Fatal Flaws in Einsteinís Special Theory of Relativity
Copyright © 2012 Joseph A. Rybczyk
††††††††††† In complete opposition to all of the experimental evidence that is claimed to verify Einsteinís special theory of relativity there is one fundamental aspect that defies explanation; the principle that light does not take on the speed of the source.† To understand the problem with this principle one must abandon the three axes coordinate system that the special theory of relativity is founded upon and reexamine the theory using the spherical reference frames of millennium relativity.† Such reference frames force us to consider all aspects of electromagnetic propagation and bring to light flaws that undermine the validity of Einsteinís theory.
††††††††††† An in-depth analysis of the principles of Einsteinís special theory of relativity1 shows beyond doubt that the principles of light speed constancy and time dilation cannot be valid.† Although there is a valid fundamental basis for the principle of light speed constancy under the first postulate of special relativity that holds the laws of physics to have the same form in all inertial systems, the resulting definition is different from that given by the second postulate.† Thus, the second postulate would have to be modified and in the process change the underlying nature of the theory.† The principle of time dilation, however, does not appear to have any true basis of validity at all and thereby invalidates the special theory in its entirety.† As for the so-called evidence that supposedly verifies the principles of special relativity, much of it is in the form of self-fulfilling premises whereupon the experiments are designed to verify the very principles that are being tested2.† Other experiments are of such a cryptic nature that no one can truly say just exactly what they prove or disprove3.† And still other experiments clearly disproved the principles they were designed to prove and were then reinterpreted to show precisely the opposite4.† The subject research findings are presented in as brief, clear, and precise a manner as practical considering the abstract nature of the subject matter in question.
2. Redefining the Constancy of Light Speed
††††††††††† In the absence of a propagation medium in empty space, as verified by experimental evidence5, light propagates from its source at the same speed c in all directions relative to the source regardless of the speed of the source relative to the point of observation.† This definition for light speed is consistent with the first postulate of special relativity and simply means that light must propagate from it source at speed c in the inertial frame of the source where c has the same value in all such inertial systems.† What it does not mean is that light from a moving source has that same speed c in the frame that the sourceís motion is referenced to.† Consistent with this point of view we can associate a real or hypothetical light source with the point of origin of any inertial frame and use its spherical propagation geometry to reference the mechanics of motion between one such frame and any other inertial frame.† Such mechanics of motion involves both the physical source and its propagated light within its own inertial frame and that of another frame that the sourceís motion is referenced to.† To better understand such behavior let us now refer to Figures 1 and 2.
††††††††††† In Figure 1 a point light source is shown at the point of origin in the inertial frame of the source that the propagating sphere of light S1 was emitted from.† The sphere may be thought of as consisting of tiny particles such as photons, or alternately as the leading edge of the waves associated with such particles as they move away at speed c from the source where they were emitted at time T = 0 in the frame of the source.† It should be understood that normally there are many such spheres sequentially propagating away from the source in the order of emission. †The sphere shown is simply one such sphere selected for purposes of relating the motion mechanics of one sphere to another from a different inertial frame that the motion of the source under discussion is moving relative to.
Figure 1 Light Propagation Sphere
Such relationship is illustrated in Figure 2 where sphere S1 was emitted by a real or hypothetical stationary source at point e at the same instant that sphere S2 was emitted at that same point e in the stationary frame as its moving source traveled distance vT to the right.† Distance vT is then defined as the stationary frame distance the moving source traveled at speed v during time interval T.† During that same time interval sphere S1 expanded away from point e at radial speed c during which sphere S2 simultaneously expanded away at the same radial speed c from the moving source at its moving point of origin.† In such relationships the stationary frame sphere S1 remains centered over stationary point e as it expands out to infinity at speed c while the moving frame sphere S2 moves along with the moving source at speed v while it also expands out to infinity at speed c.
Figure 2 Dual Propagation Spheres
Whereas Figure 2 gives the relationships between the two frames of reference as covered in detail in the authorís previous works on the cause and effect theory of light propagation6, it does not represent the relationships such frames would have under the special theory of relativity as will be discussed next.
