced with motion (29). The difference between structural and total energy is the kinetic energy. In his model the kinetic energy is equal to mv2, or twice the classical kinetic energy. One-half of the kinetic energy is supplied by the action of a force on the particle and one-half of the kinetic energy is supplied by a reduction in the structural energy.
The other author (DWT) has noted that if we make the total energy content of a matter particle proportional to ct, the opposing correlations of energy and clock rate can be explained (30). In the case of motion the vibration time, t (the reciprocal of clock rate), increases with energy because of the asymmetry of energy vibration discussed above and c remains constant (relative to the ILSF). In the case of gravity, the change in c is twice the change in clock rate, because the clock rate change and contraction of the particle each account for half of the change in c. Thus, ct is reduced even as t increases. Thus, with both motion and gravity Et = kct, where k is a constant unique for each type of particle and Et is the total energy content of that particle.
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Résumé
À partir d’une perspective de positiviste, les deux théories de la relativité d’Einstein (théorie spéciale de la relativité et théorie générale de la relativité) ont permi de faire des prédictions d’observations très précises. Mais d’un point de vue réaliste, elles n’ont pas fourni d’explications satisfaisantes pour beaucoup de phénomènes, ou n’ont pas réussi à relier les deux théories l’une à l’autre ou avec la mécanique quantique. Nous supposons que l’expérience pratique avec des horloges précises a fourni une interprétation et une unification réaliste des deux théories de la relativité. Notre interpretation des prédictions observées des deux théories de la relativité d’Einstein mène logiquement à la conclusion que l’effet primaire d’un champ gravitationel est un gradient de la vitesse de la lumière et que tous les autres effets observés d’un potentiel gravitationel, y compris la courbure de la lumière, le ralentissement des horloges et la force de gravité, résultent directement ou indirectement du gradient de la vitesse de la lumière.