Relativity Challenge

The light-speed postulate (LSP) of Einstein’s special theory of relativity (STR) has the following consequence when a light pulse is sent between two fixed points in a given inertial rest frame S’. Assume that the distance between the two points measured by a stationary observer in S’ is L’ and the elapsed time is T’, whereas the corresponding values obtained by an observer in another inertial rest frame S moving with speed v along the x axis are L and T, respectively. Assume further that all these numerical values have been measured according to STR protocols. Since both observers must measure the same value c for the light speed according to the LSP, the following proportionality relationship holds: L’/T’ = L/T = c, whereupon one concludes that L’/L = T’/T.

According to the FitzGerald-Lorentz length contraction (FLC) prediction of STR, however, the ratio L’/L varies with orientation of the line connecting the two points, whereas T/T’ is completely independent of orientation when time dilation occurs. These facts make it impossible to satisfy the latter equality (L’/L = T’/T) on a completely general basis. The FLC and the LSP are therefore mutually incompatible. This example therefore proves that STR is self-contradictory and needs to be amended.

The above result puts the focus on the Lorentz transformation (LT), which is the cornerstone of STR. Eliminating the LSP is not a realistic option for removing the contradiction since the LT is derived on the basis of the LSP. That leads one to the seemingly unlikely conclusion that the LT itself is invalid since the FLC is derived from the LT. This possibility is discussed in detail in Ref. [1]. Detailed examination of the time equation of the LT reinforces this conclusion. Consider the case of an object moving relative to S and S’. The component of the object’s velocity in the x direction measured by the observer in S is u_x=Δx/Δt, i.e. Δx is the distance traveled in the x direction in time Δt. According to the LT, the corresponding elapsed time Δt’ measured by the stationary observer in S’ is given by the LT as:

Δt’ = (1-v²c^-2)^-0.5 (Δt – vΔxc^-2).

Note that the ratio of the respective clock rates in S’ and S is equal to Δt’/Δt and must remain constant as long as no change in the state of motion of either S or S’ occurs. Yet according to the above LT equation, Δt’/Δt = (1-v²c^-2)^-0.5 (1 - vu_xc^-2). The conclusion from the LT is therefore that the ratio of clock rates depends on the velocity of the object being measured, which result therefore violates the above condition of clock-rate ratio constancy.

Eliminating the FLC and the LT from STR has critical advantages when it comes to the interpretation of key experiments. As discussed above, the LSP by itself indicates that L>L’ when T>T’. The Ives-Stilwell study[2] of the transverse Doppler effect first carried out in 1938 is always interpreted to be a validation of the STR prediction of time dilation. However, the fact is that wavelengths are actually measured in the experiment and they are observed to increase with the speed of the light source. The LSP is then used to argue that light frequencies must have decreased, in accord with the STR prediction of time dilation, but no mention is generally made of the fact that the observed increase in wavelengths in the rest frame of the light source constitutes a violation of the FLC prediction of STR. Moreover, the relativity principle (RP) demands that the dimensions of all stationary objects must have increased by the same fraction in the latter rest frame, including especially those of the experimental apparatus used to measure the wavelengths. The transverse Doppler measurements therefore indicate that isotropic length expansion accompanies time dilation in a given rest frame, not the anisotropic length contraction expected from the FLC and the LT. A similar conclusion results from analysis of the muon decay experiments carried out by Rossi et al.[3]

Based on the above observations, the following conclusions are unavoidable: 1) the FLC and LT must be eliminated from STR; 2) retaining the LSP requires that isotropic length expansion accompany time dilation in a given rest frame; 3) as discussed elsewhere,[1,4,5] a suitably amended Lorentz transformation (ALT) that satisfies Einstein’s original two postulates of relativity must allow for a constant proportionality between clock rates in any two inertial systems, i.e. the only allowable equation between measured elapsed times in the two inertial systems must satisfy: Δt’ = Δt/Q, where Q is a constant depending only on the states of motion for the two inertial rest frames.

References

1) R. J. Buenker, Relativity Contradictions Unveiled, Kinematics, Gravitation and Light Refraction (Apeiron, Montreal, 2014), p. 55.

2) W. H. E. Ives and G. R. Stilwell, J. Opt. Soc. Am. 28, 215 (1938).

3) B. Rossi, N. H. Hilberry and J. B. Hoag, Phys. Rev. 56, 837 (1939).

4) R. J. Buenker, Apeiron 19, 282 (2012).

5) R. J. Buenker, Phys. Essays 26, 494 (2013).


Consequences of Losing the Challenge

Failure to disprove the contention that Einstein’s light-speed postulate (LSP) is consistent with isotropic length expansion accompanying time dilation, and therefore not win the challenge, has many significant consequences. The most important ones are listed below:

1) FitzGerald-Lorentz length contraction (FLC) is shown to be incompatible with the LSP and therefore invalid.

2) Einstein’s Lorentz transformation (LT) is also shown to be invalid since the FLC follows directly from it.

3) The predicted symmetry between the rates of clocks in motion (and other properties such as lengths and masses) also follows directly from the LT and is therefore also placed in question.

4) Lorentz invariance (x²-y²-z²-c²t² = x’²-y’²-z’²-c²t’²) is obtained by squaring the LT and is therefore invalid. The argument that both sides of the invariance equations vanish for light pulses and therefore must be equated to one another is incorrect; one side can be multiplied with a constant without destroying the equality for light pulses.

5) The LT has led to the firm conviction among physicists that space and time form a single four-dimensional entity (known as “spacetime).” This conclusion runs contrary to the Newtonian view that space and time are fundamentally distinct. The mixing concept arises from the time equation of the LT: t’=(1-v²c^-2)^-0.5(t-vxc^-2). It therefore becomes highly questionable once it is realized that the LT itself is invalid. Moreover, the relativistic “four-vector” characteristic of the special theory of relativity STR for other physical properties needs to be reevaluated on this basis.

6) The above LT time equation also has led to the conclusion that events which are simultaneous for one observer may not be so for another (if v>0 and the events take place at different locations (x≠0), then t and t’ both cannot be equal to zero). This lack of remote simultaneity in STR rests solely on the LT and also goes against the Newtonian vision of the universe.

7) The LT has also caused physicists to reject the possibility of v>c speeds because this would lead to time reversal on the basis of the above equation. Experiments have nonetheless indicated that light can travel faster than c in regions of anomalous dispersion. Eliminating the LT from STR would also remove the theoretical objection to such occurrences.

Unless a flaw can be detected in the length-expansion conclusion, it must be acknowledged that STR as it is currently taught in our textbooks and universities is in need of fundamental change.