Chapter 28

 

RELATIVISTIC KINEMATICS:  CONTRACTIONS AND DILATIONS

 

Einstein interpreted his Lorentz transformations in arbitrary ways and he applied their artificial results to space and time measurements of a distant moving body or frame.  The mathematical consequences of such applications were a theoretical contraction of the length of such moving body and a theoretical dilation (slowing down) of time intervals on such moving body, all in the direction of its relative motion.  Einstein’s primary reason for inventing such spurious kinematic concepts was to remain mathematically consistent with, and to bolster, his second postulate concerning the absolutely constant propagation velocity of light at c.  It turns out, however, that what all these contrived kinematic concepts really meant was:  that ‘motion affects coordinate measurements.’

 

 

A.  Einstein’s rationale for his invention of Relativistic Kinematics depends upon many ad hoc concepts and false premises.

 

            In Chapter 11 of Einstein’s book, Relativity, entitled ‘the Lorentz transformation,’ he explained in plain language the various reasons why he adopted Lorentz’s April 1904 space and time transformation equations for his Special Theory, why he applied such transformation equations both to the velocity of light and to material inertial reference frames, and why he was forced to invent the mathematical concepts of Relativistic Kinematics:  the Contraction of Distance and the Dilation (slowing down) of Time intervals, in the direction of relative velocity.  We shall now describe and analyze Einstein’s rationales and attempted justifications for these ad hoc concepts and applications, in sequential order.

            First, Einstein referred to “the apparent incompatibility of the law of propagation of light with the principle of relativity,” which he called the ‘difficulties.’  (Einstein, Relativity, p. 34)  Actually these ‘difficulties’ were a result of Einstein’s impossible concept and fundamental major false premise:  that a ray of light must have the same velocity c relative to the stationary embankment and relative to the carriage moving down the track at v, rather than velocity c – v relative to the moving carriage.  Einstein failed to realize that this velocity c – v (or c + v) was merely a relative velocity of the light ray that quite naturally results when one applies the Galilean transformation (x' = x – vt) to a light ray transmitting at c between reference frames x and x' moving at the relative velocity of v.  (see Chapters 21 and 22)

            Second, Einstein asserted that such incompatibility (the ‘difficulties’) was caused by the way that classical physicists added velocities, i.e. v1 + v2 = v3.  (see Figure 7.1)  He then claimed that if his ad hoc hypothesis (that time intervals and distance intervals are not absolute but rather are dependent upon the relative velocity of inertial reference frames[1]) was accepted as valid, then the difficulties with the velocity of light would disappear “because the [classical]…addition of velocities…becomes invalid.”[2]  (Id.)

            Third, Einstein then asked the question:  “How have we to modify the [classical addition of velocities so]…that every ray of light [in the Cosmos] possesses the velocity of transmission c relative to the embankment and relative to the train [or any other inertial coordinate system K' with magnitudes of x', y', z', t' located anywhere]. [3] (Einstein, Relativity, pp. 34 – 36)  In effect, Einstein also asked:  “what are the [coordinates] values x', y', z', t' of an event with respect to K', when the [coordinate] magnitudes x, y, z, t of the same event with respect to K are given,” and vice-versa?  (Id., p. 36)

            Fourth, Einstein answered the above third questions, as follows:  The “relation between place [space] and time of the individual events relative to both reference-bodies [Id., p. 35]…must be so chosen that the law of the transmission of light in vacuo is satisfied for one and the same ray of light…with respect to K and K'…This problem is solved by means of the [Lorentz transformation] equations.”[4]  (Id., pp. 36 – 37)

            However, Einstein neglected to mention:  1) that his above requirement (that the absolutely constant velocity of light at c relative to anything anywhere must be satisfied in order to mathematically relate the coordinates of any two inertial reference frames) necessarily further requires that such rigid reference bodies (frames) must be contracted (physically shortened) in the direction of their relative velocity, and that the time intervals on such reference bodies must also be dilated (made shorter) in the direction of such relative velocity;  2) that all of the above relativistic concepts are completely ad hoc and meaningless, as well as physically and empirically impossible; and  3) that there never was a real problem concerning the velocity of light that needed solving.  (see the Preamble)  Einstein’s concepts of Length (or Distance) Contraction and Time Dilation (depending upon relative velocity) are often collectively called Relativistic Kinematics.

            Fifth, Einstein concluded his Chapter 11, as follows:

“in accordance with the Lorentz transformation, the law of the transmission of light in vacuo is satisfied both for the reference-body K and for the reference-body K'.  A light-signal is sent along the positive x-axis, and this light-stimulus advances in accordance with the equation

x = ct,

i.e. with the velocity c.  According to the equations of the Lorentz transformation, this simple relation between x and t involves a relation between x' and t'.  In point of fact, if we substitute for x [a material body] the value ct [the velocity of light over a time interval] in the first and fourth equations of the Lorentz transformation, we obtain:

 

             

from which, by division, the expression

x' = ct'

immediately follows.[5]  If referred to the system K', the propagation of light takes place according to this equation.  We thus see that the velocity of transmission relative to the reference-body K' is also equal to c.  The same result is obtained for rays of light advancing in any other direction whatsoever.[6]  Of course this is not surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.”[7]  (Einstein, Relativity, pp. 38 – 39)

 

            The above algebraic results mathematically satisfied both Einstein’s second postulate (that every inertial observer, regardless of his linear velocity, would measure the same velocity c for a light ray), and his first postulate, his radically expanded Principle of Relativity (that the velocity of every ray of light would always have the same co-variant constant magnitude of velocity c with respect to every inertial reference frame regardless of its linear velocity).  The only problems with Einstein’s highly contrived mathematical results are:  1) that they depend upon numerous ad hoc concepts and false premises;  2) that Einstein’s absolutely constant velocity of light at c relative to anything everywhere is an empirically impossible concept (see Chapter 21 and the Preamble);  3) that Relativistic Kinematics, which was necessary to make Einstein’s second postulate plausible and mathematically consistent with the rest of physics, also ended up distorting much of physics and science in general; and  4) there never was a problem that needed fixing in the first place.  (see the Preamble)

 

B.  The Real Reasons for Einstein’s Relativistic Kinematics

Why did Einstein feel compelled to abandon classical kinematics and create an entirely new velocity dependent mathematical concept of Relativistic Kinematics?  Einstein himself answered this question for us in Chapter 11 of his book Relativity.  In order to relate the coordinates of the same event between two inertial reference frames K and K' anywhere in the cosmos, the

“relation between place and time of [such event]…must be so chosen that the law of the transmission of light in vacuo[8] is satisfied for one and the same ray of light…with respect to K and K'…this problem is solved by means of the [Lorentz transformation] equations.”  (Einstein, Relativity, pp. 35, 36 and 37; also see Chapter 28A)

 

On the contrary, the “relation between place and time” must not be chosen nor mathematically manipulated, as Einstein asserted, because the perfectly natural classical relation between place and time satisfies Maxwell’s law for the transmission of light at c in vacuo.  (see Chapters 21, 23 and the Preamble)

Einstein then mathematically manipulated and artificially interpreted the space and time equations of the Lorentz transformation in such a way that the velocity of the transmission of a light ray was always an invariant magnitude of c relative to every inertial reference system K and K' in the Cosmos at any time, regardless of their linear velocities relative to “one and the same ray of light.”  Einstein called this mathematical ‘trick,’ “co-variance” (Id., p. 48), and he concluded that this result should not be “surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.”  (Id., p. 39)

