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].


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.

Monday, March 3, 2014

New Publication

Relativity Contradictions Unveiled:
Kinematics, Gravity and Light Refraction

available as a Paperback from

Physicists have been taught that lengths contract when clock rates slow on a moving object. However, in order to satisfy the light-speed constancy postulate, it is essential that lengths expand whenever clocks slow down, and in exactly the same proportion. The fact that relativity theory leads to opposite predictions of experimental results depending on how it is applied is traced to an assumption Einstein made in his original derivation of the Lorentz transformation. By relying instead on the everyday experience of the GPS methodology, it is possible to define a different space-time transformation that still satisfies Einstein’s postulates but removes all contradictions in the existing theory. 

It also enables a return to a purely objective view of the measurement process by assuming that the standard units in which the laws of physics are expressed vary systematically between different rest frames. This approach allows for quantitative prediction of key experimental results caused by gravity such as the angle of displacement of star images during solar eclipses. It also leads to a challenge to Einstein’s General Theory of Relativity regarding the precession of orbiting satellites. These results permit a much more sanguine assessment of Newton’s vision of the Universe in terms of a strict separation between space and time. The book also points out a previously unnoticed connection between his corpuscular theory of light and the key quantum mechanical relationships first discovered at the dawn of the 20th century.

Saturday, June 4, 2011

Measuring Mesons and Length Contraction

Experiments on the variation of cosmic-ray intensity with altitude provided one of the first confirmations of time dilation [1,2].  Rossi and Hall [1] found an absorption anomaly of “mesotrons” due to spontaneous decay and used relativity theory to show that the effect must be more pronounced for particles of relatively low energy because of their shorter lifetimes.  They also made a connection with relativistic length variations.  Specifically, they pointed out that the “average range before decay” L, i.e. the average distance traveled by the particles before disintegrating, must be proportional to the observed lifetime τ and their speed β = v/c: L = β τ.  This formula shows that the distance traveled by the particles has a different value for two observers in relative motion.  Specifically, it shows that the observer with the slower clock (and therefore the shorter corresponding measured lifetime τ) must find a smaller value for the distance L traveled by the particles before decay.  This conclusion follows from the fact that the speed β is the same for all observers, as expected from application of Einstein’s velocity transformation (VT [3]).
The above experience has been discussed in various textbooks in connection with length contraction.  Weidner and Sells [4] considered a case in which the decaying particles move with speed β=0.98 at a height of L=2260 m toward the earth’s surface.  The authors point out that the measured lifetime of the particles is therefore 5.0 τ0 in this rest frame (S) which is long enough so that exactly one-half of them reach the earth.  An observer traveling with the particles (in S’) must also find the same fraction, even though the lifetime from his vantage point is much shorter (τ0).  The explanation is that the corresponding distance traveled is also smaller by the same factor of 5.0, in agreement with the above range formula [1].  The authors [4] conclude: “because of the space-contraction phenomenon, the Earth’s distance from him is contracted.”  Another version of the same argument is given in an introductory textbook [5].  In this case, the example of a rocket ship passing between two fixed points in space is used.  Consistent with the VT, it is assumed that two observers agree on the velocity (speed and direction) of the rocket.  It is concluded that the observer in S’ with the slower clock measures the smaller value for this distance.  The following equations in standard notation for the two rest frames S and S’ summarize these results [γ= (1-v2/c2)-0.5 ]: t’= t/γ, x’=x/γ and y’= y/γ.  Note that the direction of travel is immaterial in computing the distance. 

In his 1905 paper [3], Einstein derived the length contraction effect and time dilation from the Lorentz transformation (LT).  The following equations summarize these results: t’= t/γ, x’= γx and y’= y.  Although both textbooks [4,5] conclude that their example serves as a verification of the phenomenon of relativistic length contraction, comparison of the above two sets of formulas shows that the opposite is the case.  In Einstein’s result lengths measured by the observer in S in the x direction are contracted, whereas in the textbook examples, lengths measured by the observer in S’ are contracted in all directions.  It is clearly necessary to resolve this discrepancy.

1)            B. Rossi and D. B. Hall, Phys. Rev. 59, 223 (1941).
2)            B. Rossi, K. Greisen, J. C. Stearns and D. K. Froman, Phys. Rev. 61, 675 (1942).
3)            A. Einstein, Ann. Physik 17, 891 (1905).
4)            R. T. Weidner and R. L. Sells, Elementary Modern Physics (Allyn and   Bacon, Boston, 1962), p. 410.
5)             R. A. Serway and R. J. Beichner, Physics for Scientists and Engineers,  5th Edition (Harcourt, Orlando, 1999), p.1262.

Monday, May 16, 2011

Logical Basis of Fitzgerald-Lorentz Length Contraction

Fitzgerald-Lorentz length contraction (FLC) is derived from the Lorentz transformation (LT) of the special theory of relativity (SR1). The following discussion analyzes the logical basis for the FLC prediction.

