Revised Relativity

AEA Technology
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Abstract

At non-relativistic speeds, observers in different frames of reference measure different energy changes for the the same event . Howe's proposition [1] that wavelike properties can be attributed to a purely quantum mechanical property, the De Broglie vector, leads to a review of wave theory, corpuscular theory, Special Relativity and Quantum Mechanics. The result is the proposition of a single equation that accounts for both these observations and relativistic observations. The result depends on the postulate that the speed of light is not constant for all observers.

1. Introduction

Howe [1] has considered relativity from the point of view of frames of reference, using a tape recorder analogy. The analogy highlights the different views of the change in kinetic energy for a single event when viewed from different frames of reference. This paper was conceived because of the inability of current theories to address this issue. Essentially there have been three main theories of the transmission of energy.

2. Wave Theory

Wave theory suggested that energy is transmitted through the "Ether" (a medium through which energy waves could propagate). The key to wave theory is that energy will be transmitted at a constant speed through the ether and that all observers will agree about its speed, taking into account the relative motion of their own frame of reference. This implies that, in a non-relativistic universe, different values for the speed of light should be measured when the Earth travels at differing speeds in differing directions (because the measured speed should be the addition of the two speeds). Michelson and Morley carried out an experiment [2] to detect the Earth's motion through the Ether. However, they were unable to detect any difference in the speed of light when measured in different directions. Kennedy and Thorndyke [3] later verified that there was no observed change in the measured speed of light when the surface of the Earth travels in different directions. There have been two alternative theories proposed which satisfy this observation.

3. Corpuscular theory

Corpuscular theory assumes that energy is transmitted as corpuscles, tiny packets of energy. This is in keeping with the ideas of quantum mechanics, which proposes that all energy and sub-atomic phenomena occur as discrete quantifiable "particles", in integer multiples of a base value. The problem with corpuscular theory is that it predicts that all velocities will be additive, so that in one frame of reference the speed of a corpuscle transmitted from another frame of reference will be the sum of the relative velocity of the frames of reference and the speed of the corpuscle relative to its originating frame of reference. However, de Sitter suggested observations of binary stars that could support the theory. He proposed that, given sufficient distance (e.g. 20000 Ly) for certain binary systems, light transmitted when one of the stars was travelling towards the Earth would arrive before light transmitted while the same star was travelling away from the Earth. This would result in apparitions, several images of the star, some of which appear to move in opposite directions. All observations of likely stars have failed to provide any such evidence. Thus corpuscular theory has fallen into disfavour.

4. Quantum Mechanics

Before addressing Special Relativity, it is useful here to consider the world of Quantum Mechanics. Quantum mechanics has proved a very successful description of events on the sub-atomic scale. It easily extends to energy by proposing that energy is transmitted as photons. There is much evidence to support this, including the detection of discrete photons in experiments and in astronomical observations. The problem associated with quantum mechanics arises from the fact that discrete particles behave according to wave theory when considered in large numbers (see e.g. [4]). Howe has proposed mechanisms for avoiding the need for wave theory for diffraction and refraction [5,6]. This suggests that quantum mechanics may be able to support an entirely corpuscular model, if the problem of velocity addition can be overcome.

5. Special Relativity

The concept of Special Relativity was grounded in the then current view of waves through the Ether. Einstein, in his 1905 paper [7], proposed that the speed of light was constant for all observers, leading to Special Relativity. Relativity depends on the Lorentz transformation, which assumes that space-time is related to velocity. However, the conclusions drawn from the Michelson and Morley experiment have omitted a fundamental element. If the wave theory can be dispensed with completely and a purely quantum approach adopted, the only conclusion that can be drawn from the results of the experiment is that the speed of photons is constant within a frame of reference. Special Relativity fails to account for the different values of kinetic energy change measured from different frames of reference for the same event at non-relativistic speeds.

Special Relativity also provides an unsatisfactory explanation of the phenomenon of red shift. Red shift is observed by astronomers when the motion of stars and galaxies relative to Earth is away from the Earth. If the speed of light is constant for all observers, the only satisfactory explanation of this phenomenon must rely solely on wave theory. In wave theory, the interval between successive nodes of the waves is increased because of the relative motion of the emitting body. In Special Relativity, this effect is accounted for by time dilation. In both cases, the explanation relies on an increased time interval between successive nodes of a wave train. The arrival of light as discrete photons is in direct conflict with this hypothesis. Furthermore, Howe [1] has suggested that the energy of a photon is related to its De Broglie frequency. If this hypothesis is sustained, either the speed of the photon has changed or what Howe calls its mass equivalence has changed. However, the mass equivalence is assumed to remain unchanged in all frames of reference. Hence, using this hypothesis, the speed of a photon would not be constant for all observers.

6. Relativistic Quanta

Figure 1: The transmission of particles seen from two frames of reference by two observers, O and O'. The view of O is represented with O' moving to the right with speed U. The times t₁ to t₃ are the times observed by O and the time t'₂ is that observed by O'.