            Thus, Einstein ‘related’ the coordinates of a light event between K and K' by algebraically making his second postulate concerning the absolute invariance of the velocity of light at c covariantly apply to both K and K' at the same time.  How did Einstein and the Lorentz transformations perform this mathematical magic?  The Lorentz transformations artificially change or eliminate the relative velocity v between two spatially separated inertial reference frames so that mathematically they are relatively stationary.  (see Hoffmann, 1983, pp. 86 – 87)  In the process, the Lorentz transformations (along with certain critical and artificial interpretations) mathematically shorten or contract the coordinate measurements of space and mathematically expand or dilate the coordinate measurements of time intervals.[9]  (see D’Abro, 1927, 1950, p. 163)

Remember that the primary goal for Einstein’s Special Theory was to mathematically require that all linearly moving inertial observers would measure with clocks and coordinates the transmission velocity of a propagating light ray to possess the absolutely invariant velocity of c, rather than its natural and empirical relative velocity of c – v or c + v…the way the Galilean transformations predicted.  (Chapters 19 and 21)  The Galilean coordinate transformations merely mathematically summarized the empirical classical concepts of kinematics for space and time measurements.  (Goldberg, p. 73)  Thus, for Einstein to accomplish his mathematical goal, both the Galilean coordinate transformations and all of empirical classical kinematics (upon which they were based) would have to be mathematically changed in order for Einstein’s artificially and absolutely constant velocity of light at c to remain consistent with his coordinate measurements of light and matter in motion.

            Einstein needed his twin ad hoc concepts of the Relativity of Simultaneity (time intervals) and the Relativity of Distance (length), not only to justify substitution of the Lorentz transformations for the Galilean transformations (Chapter 27), but also as a precursor for the primary mathematical consequences that could be produced by applying the Lorentz transformations to matter:  his new mathematical relativistic kinematic concepts of ‘Time Dilation’ and ‘Length Contraction.’  These two primary mathematical consequences and concepts were, in turn, necessary components of most of his later relativistic mathematical consequences,[10] as well as necessary to keep Einstein’s absolutely invariant measurement of light velocity at c mathematically consistent with all space and time coordinate measurements made by inertial observers. 

Again, D’Abro summarized the above situation and Einstein’s mathematical solutions for it, as follows:

“Now it is obvious at first sight that if our space and time measurements were such as classical science believed them to be, it would be impossible for a ray of light to pass us with the same speed regardless of whether we were rushing towards it or fleeing away from it [Einstein’s second postulate for the absolute invariance of c].  A simple mathematical calculation shows us, however, that we can make our results of measurement compatible with [Einstein’s] postulate of invariance provided we recognize that our space and time measurements are slightly different from what classical science has assumed.  This is purely a mathematical problem and can be solved by mathematical means.[11] It leads us, of course, to the Lorentz-Einstein transformations; and from these transformations it is easy to see that rods in relative motion must be shortened [contracted], durations [time intervals] of phenomena extended [made longer or dilated], and the simultaneity of spatially separated events [coordinate measurements] disrupted.”  (D’Abro, 1927, p. 163)

 

D’Abro’s above assertions and conclusions vividly demonstrate that all of Einstein’s mathematical and relativistic changes to classical kinematic concepts were merely part of his grand ad hoc plan to achieve his above described primary goal (the absolutely constant velocity of light at c) by any mathematical manipulations or other means necessary.  Thus, for Einstein, this end justified any means![12]

Particle physicist Lee Smolin agreed with the above conclusions and further explained them.  Einstein needed his twin artificial concepts for measuring time and space (the Relativity of Simultaneity and the Relativity of Distance), and his mathematical reformulations of them (Time Dilation and Length Contraction), in order to make his empirically impossible absolutely constant velocity of light at c theoretically possible and to avoid the obvious contradictions which it posed for the measurement of other physical phenomena.  As stated by Smolin:

Einstein asserted “that different observers measure a photon to have the same speed, even if they are moving with respect to each other, because they measure space and time differently.  Their measurements of time and distance vary from each other in such a way that one speed, that of light, is universal.”[13] (Smolin, pp. 227 – 228)

 

Smolin then characterized Einstein’s ad hoc mathematical manipulations and dubious artificial interpretations, which caused such different time and space measurements, as “playing a trick,” and “the trick that made relativity special.”  (Id., p. 229)

            Once in possession of the Lorentz transformations, Einstein no longer had to rationalize or justify his twin concepts of the Relativity of Length and the Relativity of Time.  Such twin concepts would then automatically and mathematically follow from the Lorentz transformations in the form of new relativistic kinematic mathematical consequences:  the Contraction of Length and the Dilation [slowing down] of Time.  The fact that these fallacious mathematical concepts would, in turn, result in a drastic modification of mechanics and other realms of physics, seemed to be of little concern to Einstein.  If this was the price for achieving his impossible theoretical goal with regard to the absolutely constant velocity of light at c then so be it.  In order to attempt to rationalize such radical modifications of classical physics, Einstein even claimed that his Lorentz transformations were “concerned with the nature of space and time in general.”  (Miller, p. 195)

 

C.  ‘Proper’ Measurements & Einstein’s Kinematic Interpretations

            At the core of Einstein’s concepts of Relativistic Kinematics was a theoretical 1905 technical problem of measurement.  For example, an observer on a railway embankment physically measures the length of a rod situated in a stationary railway carriage with a rigid meter stick to be L meters.  (Figure 28.1A)  Later, the same stationary observer on the railway embankment desires to re-measure the length interval or time interval of the same rod which is now passing by him at velocity v.  To do so, he must simultaneously measure the position coordinates and time coordinates at both ends of the rod.  (Figure 28.1B)  If he measures the position and time coordinates at each end of the rod at different instants of time (i.e. non-simultaneously), his hand and eye coordinate measurements will result in either a longer or a shorter distance interval or time interval than L meters.  (Resnick, 1992, pp. 480 – 481; see Figure 28.1B)  What is the answer to this 1905 problem of measurement?

            Einstein’s answer was that length intervals and time intervals depend upon the state of motion of the observer (measurer) relative to that which is being measured.  (Id., p. 481)  In other words, they depend upon measurements between two different frames of reference.  In short, such measurements are ‘velocity dependent.’  Based on this criterion, Einstein asserted that length intervals and time intervals of objects viewed between inertially moving reference frames must be measured by applying the Lorentz transformations to such objects and their relative velocity v.  (Einstein, ‘Relativity,’ pp. 34 – 37)  Theoretically, the Lorentz transformations would mathematically factor the relative velocity of the frames into the relativistic space and time coordinate measurements, and the mathematical result would be magnitudes of the resulting distorted measurements. 