3. Dual Spheres under Special Relativity
††††††††††† In special relativity the relationship between the dual propagation spheres is defined by the special relativity light clock principles.† As shown in previous works by this author7, it is not necessary to use the entire light clock relationships as given in Einsteinís theory in order to demonstrate the relationship between dilated time in the moving frame and the normal time in the stationary frame that the moving frameís speed v is referenced to.† Since the special relativity light clock utilizes two identical back to back Pythagorean triangles that contain the same fundamental relationships, only one such triangle is really necessary to demonstrate those relationships as they exist between two propagation spheres of the nature being discussed.† Referring now to Figure 3 we have a modified form of the dual sphere relationships previously given in Figure 2.† Specifically, the triangle has been changed to a Pythagorean triangle with the perpendicular side representing the radius of the moving sphere S2.† Since this side is of a shorter length than the hypotenuse side that represents the radius of sphere S1, either the propagation speed of light must be greater in the stationary sphere S1, or the propagation time in the stationary frame must be greater than the propagation time in the moving frame.† According to special relativity the speed of light from a moving source is still c in the frame of the stationary observer.† Thus time t in the moving frame is less than time T in the stationary frame as indicated in the illustration.
Figure 3 Time Dilation
In brief, the point of light that travels perpendicular distance ct in the frame of the moving source simultaneously travels distance cT in the stationary frame that the sourceís speed v is referenced to.† This principle, in itself, is inconsistent with the principle of vector addition that properly accounts for the dual paths traveled by the same particle of light by attributing different speeds along the two different paths if they are not equal in length.† But even this troubling aspect of Einsteinís theory is not the most serious issue we have to deal with.
††††††††††† According to the principles of the special relativity Doppler effect, light does not take on the speed of the source but rather propagates in all directions at speed c from the stationary frame point of emission as the source continues along its path of motion.† According to the strictest interpretation of this principle, propagation sphere S2 in the frame of the moving source has the alternate form of propagation sphere S1 in relation to the stationary frame as illustrated in Figure 3.† In fact by simply identifying the location of the point of observation along the surface of stationary frame sphere S1, in Figure 3, we have all of the information needed to derive the special relativity Doppler effect formula for electromagnetic propagation as will be accomplished next.† Note; the very fact that this can be done verifies beyond reasonable doubt that the dual sphere relationships used properly represent the fundamental principles of special relativity.
††††††††††† Referring now to Figure 4, which is nothing more than a repeat of Figure 3 with the exception that now the angles of approach and recession have been included for both conditions of observation, we can begin the derivation process.† For the classical component of the formula we have
where λo is the observed wavelength in the stationary frame of the observer, λe is the emitted wavelength in the moving frame of the source, c is the speed of light, v is the speed of the source, θ is the angle of observation, and the sign where shown is + for recession and - for approach.† The angle θ can be any angle from 0 to 90 degrees for either approach or recession.† In Figure 4 the angle of approach is given as θa and the angle of recession is given as θr.† In the illustration the point of observation o1, by way of example, is shown at the transverse angle of 90 degrees relative to the point of emission e along the path of motion.† For use with the Doppler formulas, however, the observation point can be anywhere along the surface of sphere S1.
Figure 4 Special Relativity Doppler Effect
At this point in the analysis we have already encountered the most serious flaw in Einsteinís special theory of relativity.† There is simply no rational explanation as to how points along the moving frame propagation sphere S2 can simultaneously be located along the surface of the stationary frame sphere S1 except at the points along the surfaces of both spheres where they are in contact with each other, such as represented by observation point o2.† As a matter of fact, as discussed later in Section 6, the authorís recently introduced cause and effect formula is in agreement with the special relativity formula for the effect observed in the stationary frame at the transverse angle of 90 degrees, but for completely different reasons from those given in special relativity.
††††††††††† Although we have already shown the fatal flaw in the special relativity Doppler treatment, for purposes of discussion we can complete the derivation process by deriving and then adding the special relativity Lorentz redshift effect to the classical component previously derived.† Still referring to Figure 4 we can define the Pythagorean triangle by its distance relationships as
and then solve for T to derive
where T is the time interval in the stationary frame that corresponds to dilated time t in the moving source frame.† The fraction on the right is simply another form of the special relativity gamma factor that can now be applied to the classical component of the special relativity Doppler formula to account for the effect of time dilation in the moving frame of the source and thereby permit derivation of the complete special relativity formula.† This gives us
that simplifies to
where λo is the observed wavelength in the stationary frame, λe is the emitted wavelength in the moving frame of the source, c is the speed of light in empty space, v is the speed of the source relative to stationary point e, θ is the angle of observation from 0 to 90 degrees and the sign where indicated is + for recession and - for approach.