An attempt has been made to devise a theory that fits with the above noted evidence. Consider two observers, O and O' respectively, in frames of reference ⁰F₀ and ¹F₁, as depicted in Figure 1. Assume that O' is moving at a speed U with respect to O. Assume also that both observers agree that their clocks registered zero at the instant they passed each other. Consider that the two observers have agreed that O will send a particle to O' with speed V, as observed from ⁰F₀ and that, at the instant O' receives the particle, she will send an identical particle to O with speed V as observed from ¹F₁. If O' measures the time of arrival t'₂ = k(V) t₁ then, by relativistic symmetry, t₃ = k(V) t'₂. So t₃ = k²(V) t₁. Now

Now in a Newtonian world, a(U, V) = - (V - U), so g(U) = 1. In the world of Special Relativity, when V = c and a(U, V) = -c, we have

This reveals Equation 10 to be the most general form of the time dilation equation. The question now arises as to whether or not there is a function for a(U, V) that will satisfy both relativistic and Newtonian observations. This must include the observation that, in a Newtonian world, observers in different reference frames will disagree about the energy change for the same event. It must also account for red shift allowing for the constancy of mass equivalence.

We now hypothesise that when V equals the speed of light, c, as observed within a single frame of reference, (i.e. when a photon is emitted) all observers will agree on the energy change, 1/2 mc², where m is the mass equivalence postulated by Howe [1]. Thus, the total energy would be 1/2 m (c² ± U²), where U is the speed of the frame of reference from which the photon originated, relative to the frame of reference of the observer. The sign of U² is positive for converging observers and negative for diverging observers. So

If we introduce the relativistic relationship 1-V/c, we can propose Equation 14, which satisfies all conditions:

d⁰E₂ is the energy change observed in reference frame ⁰F₀ when a particle moves from reference frame ¹F₁ with speed U, relative to reference frame ⁰F₀, to reference frame ²F₂with speed V, relative to reference frame ¹F₁, and with speed a (U, V), relative to reference frame ⁰F₀. The first two terms represents the Newtonian view of the combined speed while the third term represents the Newtonian view of the speed of ¹F₁, relative to ⁰F₀. Using this relationship we conclude that

satisfying the requirement that all observers will agree on the energy change. If U = V = c/2 we have

So a(c/2, c/2) = 0.79c, significantly less than c/2 + c/2. If U = 3x10⁴ ms^-1 (approximately the speed of the Earth around the Sun), then the resultant speed of a photon emitted in the direction of travel would be

So a(.0001c, c) = 1.000000005c, or about 1.5 ms^-1 faster than the measured speed of light. An order of magnitude improvement in the currently available accuracy of the measurement of the speed of light would be required to detect this with any confidence.

7. Implications

Using Equation 17, Howe [8] has shown that a binary system with a star of 1 solar mass and a semi-major axis of 1 AU, at a distance of 20 MLy would not display any de Sitter apparitions, even if the components were resolvable. A binary system with a star of 1 solar mass with a semi-major axis of 0.01 AU at a distance of 200 Ly would also not display any de Sitter apparitions. A system with a star of 100 solar masses with a semi-major axis of 0.1 AU at a distance of 200 Ly would have detectable de Sitter apparitions. However, this represents an angular semi-major axis of only 1.6 mas, which is close to the limit of resolution. Howe has considered 7 spectroscopic binaries reported by Hummel et. al. [9] and, using the above model, found no case where there could be de Sitter apparitions unless the stars were more than 2 orders of magnitude more distant than their measured distance.

There are also implications for red shift. There is a difference in the calculated red shift compared with Special Relativity, as shown in Figure 2.

Figure 2: The calculated values of U/c for different red shifts as predicted by Special Relativity and Revised Relativity. At small values of red shift the Values of U/c are considerably greater for Revised Relativity .

In the case of Special Relativity, from Equation 8 , with a(U,c) = -c, the red shift is related to U, the speed of recession of the emitting object, by

It can be seen from the figure that Revised Relativity predicts quite small red shifts associated with objects receding at much greater speeds than would be expected using the assumptions of Special Relativity. This may have a significant effect on the estimation of the Hubble constant, H₀, the value of which has been constantly revised over the years.

8. Conclusions

By considering pre-existing models, a revised model of relativity has been proposed where the speed of light is not constant for all observers. The model allows for relativistic concepts to be combined with the Newtonian view. Differences in the measured speed of light are likely to be difficult to detect. The model satisfies the observation that de Sitter apparitions have not been observed from binary stars. The value of the Hubble constant may need further revision.

References

[1] L D Howe A quantum approach to relativity, www.innovationgame.com/physics (2000).
[2] R S Shanckland: American Journal of Physics 32 p16
[3] R J Kennedy and E M Thorndyke Physical Review 42 p400 (1932)
[4] R Feynman The Character of Physical Law, MIT Press (1967)
[5] L D Howe A Possible Mechanism for Wavelike Observations of Quantum Particles, www.innovationgame.com/physics(2001)
[6] L D Howe Refraction of Quantum Particles Without Waves, www.innovationgame.com/physics(2001)
[7] A Einstein, H A Lorentz, H Minkovski & H Weyl, The Principle of Relativity, Dover
[8] L D Howe Calculations of de Sitter Apparitions using Revised Relativity, www.innovationgame.com/physics(2001)
[9] C A Hummel et al. Astronomical Journal 110 p376 (1995)

L D HOWE