The mathematical consequence (along with certain critical and artificial interpretations and computations) would be:  that the rod to be measured would appear to contract in length and the time on its frame would appear to dilate (slow down) in proportion to 1:√1 – v2/c2, which of course would be consistent with Einstein’s twin concepts of the Relativity of Distance (length) and the Relativity of Simultaneity (time intervals).  Einstein also claimed that these apparent mathematical kinematic consequences were the “physical meaning of the [Lorentz transformation] equations obtained in respect to moving rigid bodies and moving clocks.”[14]  (Einstein, Relativity, p. 48)

            Contrary to the above, the real answers appear to be as follows:  While it is true that motion can affect visual and physical (hand and eye) coordinate measurements by human observers, for normal velocities of ordinary life the problem remains primarily a technical one.  In the 21st century the position and time measurements for both ends of a moving body can be simultaneously determined with laser beams and sensors, and its length interval and time interval can be calculated by digital computers, even between different reference frames.  Neither Special Relativity nor the Lorentz transformations should have any current relevance to these measurements.  On the other hand, for high-energy particles or very distant bodies where such empirical measurements are not technically possible, rough mathematical and theoretical approximations along with certain empirical assumptions remain the only current alternative.[15] 

Before we proceed further, let us further answer the question:  What does the word ‘proper’ mean in Special Relativity?  An inertial “frame of reference that is fixed…to a particular object and always moves with it”[16] is called the object’s ‘rest frame,’[17] “and measurements made in it are called proper.”  (French, p. 106)  “The length of a body measured in its rest frame is called its proper length.”  (Id.)  ‘Proper time’ is the “time as measured always at some fixed point in a particular frame of reference.”  (Id.)  Since (in Einstein’s Special Theory) there is a synchronized clock at such fixed point, its proper time is the same as the ‘common time of the inertial frame.’  (Chapter 25)

The time interval between two events is also considered to be a ‘proper time interval’ if it is measured by only one clock which is stationary in the same frame.[18]  (see Rosser, p. 47)  On the other hand, it is considered to be a ‘non-proper time interval’ if such measurement must be made by two unsynchronized clocks, or two clocks in different frames.[19]  (French, p. 106; see Figure 28.2)  In other words, all proper measurements in Special Relativity are ‘reference frame dependent.’

Let us now further discuss the mathematical and other methods by which Einstein arrived at his new relativistic kinematics. Just as was the case with Lorentz in 1904, Einstein’s Lorentz transformation equations for position and distance traveled,

x = x' + vt                                 x' = x – vt

   √1 – v2/c2                                  √1 – v2/c2,

 

on their face would require an expansion of the distance or space separating x and x':  such positive distance apart divided by a number less than one.  But Einstein’s Special Theory, just like Lorentz’s, required a contraction of such distance.  Therefore, a mathematical interpretation and coordinate manipulation was necessary to turn an expansion into a contraction.[20]  For this reason, in Chapter 12 of Relativity, Einstein interpreted his Lorentz space equations for distance traveled in such a way as to produce a contraction of distance or length in one reference frame when viewed from the other.  (Einstein, Relativity, pp. 40 – 41)  Just like Lorentz, the mathematical method which Einstein used to turn an expansion into a contraction was multiplication.[21] (Figure 28.3) 

            In order to mathematically produce his contraction, Einstein might have chosen to measure the rear end R of the rod first, and then the front F (or beginning end) of the rod.  But this would have produced an unwelcome coordinate contraction of time.  (see Figure 28.4A)  So instead, Einstein intentionally chose to measure the front (or beginning end) of the rod first, in order to produce a coordinate expansion of length.  (see Figure 28.4B)  However, this unwelcome expansion of the rod could then easily be manipulated and turned into a contraction by multiplication, which Einstein did.    These are some of the mathematical tricks which Einstein used to further his relativistic agenda.[22]  So much for the integrity of mathematical interpretations and clock and coordinate measurements.

Einstein then continued this strategy, but arbitrarily chose a different mathematical methodology so that his Lorentz transformation equations for time



would on their face be interpreted to produce a reciprocal expansion (or dilation) of time in both reference frames.[23]  This different mathematical methodology was division. [24] (see Figure 28.5)  More tricks of the mathematical trade.

            Let us now combine both of Einstein’s thought experiments for Length Contraction (Figure 28.3) and for Time Dilation (Figure 28.5), and scrutinize them together.  On system K' we have one rod which is measured to be 1 meter at rest in K', and the time interval between the front and the rear of such meter rod is one second as measured by a clock at rest in K'.  What will be the magnitude of contraction of such meter rod and the magnitude of time dilation on it as measured by K if the relative velocity between K and K' is 60% of c?  The answers to this question are as follows.

            Einstein stated that the length of the rod is one meter in K' as measured in K', but if K' is moving at v relative to K the length of the rod would be measured as “√1 – v2/c2 of a meter” in K.  (Einstein, Relativity, p. 41)  Therefore, if the relative velocity is v = 60% of c, then 1 meter times √1 – v2/c2 = 20% contraction of the meter rod as measured in K.  (see Chart 15.4C)

            Einstein also stated that the “time interval…between two strokes of the clock [as judged from K] is not one second, but 1 divided by √1 – v2/c2 seconds.”  Therefore, if the relative velocity is v = 60% of c, then 1 second divided by √1 – v2/c2 = 1.25% expansion of the time interval (one second) on the meter rod, as measured in K.  (see Chart 16.3)

            If we plot on the same graph all of the magnitudes of Length Contraction of matter (L = L0√1 – v2/c2) and all of the magnitudes of Time Dilation (expansion of time)

(T = T0 ÷ √1 – v2/c2) for all relative velocities from 0 to 300,000 km/s, they will be shown on Figure 16.2.  But now we have a conflict and a contradiction.  How can the magnitudes of the Length Contraction curve (Figure 16.2A) be so asymmetrical, non-reciprocal and out-of-correlation with the magnitudes of the Time Dilation curve (Figure 16.2B) for the same reference frame?[25]  These dramatically inconsistent mathematical kinematic results constitute major internal self-contradictions for Einstein’s Special Theory.  (see Memo 28.14)

Both of Einstein’s different mathematical methodologies, his algebraic and coordinate tricks, and his strained interpretations apply reciprocally to each different reference frame, because a meter rod or clock situated in the relatively stationary system K can be considered to be moving in the opposite direction with a minus velocity (-v) relative to system K'.  (see Einstein, Relativity, p. 41)  Based on these assumptions, it turns out that if Einstein’s two reference frames had been moving in different or opposite directions (i.e. approaching each other), then different relativistic results should have occurred.[26]  (see Figures 28.6 and 28.7) 

Similarly, if Einstein had arbitrarily switched his different mathematical and coordinate methodologies and tricks (and his interpretations of them) between distance and time, this would have mathematically resulted in an expansion of distance or length and a contraction of time or duration.  (see Figures 28.8 and 28.9)  But, of course, neither of the above scenarios would have advanced Einstein’s Special Theory.  In fact, such switching certainly would have destroyed it.  Therefore, both of the above scenarios constitute more potential internal self-contradictions for Einstein’s Special Theory.

As previously explained, one could also easily interpret the Lorentz transformations to mean something entirely different than Einstein’s above interpretations.  For example, the numerator x' = x – vt could be interpreted to mean not a straight line between two points x and x', but rather a curved geodesic line like the surface of the spherical Earth with x and x' separated by a curved distance vt.  This curved geodesic distance could be plotted on a different set of flexible coordinates (i.e. Gaussian coordinates) like Einstein did with his General Theory.  The denominator       √1 – v2/c2 could be interpreted to describe the quarter arc of a circle or the quarter geodesic distance of a sphere, √1 – x2/y2.  (see Figure 16.6)  The denominator could be interpreted to become smaller than the number one depending upon the velocity v of the sphere.  The entire set of Lorentz transformations could then be interpreted to mean that when the numerator is divided by a smaller denominator the sphere gets larger and the distance vt between x and x' expands, and the time interval between x and x' also expands.

            Again, if these different assumptions are designated as postulates, then the reciprocal Lorentz transformation equations for both time and distance could be ‘derived’ from such assumptions and certain interpretations.  The author is confident that any imaginative mathematician could also come up with other very different assumptions, and could also ‘derive’ the same Lorentz transformation equations from them, albeit they would most likely be interpreted quite differently.

Very importantly, and above all, the above discussion (and such related illustrations and descriptions) in this section demonstrates quite vividly that by the simple means of changing assumptions, conventions, choices for coordinate measurements, directions, mathematical methodology and manipulations, computations, analogies, interpretations, rationalizations and the like, a clever mathematician (like Einstein) can arrive at almost any result he or she desires.[27] If the results of algebraic equations can so easily be manipulated by imagination and mathematical skill to achieve a particular agenda, what validity do they have for science?  Sometimes, not much!  Sometimes (as with Special Relativity), they even distort reality and science.

