by Robert J. Buenker
Bergische Universität, Wuppertal


The present blog calls attention to an undeclared assumption made by Albert Einstein in his landmark paper [Ann. Physik 17, 891 (1905)] in which he introduced the special theory of relativity (SR). The emphasis in textbooks and periodicals is always on his two postulates of relativity (the relativity principle and the constancy of the speed of light in free space), but the well-known results of his theory such as Fitzgerald-Lorentz length contraction and the symmetry of time dilation (two clocks in motion each running slower than the other) are based just as directly on this totally unsubstantiated assumption as on the latter (please follow this link for the full text of this introduction).

For my proposal for an Alternative Lorentz Transformation (ALT), click here.

Friday, July 11, 2014

Relativity Challenge (II)

The Lorentz transformation (LT) of Einstein’s special theory of relativity (STR) is one of the most influential set of equations in theoretical physics. For example, it is responsible for the key concepts of “spacetime continuum” and remote non-simultaneity of events that have revolutionized the way physicists think about the relationship between time and space in the universe. Nonetheless, the LT has been criticized by many authors almost since its inception because of inconsistencies that arise in certain applications. There has been a nearly universal tendency on the part of physicists to dismiss such irregularities because of the large number of successful experimental verifications attributed to the LT. In recent times, however, it has been pointed out [1-3] that there are many Lorentz-type transformations that satisfy both postulates of relativity, not just the LT itself. 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 ux=Δx/Δt. According to the LT, the corresponding elapsed time Δt’ measured by the stationary observer in S’ is given as: Δt’ = (1-v2c-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-v2c-2)-0.5(1-vuxc-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).

Monday, July 7, 2014

Relativity Challenge (I)

The following challenges have been issued to physicists and other students of Einstein's Special Theory of Relativity (STR). The arguments presented in the challenges prove among other things that the Lorentz Transformation (LT) of STR is self-contradictory.

Failure to disprove all of the claims in the challenges is tantamount to admitting that STR needs to be amended relative to its currently accepted form. The consequences of doing this are wide-ranging, as indicated in the following page under the heading "Consequences of Losing the Challenge." For example, it is no longer possible to claim that relativity theory proves that space and time are inextricably mixed. Time is distinct from space, just as our intuition tells us. This is also perfectly consistent with Newton's original view of space and time.

In view of the serious nature of these challenges, it is important that physicists all over the world attempt to find fault with them. All such attempts will be presented in the current blog. They will be followed by arguments indicating any errors in the reasoning given in connection with these attempts.

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 are L and T, respectively. 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. This example therefore proves that STR is self-contradictory and needs to be amended. In particular, it shows that both the FLC and the Lorentz transformation (LT) on which it is based are invalid although the LSP itself is still tenable.