New Book Released:

Relativity Theory Based on the Uniform Scaling of Physical Properties

available as a Paperback from Amazon.com

The purpose of the book is to provide a comprehensive overview of topics that have been covered in publications of the past 20 years. A key point is a proof that the Lorentz transformation is not internally consistent and is therefore invalid. It points out a corollary to Newton’s First Law of Kinetics which is closely related to the Law of Causality. This leads to a new space-time transformation and a procedure for computing differences in the units of time, distance and inertial mass between different rest frames. This procedure is used in the Global Positioning Navigation System in order to ensure that atomic clocks on satellites run at the same rate as their counterparts on the earth’s surface. Use is made of an alternative method introduced by Schiff in 1960 for computing the apparent displacement of star images during solar eclipses. This method is extended to also give accurate predictions of the precession of planetary orbits, which makes Schiff’s method comparable in accuracy to Einstein’s General Relativity while being considerably simpler to apply in practice.

 

 

 

Inertial Clocks and Remote Non-Simultaneity 

Symposium on Special Theory of Relativity, June 4, 2020

A video conference attended by students and faculty members of 43 Indian universities.

Part I

Part II

Uniform Scaling Tutorial

 

 

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 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-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-vu_xc^-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).

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.

New Publication

Relativity Contradictions Unveiled:
Kinematics, Gravity and Light Refraction

available as a Paperback from Amazon.com

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.

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,  5^th Edition (Harcourt, Orlando, 1999), p.1262.

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.<sup>2

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