 

D.  Einstein’s Mathematical Concept of Length Contraction

The concept of Length Contraction was first conceived by H. A. Lorentz in his April 1904 treatise.  It was a mathematical consequence of Lorentz’s radical transformation equations.[28]  Lorentz applied his concept of Length Contraction in an ad hoc attempt to explain why the M & M experiment and other light experiments had failed to detect the absolute motion of the Earth with respect to the theoretical stationary ether.  (see Chapter 16)  It is quite obvious to many people that Einstein in 1905 borrowed Lorentz’s Length Contraction concept for his own Special Theory, modified it to apply to relative motion rather than to absolute motion, and gave it a new interpretation.

In 1905, Einstein theorized that lengths could be precisely measured by two different methods.  Assume that two observers on the surface of the Earth wish to measure the length of a telephone pole.  Observer 1 standing next to the pole will directly and precisely measure it with his rigid meter rod to have a length of L.[29]  However, Observer 2 who is 100 meters away on a stationary railway carriage must use a different and indirect method.  Observer 2 perceives the distant pole to be much shorter than the similar telephone pole that he is standing next to, but he knows from experience that it has not physically shrunk.  (see Figure 3.8)  Therefore, Observer 2 chooses to measure the pole with Cartesian coordinates and mathematics (specifically the Pythagorean Theorem and trigonometry), and with this indirect method he also precisely mathematically measures the distant pole to have a length of L. 

            As previously mentioned, in 1905 the measurement of coordinates was performed with the hand and eye method.  The observer’s eye would visually determine a coordinate and then his hand would plot it on a graph of Cartesian coordinates.  This laborious process would take a certain amount of time to plot each coordinate.  But there was no problem so long as the distance between the object to be measured and the observer (measurer) did not change.

            Now assume that the railway carriage suddenly begins to move linearly away from the distant telephone pole in a straight line at the uniform velocity of v, and Observer 2 wishes to again measure it with the same indirect method.  Now he has a problem:  relative motion.  Any hand and eye measurement of the pole using coordinates and mathematics will now obviously be very imprecise and distorted by such relative motion.  If Observer 2 disregards this fact and decides to re-measure the distant pole using exactly the same hand and eye method as before such relative motion began, the time delay between each hand and eye coordinate measurement will obviously cause the measured coordinate length of the pole to be distorted and different than before. [30]  (see Resnick, 1992, p. 480)  A naive person might even say that the pole had changed in length.[31]  Einstein called this change in measured length because of relative motion the ‘Relativity of Length.’[32]  (Einstein, 1905d [Dover, 1952, pp. 41 – 42]; see Chapter 26C)  Based on this artificial concept, Einstein claimed ad hoc in his Special Theory that the measured length of any material object was dependent upon its relative velocity.

During his 1905 attempt to rationalize his concept of the Relativity of Length, Einstein (in Section 2 of his Special Theory) criticized “current kinematics” because it tacitly assumed that the length of a moving rigid body was “precisely equal” to the length of such body when it was stationary.  (Einstein, 1905d [Dover, 1952, p. 42])  “In other words, that a moving rigid body at epoch t may in geometrical respects be perfectly represented by the same body at rest in a definite position.”  (Id.) 

According to Einstein (in Section 2), an observer S' on the relatively moving frame who moves with the rigid rod to be measured (and is relatively at rest with respect to such rod) can measure its ‘geometrical’ (unaltered) shape.  (Id., p. 41)  On the other hand (in Section 4 of his Special Theory, entitled the “Physical Meaning of the [Lorentz] Equations Obtained in Respect to Moving Rigid Bodies”), Einstein theorized, inferred and conjectured that the relative motion between the two reference frames (S and S') distorts the coordinate measurements of the observer (measurer) on the stationary frame S, so that the S observer measures the rod’s ‘kinematic’ (distorted or contracted) shape.[33]  (Id., p. 48; see Miller, p. 191)  In Einstein’s own words:

 “A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion—viewed from the stationary system—the form of an ellipsoid of revolution with the axes [in the direction of motion].” [34]  (Einstein, 1905d [Dover, 1952, p. 48])

 

After Einstein used his artificial and ad hoc coordinate concept of the Relativity of Length (based on relative motion) to justify substituting the Lorentz transformations for the Galilean transformations (see Chapters 26 and 27), he conjectured in Section 4 of his Special Theory that the sphere moving at relative velocity v appeared from coordinate measurements to be “shortened in the ratio 1:√1 – v2/c2.”[35]  (Id., p. 48)

We must now ask the question:  If Einstein’s artificially contracted coordinate measurement of length was not empirically valid based on empirical examples, simple logic and his relativistic concept of the Relativity of Length (see Chapters 26B and 26C), how could such contracted measurement suddenly become physically valid based on Einstein’s arbitrary kinematic conjectures and his dubious mathematical equations, conventions and interpretations described in Section 4 of his 1905 Special Theory?  The answer is:  they could not and did not.  Einstein’s 1905 axiomatic and distorted mathematical concept of Length Contraction was always artificial, arbitrary, contrived, ad hoc and empirically invalid.  For the same reasons, Einstein’s conjecture that length was ‘relative velocity dependent’ was also ad hoc and empirically invalid.

In Section 4 of his 1905 Special Theory, entitled:  Physical Meaning of the Equations Obtained in Respect to…Moving Rigid Bodies…,” Einstein specifically claimed that the dimensions of every rigid body which moves in the direction of its velocity “appear shortened in the ratio 1:√1 – v2/c2, i.e. the greater the value of v, the greater the shortening.”  (Id., p. 48)

“For v = c all moving objects—viewed from the ‘stationary’ system—shrivel up into plain figures.[36]  For velocities greater than that of light our deliberations become meaningless...”  (Id.)

 

It is clear that the same results hold good of bodies at rest in the ‘stationary’ system, viewed from a system in uniform motion.”  (Id., p. 49)

 

It is also clear that Einstein was again attempting to mislead and convince the reader that his mathematical theory was physically and empirically valid.  Why else would he use words such as ‘physical meaning,’ ‘appear,’ ‘shrivel up,’ and ‘viewed’?[37]

Thereafter, in his1916 book, Relativity, Einstein somewhat revised his ad hoc arguments concerning the Relativity of Length by referring to thought examples.  Remember that, in Chapter 26C, Einstein in 1916 attempted to convince us by contrived thought examples and fool’s logic that the length of a rigid body on a moving train was shorter than its length when at rest on the stationary embankment.  However, when scrutinized, this claimed phenomenon which he again called the ‘Relativity of Length’ turned out to be just a verbal and coordinate illusion.  (see Figure 26.5)  Thus, Einstein failed in his attempt (based on obviously contrived examples and fool’s logic) to convince us that the rigid body had physically contracted because of its relative velocity.  In other words, he failed to convince us that the length of the rigid body was ‘relative velocity dependent.’