4. The Special Relativity Doppler Paradox
††††††††††† Before continuing with the analysis it is important to emphasize what was just shown in Section 3.† In so doing, it should be understood that what is being claimed is not dependent on the specific form of the analysis just conducted.† It follows from any other derivation process involving the special relativity Doppler formula in any of its many forms.† In plain words, the classical component of the formula directly follows from the special relativity postulate that light does not take on the speed of the source but propagates thorough empty space at speed c regardless of the speed of the source.† This means that the light from a moving source propagates toward the stationary observer in the stationary frame of reference from the point where the source was at in the stationary frame (i.e., point e in Figure 4) at the instant the received light was emitted.† This is the behavior associated with a light propagation medium in the inertial frame of the observer.† That is the only reasonable explanation as to how light can propagate to observers anywhere along the surface of the stationary frame propagation sphere S1, as illustrated in Figure 4, in direct accordance with the mathematical definition of the classical component of the special relativity Doppler formula.† Yet this very process is in complete opposition to the special relativity Lorentz redshift effect since that effect directly follows from the principle of vector addition.† Actually, it is a modified form of vector addition where the difference in the distance traveled by the same particle in the stationary frame and moving frame is attributed to a difference in time rather than a difference in speed.
What we have then, is a dual behavior of light propagation.† In one regard, light propagates to the observer from the point at which it was emitted by the moving source in the observerís frame of reference as if there is a propagation medium at rest in that frame.† In the other regard the light exhibits the behavior associated with vector addition but with a difference in time instead of speed accounting for any difference in the lengths of the two paths traveled by the same particle.† Of these two conflicting definitions of light behavior, the one involving a medium is by far the most troubling.† For example, if there is such a medium in the stationary frame then it would appear that it would also affect the light in the moving frame of the source.† The questions that arise in that regard are almost endless as will become apparent as the analysis continues.† But first we will discuss the problem with the special relativity light clock principle.
5. The Fallacy of the Special Relativity Light Clock
††††††††††† Upon close examination of the special relativity light clock principle there is an apparent fallacy that is not readily apparent in Einsteinís treatment but becomes rather obvious in the dual sphere treatment.† It involves the apparently unjustified privileged status Einstein assigns to the light along the path perpendicular to the path of source travel.† Since the speed of light is the same in all directions in the frame of the source, as shown in Figure 5, the only difference in choosing one direction over another in the source frame is the effect that choice will have in the stationary frame.
Figure 5 Light Clock Fallacy
As can be seen in Figure 5, if the moving frame path ct that was simultaneously traveled along with stationary frame path cT1 is used and if light has the same speed c in the stationary frame, then stationary frame time interval T1 is a greater time interval than T2 that corresponds to the special relativity choice.† Conversely, if the path ct that was traveled simultaneously with path cT3 is used then stationary frame time interval T3 is not only less than interval T2 but it is also less than moving frame time interval t.† Yet, if any of the choices shown has privilege over the others, it is this choice; for it is this choice that is at the transverse angle of 90 degrees to the path of source motion in the stationary frame of the observer.† That is, according to the classical component of the special relativity Doppler effect formula it is at this stationary frame observation point o3 that there is no classical Doppler effect as defined in the theory.† Thus, by definition, only the Lorentz redshift effect is observed at this point.† But, as can be seen, there is a conflict involving the time dilation treatment because it is the greater stationary frame time T2 that is used along with moving frame time t in the Lorentz redshift factor and not time T3 that is even less than time t.
††††††††††† If what was just discussed was the only problem with the special relativity treatment it is serious enough to invalidate the theory.† But the problem is even greater than that.† In reviewing Figure 5 it is readily seen that although there is only one time interval involved in the distance propagated by the moving frame sphere S4, there are an entire range of different time intervals involved with regard to where the moving frame sphere intersects the stationary frame sphere.† That is, depending on the location of the observer in the stationary frame, e.g., at points, o1, o2, o3, etc., a different amount of stationary frame time will have transpired.† More specifically, time in the stationary frame is dependent upon the direction the light from emission point e must travel in relation to the direction of source motion.† It is greatest in the direction of longitudinal approach and least in the direction of longitudinal recession.† The only apparent solution to this problem is if the speed of light from a moving source varies with direction in the stationary frame instead of time as will be discussed next.
6. The Cause and Effect Solution
††††††††††† In complete compliance with the known laws of physics light emitted in all directions from a light source that is not under any form of acceleration will propagate at the same speed c in all directions away from the source as illustrated in Figure 6.
Figure 6 Cause and Effect Principles
That is, since there has never been any evidence of a light propagation medium, such light emitted at the same instant will remain centered on the source in the form of an expanding sphere of light as shown in the illustration.† Moreover, given the principle of relativity any uniform motion between the source and observer can be attributed to the source as shown.† Then, given the principle of vector addition, the same sphere of light, So in the illustration, will simultaneously propagate away from the stationary point e where it was emitted in the stationary frame that the speed v of the source is referenced to.† And subsequently, stationary observers located at points o1 through o6 will observe the light as having traveled a different distance to reach them from point e at the same instant in time.† Since the same light was emitted at point e during the same instant when the source traveled past it, either time in the frame of the stationary observers varies or the speed of the light from the moving source varies depending, in both cases, on the observerís relative location to point e.† Of the two choices only the variance of light speed, as given in the cause and effect theory, appears to make sense.† That is, unless someone can show evidence that time varies throughout the stationary frame of reference, depending not only on the observerís position relative to the source, but also on which of an infinite number of different sources is chosen.