Einstein used two postulates in his derivation of the LT: 1) the relativity principle (RP) and 2) the constancy of the speed of light in free space (c m/s) independent of the state of motion of the observer and the light source. The resulting equations lead to the conclusion that time dilation (the slowing down of clocks) in a moving rest frame is accompanied by the FLC, i.e., contraction of the lengths of objects located there. The amount of the contraction varies with orientation of the object (stationary in rest frame S’) to the observer (stationary in rest frame S): it is maximal along a line parallel to the relative velocity of S and S’, while no change is observed in a transverse direction.

The relationship between length variations and time dilation can be obtained directly from the above two postulates, however, without making use of the LT. To demonstrate this, consider the following example in which the length of a metal bar is determined under two different circumstances by measuring the elapsed time required for a light pulse to traverse it. Initially, the metal bar and two identical (proper) clocks are stationary in rest frame S. The elapsed time for light to traverse the metal bar is found to be ΔT=L/c s, showing that its length is L m at this stage in the experiment.

The bar and one of the clocks are then accelerated until they attain constant velocity relative to S and are thereafter stationary in S’. At this point in the argument, the RP is invoked. Accordingly, no change in either the length of the metal bar (L m) or the elapsed time for its light traversal (L/c s) is found by the observer in S’. Next we assume that time dilation has occurred, causing the clock in S’ to run Q>1 times slower than its counterpart left behind in S. The question is thus what this tells us about any possible change, if any, in the length of the metal bar that accompanies the time dilation in S’. Clearly, the corresponding elapsed time in S must have increased to QL/c s because of the aforementioned difference in rates of the two clocks. According to the second postulate this means that the observer in S now finds that the length of the metal bar has also increased by the same factor. It has changed from its initial value of L m to its current value while stationary in S’ to QL m. Moreover, the increase in length is the same in all directions because the local time measurement in S’ is completely independent of the orientation of the metal bar to the observer in S.

The above example indicates that isotropic length expansion accompanies time dilation, not the anisotropic length contraction of the FLC predicted by Einstein on the basis of the LT1. The deduction of length expansion is based solely on the two relativistic postulates (RP and the constancy of the speed of light). Since the latter have received extensive experimental verification, there is no reason to doubt the correctness of this conclusion.

What it shows is that the theory of special relativity is not internally consistent. If one uses the above postulates directly to predict changes in length upon acceleration, the answer is opposite to what is deduced on the basis of the Lorentz transformation (LT). There is a simple explanation for this discrepancy. Einstein made an additional assumption in deriving the LT which was not declared as such. He claimed (see the four equations at the bottom of p. 900 in his original paper1 that a function φ defined there only depends on v, the relative speed of S and S’. One obtains a qualitatively different result if one chooses φ instead so as to satisfy the basic assumption of time dilation, namely that the rates of clocks in relative motion are strictly proportional to one another, i.e. t=Qt’ in the notation used in the above example. The resulting alternative LT still satisfies Einstein’s two postulates, but predicts that the lengths of objects expand isotropically rather than contract when clock rates slow as a result of acceleration. More details may be found elsewhere.2

1 A. Einstein, Ann. Physik 17, 891 (1905).
2 R. J. Buenker, Apeiron 15, 382 (2008).


The following exchange has taken place between Dr. Buenker and two colleagues, one (Dr. A) a distinguished author of a book on relativity and the other (Dr. C), an associate editor of a respected physics journal. The remarks from Dr. C below were sent directly to Dr. A.

Dr. C to Dr. A: To the observer in S, the ends of the bar are in motion. It’s not simple to deduce a length from this measurement, and that’s why you need the LT, and that gives contraction. There are two parts of the path, going in the direction of v and opposite v. And since the bar’s angle to v matters, the length will depend on the angle.

General Reply I: Dr. A simply assumes the LT is correct. He ignores the fact that Einstein used an undeclared assumption to arrive at the LT, and therefore that it is by no means proven that the LT is correct. The point of the present discussion is to show that Einstein’s two postulates in conjunction with the definition of time dilation obtain a different result, namely isotropic length expansion accompanying time dilation, without involving the LT. Dr. C does not deny this in the above response, which indicates that he has no counter-argument to the procedure that avoids the LT entirely. The following reply was sent directly to Dr. C:

Dr. Buenker to Dr. C (April 26, 2011): The point where we diverge in our views is when you say “To S, the ends of the bar are in motion…” The observer in S does not even have to see the bar to measure its length. He can deduce the value with arbitrary accuracy if he knows a) the elapsed time for light to traverse the bar that is measured locally in S’ and b) how much faster his proper clock in S runs than the proper clock in S’. He can wait for days before receiving (e.g. by e-mail) the value in a) to make his calculation. He also has to know what the “conversion factor” for elapsed times was at the time of the local measurement in S’.

The other point of disagreement is your position that the LT must give the correct answer. '''I invite you to look at Einstein’s 1905 paper on p. 900.''' He claims that the function φ defined there only depends on the relative speed v of S and S’. '''That is an undeclared assumption. It needs to be verified experimentally.''' It is possible to derive an alternative LT that also satisfies Einstein’s two postulates but is, at the same time, consistent with the assumption of strict proportionality of the rates of proper clocks in different inertial systems (t=Qt’). That version of the LT also leads directly to the conclusion that lengths expand when clock rates slow.