Nevertheless, Einstein then used this empirically invalid concept of the Relativity of Length (i.e. that the rigid body was ‘velocity dependent’) in order to rationalize his way to substituting the Lorentz transformation for distance for the Galilean transformation for distance.  (see Chapter 27)  Once in possession of the Lorentz transformations, Einstein no longer needed to attempt to logically rationalize or justify his Relativity of Length concept.  At this point, all he had to do was to interpret the Lorentz transformations as applying to a moving rigid body in a certain manner, and with certain arbitrary interpretations and mathematical manipulations its length would mathematically appear to be shorter or contracted in its direction of motion.[38] 

When the Lorentz transformation for distance (the multiplication of length L' on the moving train by a number less than 1) was applied by Einstein to such scenario with the appropriate interpretations, the coordinate length of the body on the moving train algebraically appeared to the observer on the stationary embankment to be shorter than when it was at rest.  (Figure 28.3)  Einstein called this algebraically produced concept (manipulation, illusion or trick) that resulted in an apparently shorter length…‘Length Contraction.’  Thus, in 1916, Einstein succeeded in this attempt to make the length of the rigid body on the relatively moving train theoretically appear to be shorter than the length of the rigid body on the stationary embankment, based solely upon mathematical manipulations and arbitrary interpretations.[39]

Likewise (in 1916) Einstein conjectured that “we must be able to learn something about the physical behavior of measuring rods [in motion]…from the equations of transformation…”  (Einstein, Relativity, p. 41)

“It therefore follows that the length of a rigid meter-rod moving in the direction of its length with a velocity v is √1 – v2/c2 of a meter.  The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter is the rod.  For the velocity v = c we should have √1 – v2/c2 = 0, and for still greater velocities the square-root becomes imaginary. 

 

“If, on the contrary, we had considered a meter-rod at rest in the x-axis with respect to K, then we should have found that the length of the rod as judged from K' would have been √1 – v2/c2; this is quite in accordance with the principle of relativity which forms the basis of our considerations.”  (Id.)

 

Thus, Einstein in 1916 also asserted that these artificial kinematic effects of length resulted from physical behavior, were physically shorter and literally real, and not merely coordinate measurements, illusions and mathematical tricks that result from his spurious conventions for measuring.

            Many current relativists also construe Einstein’s coordinate measurements literally, and claim the following physical consequences for relativistic length measurements:

“a body’s length is measured to be greatest when it is at rest relative to the observer.  When it moves with a velocity v relative to the observer its measured length is contracted in the direction of its motion by the factor √1 – v2/c2, whereas its dimensions perpendicular to the direction of motion are unaffected.[40]  (Resnick, 1968, p. 62)

 

Later, in Chapter 28E, we will demonstrate that some of such followers of Einstein also deny that such relativistic consequences are actually physical. 

This leads us to ask the question:  If Length Contraction is not a physical or an empirical phenomenon, but only a mathematical illusion or trick, then what is its relevance for the real world or empirical physics?  Since the answer is none, we then ask:  why are physicists and mathematicians so eager to defend Length Contraction, or to find experimental results that might somehow tend to empirically confirm it?[41]

            Many relativists also attempt to prove the empirical validity of the above mathematical illusions and kinematical consequences with thought experiments.  For example, take Einstein’s famous longitudinal ‘light clock’ thought experiment, which was described by Resnick (see Figure 28.10), and which in reality is nothing more than an illustration of Fitzgerald’s, Lorentz’s and Einstein’s invalid absolute ether contraction of matter explanations for Michelson’s null results.  (see Chapter 15; Einstein, Relativity, pp. 58 – 60; Resnick, 1968, p. 70 – 71; Cropper, pp. 211 – 213; Figure 16.3)

            There are a multitude of problems and contradictions with this complicated ‘Michelsonesque’ thought experiment, but all we need to address here are two of them.  The first problem is that an actual physical contraction of Michelson’s apparatus must be assumed in order for Michelson’s null results to be explained by any contraction theory.  Einstein’s coordinate appearance or illusion of a contraction will not do.  Similarly with the ‘light clock’ thought experiment, the S observer must first assume (based on Special Relativity) that the rod is physically shortened to L in order for the light clock thought experiment to have any meaning.[42]  However, since the contraction of the rod is what the relativists are attempting to prove with their contracting light clock thought experiments, this invalid bootstrap logic is also circular.

The second and most important reason why Einstein’s longitudinal light clock contraction of matter concept is totally empirically invalid is because the paradox of Michelson’s null results (which Einstein was attempting to explain with his contraction theory) actually resulted from several false premises.  For example, Michelson’s theoretically missing time interval and the theoretically greater distance for light to propagate in his apparatus’s direction of motion resulted from impossible measurements and physical displacements from stationary ether, which do not exist.  (see Chapters 9 – 12 for a full explanation)  Once one fully understands the false premises, it becomes obvious that there never was a missing time interval or a greater distance for light to propagate within Michelson’s apparatus.  (see Figure 12.1)  Therefore, there never was a contraction of matter nor a dilation (slowing down of) time explanation needed to explain something that did not occur.[43] 

            In a related thought experiment (see Figure 28.11), Resnick also attempted to deduce Length Contraction directly from Time Dilation.  But this axiomatic circular bootstrap deduction of one dubious concept which is subject to proof (Length Contraction), by another dubious concept which is also subject to proof (Time Dilation), does not prove anything and cannot be very convincing.  In any event, the disproof of Einstein’s Length Contraction and Time Dilation ether explanations for the paradoxes of the M & M experiment are described and demonstrated in detail in Chapters 9 – 12.

 

E.  Einstein’s Mathematical Concept of Time Dilation

The concept of Time Dilation was first conceived by H. A. Lorentz in his April 1904 treatise.  It was a mathematical consequence of Lorentz’s radical transformation equations.  (see Goldberg, pp. 99 – 100)  Theoretically, it asserted that: 

“the rate at which clocks ran in inertial frames of reference would depend on the relative speed of the frames.

 

“Lorentz swept these results aside as mathematical rather than physical.  They did not make sense within the framework in which he was operating; the framework of Galilean-Newtonian notions of time and space.”  (Goldberg, p. 100)

 

Lorentz considered Time Dilation merely as an aid to calculation with no physical significance.  (Id., p. 102; Chapter 16)  It is quite obvious to many people that Einstein in 1905 borrowed Lorentz’s Time Dilation concept for his own Special Theory, modified it to apply to relative motion rather than to absolute motion, and gave it a new physical interpretations.

In 1905, Einstein theorized that time intervals could be precisely measured by two different methods.  If an observer with a clock walked from point A to point B, the time shown by the hands of his clock at point B minus the time shown by such hands at point A would determine the time interval of his journey.[44]  But what if such observer could not carry his clock with him?  No problem.  If he could synchronize the hands of his clock at point A with the hands of the clock at point B with light signals, then the time shown by the hands of the A clock when he began his journey minus the time shown by the hands of the B clock when he ended his journey would also precisely determine the time interval of his journey.  Both of these measurements of clock time were defined by Einstein as simultaneous with the events to be measured:  the observer’s departure from A and his arrival at B.  (see Chapter 25)

            But what if such observer had to determine the time of an event that was distant from a clock that he trusted, so that no simultaneous clock time could determine the time of such event?  Say, for example, that Einstein tried to indirectly measure the length of a uniformly moving vehicle (with a large clock mounted on it) as a function of time.  If he first determined the clock time of the coordinate where he saw the rear of the vehicle and plotted it on a graph, and then determined the clock time of the coordinate where he saw the front end of the vehicle and plotted it on the graph, the time delay of the coordinate measurement in such process would cause the measured time interval of such length to be distorted, vis. much greater than when the vehicle was measured with a rigid meter stick before it began to move.[45]  A naive person might even say that the clock mounted on the moving vehicle must be running slow and that such expanded time interval was an expansion of time, which could be interpreted as a slowing down of the duration of time.  (see Figure 28.1)

