*This fact raises the possibility that a different version of the space-time transformation may exist that overcomes the aforementioned theoretical objections without sacrificing any of the successful experimental confirmations of STR previously attributed exclusively to the LT.*

To demonstrate that the LT is actually self-contradictory, it is helpful to consider the case of an object moving relative to two different inertial systems S and S’. The latter rest frames move with speed v relative to each other along their common x-x’ axis. Let us assume that the stationary observer in S finds that the object moves a distance Δx in the x direction in time Δt. The corresponding velocity component is thus u

_{x}=Δx/Δt. According to the LT, the corresponding elapsed time Δt’ measured by the stationary observer in S’ is given as: Δt’ = (1-v

^{2}c

^{-2})

^{-0.5}(Δt – vΔxc

^{-2}). Note that Q = Δt/Δt’ is the ratio of the respective (proper) clock rates and thus

*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=Q

^{-1}=(1-v

^{2}c

^{-2})

^{-0.5}(1-vu

_{x}c

^{-2}), indicating that the ratio Q also depends on the velocity of the object being measured.

*It is simply irrational to believe that the rate of either clock is affected by the constant motion of an object which could be light-years away (Einstein causality).*

**This result therefore shows unequivocally that the LT is not a physically valid transformation since it fails to satisfy the above condition of clock-rate ratio constancy in different inertial rest frames.**

As discussed elsewhere[1-3] a suitably amended Lorentz transformation (ALT) can be constructed that still conforms to both postulates of relativity but also satisfies the above condition of clock-rate constancy. The equation between measured times in the ALT replaces that of the LT with a simpler relation, namely Δt’ = Δt/Q, where Q is a constant depending only on the states of motion of the two inertial rest frames.

*It therefore does away with both the spacetime continuum and remote non-simultaneity of events.*The ALT is also compatible with the same relativistic velocity transformation (RVT) as the LT, and thus is consistent with numerous experimental results such as the aberration of starlight at the zenith and the Fresnel light-drag phenomenon, each of which can be deduced directly from the RVT alone. It also correctly predicts the increase in the second-order Doppler shift observed by Ives and Stilwell, again unlike the LT. In this case, it is clear from the relativity principle that the dimensions of all stationary objects in the rest frame of the accelerated light source must have also increased, and by the same amount in all directions (isotropic length expansion accompanying time dilation). This result contradicts the Lorentz length contraction prediction of STR, providing another proof that the LT is invalid. More details about the ALT and its relation to experiment may be found in Ref. [1].

References

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

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

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