††††††††††† In summarizing the cause and effect solution it should be understood that the principle of time dilation between inertial frames, as given in special relativity, is completely abandoned.† More specifically, time does not vary from one inertial frame to another that its speed is referenced to.† Time is universal throughout the universe.† Thus, in Figure 6 the time interval T during which the source traveled at speed v and the light sphere emitted at point e expanded at speed c is the same in both the frame of the source and the frame of the stationary observers.† Conversely, light speed L in the stationary frame varies depending on the relative position of the stationary observer to the moving source.
††††††††††† For quick reference the cause and effect Doppler formulas are given next.† For the full wavelength and frequency formulas we have
where λo and fo are the observed wavelength and frequency, λe and fe are the emitted wavelength and frequency, c is the speed of light, v is the speed of the source, and θ is the angle of observation from 0 degrees for longitudinal approach to 180 degrees for longitudinal recession.
††††††††††† The simplified formulas for longitudinal approach and recession are
where the symbols have the same definitions previously given.† Of final interest is the fact that when θ is set to 90 degrees in formulas (6) and (7) we obtain
that are identical to the special relativity results for that angle.† The significance of this final finding is that it exactly agrees with the same experiments that were used to verify the special relativity formulas at that angle8.† Yet, the special relativity time dilation redshift effect represented by the Lorentz gamma factor in equation (10) and its reciprocal in equation (11) are not a function of time dilation in the above formulas.† Thus, any such experimental evidence used in support of the special relativity Doppler effect formulas is inconclusive in verifying Einsteinís special theory of relativity.
††††††††††† The theoretical evidence documented in this paper presents serious and well defined challenges to the validity of Einsteinís special theory of relativity.† The supporting principles for such conclusion were not haphazardly arrived at and are the result of years of related continuous in-depth investigative research.† In this investigatorís opinion there is only one way to resolve the conflict the presented findings impose with regard to currently accepted theory, and that is through the conduction of new and properly designed experiments that will conclusively settle this issue for all time.† The quoting of past evidence will no longer suffice for that purpose.
1 Albert Einstein, the Special Theory of Relativity, originally published under the title, On the Electrodynamics of Moving Bodies, Annalen der Physik, 17, (1905)
2 For example, if a relativistic method is used for determining the speed of a light source that is used in an experiment to test the validity of the relativistic Doppler effect, the test could be self-fulfilling.† Conversely, if a classical method is used to determine the speed, the same experiment could be self-defeating.† Consequently, existing and newly designed experiments need to be evaluated for such issues in order to ensure valid interpretation of the results.† The problem, however, is that many experiments are of such a cryptic nature, as discussed in reference 3, that it may not be easy to determine such issues. ††
3 The design, results, and official reporting of experiments in relativistic physics are often of such a cryptic nature that only those in the same field as the experimenter have any change of performing a critical review of the results.† Such experiments should be regarded with great skepticism since they are not subject to a wide range of expertise in related areas of physics.
4 For example, the Michelson and Morley interferometer experiments given in reference 5.† The experiments failed to detect the ether medium they were designed to detect.† Lorentz distance contraction and time dilation were then conceived to explain the null results of the experiments.† Since both of the effects, distance contraction, and time dilation, are dependent upon the motion of the source relative to the observer which are different for each frame of reference, the existence of an ether medium in space was preserved.† From an alternative perspective such interpretation can also be viewed as a medium associated with each different inertial frame.
5 Albert Michelson and Edward Morley, (1887), The interferometer experiments conducted in 1887 over a period of one year by the two American physicists in an attempt to detect the ether medium postulated by Maxwell as being required for the propagation of electromagnetic waves.
6 Joseph A. Rybczyk, Cause and Effect Theory of Light Propagation, (2011), Longitudinal Cause and Effect Formulas for Light Propagation, (2011), available at http://www.mrelativity.net
7 Joseph A. Rybczyk, Millennium Theory of Relativity and associated papers, (2001 to present), All available at http://www.mrelativity.net
8 For example, Herbert E. Ives and G. R. Stilwell, An Experimental Study of the Rate of a Moving Atomic Clock, Journal of the Optical Society of America, Volume 28, (July, 1938) †
Fatal Flaws in Einsteinís Special Theory of Relativity
Copyright © 2012 Joseph A. Rybczyk
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