In 1905, in Section 2 of his Special Theory, Einstein described a contrived thought experiment wherein he axiomatically arrived at his concept of the Relativity of Simultaneity (or time).  (see Einstein, 1905d [Dover, 1952, pp. 41 – 42]; Chapter 26)  Then, after he derived his Lorentz transformations in Section 3, Einstein axiomatically applied these transformations to clocks situated in two inertial reference systems in Section 4, and concluded that the coordinate time marked by the clock in the moving system (when viewed from the stationary coordinate system) is slow by 1 – √1 – v2/c2 seconds.[46]  (Id., p. 49)   Section 4 of his 1905 Special Theory was entitled:  Physical Meaning of the Equations Obtained in Respect to…Moving Clocks…” 

In his 1916 book, Relativity, Einstein gave much more explicit examples of his concepts of the Relativity of Simultaneity and Time Dilation.  Remember that in Chapter 26 Einstein attempted to convince us with contrived examples and fool’s logic that the duration of time on a moving train was different than the duration of time on the stationary embankment.[47]   The interval of duration between ticks of a moving clock could then be interpreted to be longer in its direction of motion as measured by coordinates by a stationary observer on the embankment, than as ‘properly’ measured by an observer who was traveling with the clock.  In other words, the expanded coordinate time interval on the moving train (as measured by the distant stationary observer) was interpreted to be a slower time with fewer ticks per second of distance traveled.  (see Figure 28.5) 

However, when scrutinized, these claimed phenomena, which he again called the ‘Relativity of Simultaneity’ (or duration), turned out to be just easily explained paradoxes or verbal illusions.  In reality, they resulted from the changed position of such moving observer relative to such light events which occurred during the transmission of such light signals toward the observer; that is to say, during the distance/time interval delay of the light signal at c over such changed distances.  (see Figure 26.3)  Thus, Einstein failed in such attempt to convince us (based on obviously contrived examples and fool’s logic) that the duration of time had slowed down on the train because of its relative velocity.  In effect, he failed to convince us that time on the moving train was ‘velocity dependent.’

Nevertheless, Einstein used such obviously invalid concept of the Relativity of Simultaneity (i.e. that the moving train was ‘relative velocity dependent’) in order to rationalize his way to substituting the Lorentz transformation equations for time in place of the Galilean transformation equations for time.  (see Chapters 26 and 27)  Once in possession of the Lorentz transformations, Einstein no longer needed to logically rationalize or justify his Relativity of Simultaneity (duration of time) concept.  All that he then needed to do was to interpret the Lorentz transformations for time as applying to a moving clock.  When the Lorentz transformations for time (the time t' on a moving train divided by a number less than 1) was applied by Einstein to this situation, they automatically made the above scenario mathematically true. 

Einstein called this artificially produced mathematical concept…‘Time Dilation.’  Thus, Einstein succeeded in this mathematical attempt to arbitrarily make the duration of time appear to be slower on the relatively moving train than the duration of time on the stationary embankment, based solely upon his coordinate measurements, his mathematical manipulations, his illogical interpretations, and the Lorentz transformations for time.

            In 1916, Einstein stated that “we must be able to learn something about the physical behavior of …clocks [in motion]…from the equations of transformation…”  (Einstein, Relativity, p. 41)

“As judged [by coordinates] from K, the clock is moving with the velocity v;…the time which elapses between two strokes of the clock is not one second, but     1/√1 – v2/c2 seconds, i.e. a somewhat larger time.  As a consequence of its motion the clock [in K'] goes more slowly than when at rest.”  (Id., p. 42)

 

Thus, again as with the Contraction of Distance (length), Einstein asserted that these coordinate and kinematic effects of time were physical and real, and literally true, not merely coordinate illusions and mathematical tricks that result from his illogical conventions for measuring, his artificial interpretations, and the Lorentz transformations for time.

            Based on the Lorentz transformations, Einstein’s above interpretations, and Einstein’s derivation of ‘Time Dilation,’ many current relativists (mathematicians and physicists) construe Einstein’s artificial and empirically invalid concept of Time Dilation literally and claim the following general consequences for Einstein’s time measurements.

            1.  “A clock is measured to go at its fastest rate when it is at rest relative to the observer.  When it moves with a velocity v relative to the observer, its rate is measured to have slowed down by a factor √1 – v2/c2.”[48]  (Resnick, 1968, p. 63)  In other words, conjectures Resnick, “moving clocks run slow.”[49]  (Id., p. 77)  On the other hand, if the clock and the observer were moving relatively toward one another, then a priori the time interval should reciprocally contract and the moving clock should be perceived to be increasing its rate of ticks per second.  (see Figure 28.7, and compare with Figure 28.5)

The relativists have also suggested highly contrived thought experiments as proof or experimental confirmation of the concept of ‘Time Dilation.’  For example, they cite a perpendicular application of Einstein’s ‘moving light clock’ thought experiment (Figure 28.12), which in reality is nothing more than another illustration of false assumptions made during the 1887 M & M experiment, and its absolute ether frame interpretation.  (see Figures 9.5 and 10.1)  The conclusions in Figure 28.12 are absolute, artificial, contrived and empirically invalid for the reasons stated therein and in Chapters 9 – 12.

            2.  “Although clocks in a moving frame all appear to go at the same slow rate when observed from a stationary frame with respect to which the clocks move, the moving clocks appear to differ from one another in their readings by a phase constant which depends on their location, that is, they appear to be unsynchronized.”  (Resnick, 1968, p. 64)  In other words, moving clocks appear to be out of synchronization with each other.  (Id.)  Resnick concluded that:

“this is just another manifestation of the fact that two events that occur simultaneously in the S-frame are not, in general, measured to be simultaneous in the S'-frame, and vice versa.”  (Id.)

 

Resnick asserted that the thought experiment illustrated in Figure 28.13 explains this theoretical phenomenon.  In fact, Figure 28.13 does not illustrate what Resnick concluded; it only illustrates what happens when observers change their positions relative to a light event and relative to each other.[50]  Another real reason for the above so-called paradox was explained by D’Abro:  the Lorentz transformations cause simultaneity to be “disrupted.”  (see D’Abro, 1927, p. 162)

Thus, we must again ask the question:  If such artificial kinematic results with respect to time were not valid based on contrived examples and simple logic when we were discussing Einstein’s Relativity of Simultaneity in chapter 26, how could they suddenly become physically valid based on Einstein’s arbitrary kinematic definitions, based on his dubious mathematical conventions and interpretations, and by reason of application of the Lorentz transformations?  The answer is:  they could not and did not.  Einstein’s distorted concepts of the Relativity of Simultaneity and of Time Dilation were always artificial, arbitrary, contrived, ad hoc and empirically invalid.

Another question:  What is the theoretical magnitude of Einstein’s slowing down of the rate of time (duration)?  It is the same magnitude for time that Lorentz found in 1904.  (Chart 16.2B; Figure 16.3)  But Lorentz dismissed them as merely an artifact or mathematical ‘aid to calculation.’  (Goldberg, p. 100)  In Einstein’s theory, this magnitude resulted from dividing the ether ‘true time’ factor t + vx/c2 by the factor        √1 – v2/c2.  Similarly, in Lorentz’s theory, it results in the new factor 1/√1 – v2/c2.  (see Resnick, 1968, pp. 63 – 65)

When either Einstein’s factor or Lorentz’s factor for time is plotted on a graph, it results in an entirely different curve of magnitudes for ‘Time Dilation’ (see Figure 16.2B), than the curve of magnitudes for ‘Length Contraction.’  (see Figures 16.2A and 28.15)  The two sets of magnitudes are not at all correlated, reciprocal, equivalent, or symmetrical.  (also see Resnick’s somewhat similar illustrations, Id., p. 65)  How can the Length Contraction of a body at velocity v be so different than the Time Dilation on the same body at the same relative velocity v?  Again, this dramatic inconsistency is a major internal contradiction for Einstein’s Special Theory.  (see Memo 28.14)

It is obvious that all of the above contrived attempts by Einstein (using both logic and mathematics) to make the duration of time appear to vary on different reference frames depending upon their relative velocity was nothing more than an artificial attempt to justify his impossible second postulate for the absolutely constant velocity of light at c relative to any body in the Cosmos moving linearly at any velocity, all at the same instant.  In other words, to justify his confusion and false premise about Maxwell’s law for the transmission velocity of light at c in a vacuum, which we described in the Preamble.