There is one other experimental fact that should be considered in the present context. Measurements of the transverse Doppler effect have shown that the frequency of light waves emitted from moving sources decrease by the same fraction as the corresponding wavelength increases. The observer moving with the light source does not notice any change in either quantity, so how does one explain this? Various authors have pointed out that the decrease in frequency can be understood as the result of the slowing down of all clocks in the rest frame of the light source. But if that’s true, and I believe it is, then by the same argument one has to conclude that the diffraction gratings in S’ have all increased in dimension by the same fractional amount in all directions as the frequencies have decreased.
In closing, let me break down the argument in four easy steps:

1) The elapsed time ΔT measured locally for light to traverse the metal bar in S is L/c s (2nd Postulate);

2) The corresponding elapsed time measured locally in S’ after the bar is stationary there is also ΔT = L/c s (1st Postulate);

3) If the proper clocks in S’ have slowed by a factor of Q relative to those in S, the observer in S can safely '''deduce''' that the corresponding elapsed time on his proper clock is ΔT’ = QL/c s (Q>1, definition of the amount of time dilation);

4) The current length of the bar measured in S based on the elapsed time measurement in S’ is therefore cΔT’ = QL m, showing that isotropic length expansion has accompanied the time dilation in S’ (2nd Postulate again).

Dr. C to Dr. Buenker (April 28, 2011): Thanks for your quick and thoughtful response.
We may have different and irreconcilable philosophies about the exercise of ''gedanken'' experiments in spacetime physics.
To me, the only true results in frame S are from experiments done in frame S, not results inferred from an experiment in S' via rules that may or may not be in accord with the basic postulates. Inference from one frame's result to another is ''verboten''---each frame's experience of a set of events must make sense in that frame. The only connection between frames is the identification of the same events (spacetime points) that have different (x,y,z,t) depending on the frame. For that reason, I am not inclined as you are to deduce the length of the bar in S' from surmises in frame S.
Also, relative to your modified Lorentz transformation, I do not understand the operational meaning of u_x. Could you please explain what that quantity is?

Dr. Buenker to Dr. C (April 30, 2011): The practice that you want to exclude is used continuously in GPS technology. We wouldn’t have GPS devices in our cars today if local clock readings for events on satellites (S’) could not be reliably converted to readings on clocks located on the earth’s surface (S).
We have to be consistent with our assumptions in making logical arguments. Once it is known that the conversion factor for clock rates on the satellite is Q> 1 in the GPS technology, it is imperative that we use the same value for this conversion factor in all other applications. To exclude this assumption in a justifiable manner, it is necessary to show why a different conversion factor needs to be used in the present case. You have failed to do this is your comments to date. I submit that the reason for this is quite simply that there is no justification for excluding this assumption.

The quantity ux =x/t is the component of the velocity of the object being measured in S that is parallel to v (ux’ is the analogous quantity in S’). It appears in Einstein’s velocity transformation in all three equations:

ux’ = (ux – v )/(1 – v ux /c2), 
uy’ = uy/γ(1 – v ux /c2), 
uz’ = uz/γ(1 – v ux /c2).

The alternative LT is obtained by combining the VT with the GPS proportionality relation, t’=t/Q, which serves as the temporal equation in the latter transformation (no space-time mixing).

The VT is used in textbooks to measure distances. It ensures that any two observers agree on the speed u of some object (including a light pulse, of course) that moves between two fixed points. The observer in S’ with the slower clock measures a shorter value for the latter distance as Δr’=u Δt’. The other one in S knows that the corresponding time on his clock is Δt=Q Δt’ (Q>1), so he concludes that the distance between the same two points is Δr = u Δt = u Q Δt’ = Q Δr’. Thus, Δr> Δr’: isotropic expansion, not anisotropic length contraction.

Actually, the observer in S doesn’t have to assume anything about the relative rates of clocks in S and S’ in this example. He just has to use his own proper clock and length standard to measure the speed of the object and the elapsed time for it to travel between the two fixed points. When he does this, he will automatically obtain u and Δt. The two results for the respective distance measurements can be compared at some later date. If it does not turn out that Δr = Q Δr’, that would be proof that either the VT is not valid or that the conversion factor is something other than Q.

General Reply II (May 7, 2011): Dr. C has not replied to the main point in the discussion as of the present date, namely how to justify Einstein’s assumption that the function φ defined on p. 900 in his 1905 paper (ref. 1 above) can only depend on v, and therefore must have the constant value of unity. The LT rests squarely on this assumption, so it is not correct to say that only the two postulates are required in his original derivation. The present approach relies instead on experimental data acquired over the past 50 years to determine φ. They show that elapsed times in S and S’ are strictly proportional to one another: t=Qt’. The alternative LT is derived by combining the experimental proportionality equation with the VT. Isotropic length expansion results from the alternative LT, so the inconsistency with the GPS experiment that is present when the LT is used is completely eliminated. So also is the supposed symmetry in the timing results of two observers in relative motion as well as the necessity of claiming that remote non-simultaneity of events is the unavoidable consequence of Einstein’s two postulates of the special theory of relativity.