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.


What was/is Einstein’s assumption?  He claims on p. 900 of the above paper that an undefined “normalization” function φ can only depend on v, the relative speed of two rest frames S and S’ along the x and x’ axes of their respective coordinate systems.  As Einstein showed, this assumption is tantamount to stipulating that observers in S and S’ must agree on the values of length measurements (y’=y and z’=z) made along a direction perpendicular to that of their relative velocity.   As a result of ignoring the very fact that this is nothing but a guess on Einstein’s part, authors have consistently claimed that the y’=y equation of the Lorentz transformation (LT) is an inevitable consequence of his two postulates.  The truth is that we can avoid the y’=y condition by choosing a different value for the normalization function φ, one that depends on both the relative speed of the observers and also that of the object of their respective measurements, and still remain consistent with Einstein’s postulates.  However, this choice has to be made on the basis of independent experimental data, not on the basis of some other arbitrary assumption.

What is wrong with claiming that y’=y in SR?  The reason is that this equation itself is inconsistent with Einstein’s light speed postulate.  Consider two observers in S and S’ moving toward each other along the x’,x axis with constant speed v.  Because of time dilation, the proper clocks in S’ run slower than their counterparts in S (t’=t/γ<t, i.e. γ>1).  The goal is for both of them to measure the distance between two fixed points in S’ along the y axis, i.e. in a direction perpendicular to their relative velocity.  Consistent with the modern-day definition of the meter, they decide to do this by measuring the amount of elapsed time on their respective clocks (t’ and t) required for light to pass between the two points.  Since both observers agree that the speed of light is c, in agreement with Einstein’s second postulate, they must find that y’=ct’ and y= ct.  Because of the difference in the observers’ clock rates, there is only one possible conclusion about the relationship between their respective measured values: y’=y/γ, not y’=y.   The same ratio is found when the distance to be measured lies along the x axis parallel to the direction of relative motion: x’=x/γ.  That is also inconsistent with SR, since it claims that x’=γx as a result of relativistic length contraction.

The present blog differs from most others that have criticized Einstein’s SR in the past because it subscribes to a fundamental principle for correcting physical theories when their assumptions are violated: amend the theory in such a way so as to bring it into agreement with the new experimental data while at the same time leaving its earlier successful predictions intact.  This goal is easily achieved in the present case because of Einstein’s velocity addition theorem (VT), which was also derived in his 1905 paper.  The VT has many successful predictions/explanations to its credit: the Fresnel light drag experiment, the aberration of starlight at the zenith, Thomas spin precession, the Sagnac effect, and the general fact that the speed of light in free space is the same for all observers.  The key point is that the derivation of the VT does not depend in any way on the choice of φ.  Thus, it is possible to obtain an alternative version of the Lorentz transformation (ALT) that is just as consistent with Einstein’s postulates as the original LT, but which is internally consistent.  The choice of φ is made on the basis of the experimental result for time dilation, namely that proper clocks in different rest frames always have strictly proportional rates (and not necessarily with the ratio claimed in SR): t’=t/Q.  To do this one has to eliminate Einstein’s unsubstantiated assumption for φ and replace it with a correct version whose value also depends on the speed of the object of the measurement for each observer, not just their speed relative to one another.

Altering the value of φ removes the above contradiction with Einstein’s second postulate, but this change only affects earlier predictions of SR that have never received experimental confirmation.  For example, the relationship between the energy and momentum of accelerated particles in the laboratory is unaffected by this change in relativity theory because it only alters predictions involving space and time.  At the same time, the ALT removes the subjective character of the theory that is based on the LT.  It is always possible to say which clock is slower and by what ratio in the revised theory; one simply has to know the value of the proportionality constant Q in the above formula.  The resulting objective theory also has consequences for the measurements of all other physical variables for moving observers.  For this reason, the ALT might more appropriately be called the OLT, the objective version of the Lorentz transformation.

The usual reaction from proponents of SR when they are confronted with an inconsistency in their theory is to defend it by saying that it works so well in many other applications that it can’t possibly have any deficiencies.  This attitude is patently false and is in direct conflict with the aforementioned principle for amending physical theories in general.  It overlooks the possibility that a competing, “covering” theory can achieve the same successes as SR while at the same time avoiding the various contradictions that result because of Einstein’s unsubstantiated assumption in deriving his LT.  At the same time, it is imperative for any such covering theory to prove that it is capable of explaining all available experimental data in a clear and concise manner without introducing new untenable assumptions into the underlying postulatory structure.

To satisfy this requirement, links are provided to access many preprints and reprints that deal with the different areas where Einstein’s theory has previously been applied.  The goal is to demonstrate that the revised (objective) version of relativity theory based on the ALT and the VT is perfectly consistent with all available experimental data, while at the same time debunking the various claims of SR that are based solely on the LT; the latter include Fitzgerald-Lorentz length contraction, the supposed symmetry of the measurements of observers in relative motion, and the lack of remote simultaneity for the events they are to describe.  The reader is encouraged to participate in this process by means of rational discourse with the author.

1 comment:

  1. "The usual reaction ... by saying that it works so well in many other applications that it can’t possibly have any deficiencies" - fully agree this is not a honest defense for a scientific theory but you didn't show any critic to your version yet :o) I am not a physicist but I noticed that when physics professors (even university level) come to teach the newest branches of physics: TR and QM they are starting to rush the material. As an engineering student, I never asked questions like "Why the Lorentz transformation is the only possibility ?" or "Why did they decide that c is also the speed of gravitational waves" because I knew it probably won't impact my engineering studies. From my experience, when the material is rushed it means the teacher does not fully understand it and he knows that very well.