In this regard, recall that in early 1917, Einstein wrote the following:

“The law of light propagation is the same, whether the sun or the projected body is chosen as the body of reference.  The same ray of light travels at 300,000 kilometers per second relative to the sun and also relative to the body projected at 1,000 kilometers per second.  If this appears impossible, the reason is that the hypothesis of the absolute character of time is false.  One second of time as judged from the sun is not equal to one second of time as seen from the projected body…It turns out that one can define time relative to this body of reference such that the law of the propagation of light is obeyed relative to it.”  (Einstein, early 1917, The Principle Ideas of the Theory of Relativity [Collected Papers of Albert Einstein, Vol. 7, pp. 4 – 5, Princeton University Press, New Jersey]) 

 

Thus, Einstein’s concepts of the Relativity of Simultaneity and Time Dilation were nothing more than his ad hoc attempts to redefine time relative to a body of reference such that his impossible law of the propagation of light is obeyed relative to it.[51]  Please re-read the Preamble at this juncture for a complete understanding of what was really going on.

 

F.  Einstein’s Clock or Twin Paradox

            After Einstein described his concept of Time Dilation, he claimed that it resulted in a “peculiar consequence,” which has since been referred to as the ‘Clock Paradox.’

“If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by ½tv2/c2…”  (Einstein, 1905d [Dover, 1952, p. 49])

 

For the last century, uncountable scientists, mathematicians and others have attempted to mathematically solve this so-called paradox, but to no avail.  Professor Dingle even dedicated an entire chapter in his 1972 book to its solution, but only ended with an unanswerable question.[52]  (Dingle, 1972, pp. 185 – 201) 

It turns out that Einstein’s clock riddle is neither a paradox nor is it solvable based upon ordinary logic.  It is only a paradox or an insolvable riddle if one believes that ‘Time Dilation’ (vis. that a clock’s rate depends upon its state of motion) is a real empirical phenomenon. 

Einstein’s clock riddle is not a paradox to the author, because it is based upon the application of the Lorentz transformations.[53]  Remember that Einstein equates simultaneity with clock synchronization:  “every definition of clock synchronization is a definition of simultaneity, and vice versa” (Jammer, 2006, p. 120), and that D’Abro told us:  the Lorentz transformations cause simultaneity to be disrupted.  (D’Abro, 1927, p. 162)  Ergo, the Lorentz transformations also cause clock synchronization to be disrupted.  This is the simple answer. 

Nor is such riddle logically solvable, because (as we have demonstrated) Relativistic Kinematics and Time Dilation are ad hoc, artificial, arbitrary, internally inconsistent and contradictory concepts.  In other words, they are illogical, empirically invalid and totally meaningless.  How can a riddle be logically solvable with meaningless and illogical concepts?

A relativistic explanation might go something like the following.  When clock A begins to move at velocity v from A to B, it becomes a moving inertial system with respect to B.  Therefore, according to Special Relativity, B may apply the Lorentz transformation for time to it, which algebraically makes the duration of clock A’s ticks slow down with respect to B.  Thus, when clock A reaches point B, the hands of clock A do not mathematically or physically synchronize with the hands of clock B.  But who cares?  Such an explanation is also meaningless because Special Relativity is meaningless. 

            Einstein also conjectured that the same result occurs where clock A moves in a continuous closed curve back to point A.  (Einstein, 1905d [Dover, 1952, p. 49]) 

“Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical condition.”[54]  (Id., pp. 49 – 50)

 

This variation of Einstein’s Clock Paradox is often called the ‘Twin Paradox,’ where clocks are replaced by identical human twins.  One identical twin leaves the Earth on a long high-speed circular trip, but a priori he returns to Earth visibly younger than his stay-at-home twin due to Time Dilation.[55]  This so-called paradox suffers from the same theoretical problems and defects as the Clock Paradox.  Nevertheless, atomic clocks have repeatedly been carried by eager relativists on jets and satellites around the Earth in order to test Einstein’s concept of ‘Time Dilation.’  (see Chapter 38) 

 

G.  Conclusions Concerning Relativistic Kinematics

What was the empirical basis for Einstein’s new kinematics?  There was no empirical basis, whatsoever.  It could be said that Einstein’s new kinematics was the indirect consequence of all of his ad hoc relativistic concepts that preceded it.  Einstein’s concepts of Relativistic Kinematics were not even a direct mathematical consequence of his Lorentz transformations, because such transformations took a good deal of invalid assumptions, mathematical manipulation and imaginative interpretation by Einstein in order to construct them.  Einstein even had choices between several different dubious combinations of manipulations and interpretations; therefore his final choice was completely arbitrary and ad hoc.

Einstein repeatedly stated, asserted, claimed or implied that his twin concepts of the Relativity of Simultaneity (time intervals) and the Relativity of Distance (length) were physical concepts with physical and empirical implications.  (Chapter 26)  As we have already demonstrated in this chapter, he also repeatedly stated, claimed or implied that his mathematical kinematic concepts of ‘Length Contraction’ and ‘Time Dilation’ were physically real and had empirical implications.  Einstein needed this physical and empirical connotation in order to attempt to explain and justify:  1) the baffling M & M null results with a physical contraction of the longitudinal arm of Michelson’s apparatus (Einstein, Relativity, pp. 58 – 59);  2) his impossible second postulate where he claimed an absolutely invariant velocity for light at c relative to everything;  3) his explanation of the paradoxical results of the 1851 Fizeau experiment (Id., pp. 43 – 46); and  4) many other mysterious physical phenomena and relationships.  Most of Einstein’s relativistic followers seem to believe that such ad hoc kinematic concepts are indeed physically real, as evidenced by the many so-called ‘experimental confirmations’ of Special Relativity and his relativistic kinematics, which are described in Chapters 36, 37 and 38 of this treatise.

On the other hand, some relativists now acknowledge that all of Einstein’s bizarre kinematic concepts (including Length Contraction and Time Dilation) are only mathematical consequences, by-products, illusions, artifacts, or effects caused by the methods that Einstein used to measure space, time and motion.  For example:  they are not statements “about the physical nature of clocks” or rods.  (Goldberg, p. 120)  “The contraction is only a consequence of our way of regarding things and is not a change of a physical reality.”  (Born, p. 254)   No actual shrinkage [of the rod] is implied, [there is] merely a difference in measured results.”  (Resnick, 1992, p. 472)  Resnick goes on to explain in detail:

“Like time dilation, length contraction is an effect [of measurement] that holds for all observers in relative motion.  Questions such as ‘Does a moving measuring rod really shrink?’ have meaning only in the sense that they refer to measurements by observers in relative motion.  The essence of relativity is that results of measurements of length and time are subject to the state of motion of the observer relative to the event being measured and refer only to measurements by a particular observer in a particular frame of reference.  If different observers were to bring the rod to rest in their individual inertial frames, each would measure the same value for the length of the rod.  In this respect, special relativity is a theory of measurement that simply says ‘motion affects measurement’.”[56]  (Resnick, 1992, p. 480)

 

            If this is all that Special Relativity is, then what is all the fuss about?  Why are so many books written which laboriously try to explain it in physical and empirical terms to baffled readers, including scientists?  Why are rockets launched into space with expensive experiments intended to physically prove its concepts (i.e. that moving clocks run slow)?  Why is it taught to college physics students as if it had any real substance or physical meaning?  Why is Einstein idolized as a great genius for having concocted it?

Einstein’s concepts of varying kinematics, varying magnitudes, and varying measurements in different reference frames depending upon relative velocity even appear to contradict his postulate of relativity:  the invariance of physical laws in different reference frames.  Surely the duration of time in the Cosmos and the distance between two moving bodies of reference are laws of nature.  Yet Einstein, in his Special Theory, claimed that the magnitude of both of these phenomena were relative velocity dependent, and dependent upon the body of reference chosen.  (Einstein, Relativity, p. 60)  If they are relative velocity dependent, and dependent upon the body of reference chosen, then this violates Einstein’s own first postulate:  the Principle of Relativity.  In 1917, Einstein defined the Principle of Relativity as follows:  the laws of nature are independent of the state of motion of the body of reference.”  (Einstein, 1917a)  Does any of this make any sense?

In Einstein’s Special Theory, kinematic coordinate measurements of an object in one frame are simultaneous, proper, non-distorted (geometrical) and symmetrical, whereas kinematic coordinate measurements of the same object in the other frame are non-simultaneous, non-proper, distorted (kinematical, contracted or dilated), and asymmetrical.  In other words, Einstein’s laws of physical measurement are frame or velocity dependent.  They are not invariant in different reference frames.  Similarly, the magnitudes of contraction and dilation vary differently and dramatically for the same object in the same reference frame relative to different frames of reference, depending upon an arbitrary choice of reference frame by the observer.  (Einstein, Relativity, p. 60; also see Figure 28.15)  Again, does any of this inconsistent chaos make any sense? 

The simple and logical classical laws of kinematics and mechanics, which (prior to Special Relativity) were invariant, intuitive and symmetrical, are now chaotic relativistic laws…and for what purpose?  So that space and time measurements can be claimed to be consistent and mathematically compatible with Einstein’s artificial and impossible velocity of light at c relative to any body of reference.  (see D’Abro, 1927, 1950, p. 162, the Preamble, and Chapter 21)  Restated by Cantrell:

“Over time the second postulate has been reinterpreted to mean that all observers, regardless of their own velocity, see light propagating always at the same speed (in vacuum).  [Coordinate] lengths shorten and time slows so that the computed velocity (i.e., length [distance] divided by time) is always constant.  The paradoxes and problems created by this clever little trick are endless.” 

(see ‘Special Relativity’ at www.infinite-energy.com/iemagazine/issue59)

 

The ad hoc and impossible relativistic end does not justify its artificial, ad hoc, disruptive and chaotic relativistic means.



[1] In other words, Einstein asserted that his empirically invalid twin concepts (the Relativity of Simultaneity and the Relativity of Distance) which are also based on false premises are valid.  But see Chapters 26 and 29 in this regard.

[2] At this point, Einstein assumed that his own twin concepts (the Relativity of Simultaneity and the Relativity of Distance) were accepted as valid.

[3] In other words, Einstein was asking:  How must we modify the classical addition of velocities so that Einstein’s impossible absolutely constant velocity of light at c could be mathematically valid relative to any linearly moving reference frame?

[4] Einstein derived from his Lorentz transformations a new relativistic formula for the composition of velocities in Section 5 of his 1905 Special Theory, which also mathematically solved Einstein’s non-existent problem.  (see Chapter 29)

[5] Both of Einstein’s aforementioned substitutions were completely ad hoc.

[6] In other words, every other ray of light in the Cosmos will mathematically have the same absolutely constant velocity of c with respect to any reference body in the Cosmos, regardless of such body’s linear velocity v relative to the light ray.  This mathematical result is, of course, a logical and empirical impossibility.

[7] This last sentence demonstrates that Einstein always knew what the desired mathematical results of the Lorentz transformations would be, because they were contrived according to his point of view.

[8] This law is, of course, Einstein’s impossible second postulate concerning the absolute invariance of light at velocity c relative to anything, anywhere, at any time.  (see Chapter 21E)  It is not Maxwell’s law for constant transmission velocity of a light ray relative to its medium of a vacuum.

[9] In turn, this mathematical process artificially disrupts the simultaneity of spatially separated events which results in Einstein’s Relativity of Simultaneity concept.  (see D’Abro, 1927, 1950, p. 163)

[10] Including the relativistic Doppler effects, relativistic mass, relativistic momentum, and relativistic energy.  (see Chapters 30 and 31)

[11] This, of course, is not just a slightly different measurement of space and time, nor is it a purely mathematical problem.  Why?  Because such arbitrary mathematical manipulations of kinematics artificially change the natural relative propagation velocity of light and vastly change much of empirical physics.

[12] No matter how artificial, meaningless or empirically invalid.

[13] How convenient for Einstein’s second postulate!

[14] One might ask:  what relevance do apparent mathematical measurements (or illusions) have with respect to physical reality?  The answer, of course, is none!

[15] However, such approximations cannot be made by Lorentz transformations or by assumptions gleaned from Special Relativity, because they will only distort the approximations.

[16] In other words, the common velocity of the frame and the object.

[17] A ‘rest frame’ is sometimes also referred to as a ‘proper frame.’  (Resnick, 1968, p. 63)

[18] Nevertheless, as we discovered in Figure 27.1 and Memo 27.2, Einstein’s ‘proper’ measurements are irrelevant to what is empirically occurring.

[19] Although these ‘proper’ concepts are attributed to Einstein, he never used the term ‘proper’ in his 1905 paper.  Minkowski used the term ‘proper’ several times in his 1908 theory of Spacetime when referring to Einstein’s concept of measuring time, so perhaps Minkowski is the source of the terminology.

[20] Lorentz never made such an interpretation.  He merely manipulated his mathematics ad hoc to arrive at the required equation for a contraction (L = L0 √1 – v2/c2).  (see Chapter 16B)

[21] Lorentz’s methodology involving multiplication was ‘absolute’ because it involved ‘ether’ and absolute motion, whereas Einstein’s interpretation involving multiplication theoretically appeared to be ‘relativistic’ because it only involved relative motion.

[22] See Smolin, pp. 227 – 229.

[23] Einstein’s coordinate expansion of length (which he changed by multiplication) remained consistent with his interpretation of the expansion (or dilation) of time and aided in such interpretation.

[24] Lorentz’s methodology involving division (T = T0/√1 – v2/c2) and his interpretation thereof (with respect to stationary ether) was quite different and absolute, rather than relativistic.  (see Chapter 16B)

[25] Also see Resnick, 1968, p. 65 for similar asymmetrical curves for Length Contraction and Time Dilation.

[26] If Einstein’s two reference frames had been approaching each other, then reciprocally there should have been an expansion of distance and a contraction of time (duration).

[27] In Chapter 12 of ‘Relativity,’ Einstein implied that his Lorentz transformations described, quantified and confirmed his twin concepts of the Relativity of Simultaneity (time) and the Relativity of Distance (length), the same concepts which he used to justify substitution of his Lorentz transformations and which he was now attempting to mathematically validate with his Lorentz transformation equations, relativistic kinematics, and further interpretations.  Is such bootstrap and circular reasoning convincing?

[28] Lorentz had the wildly speculative idea that molecules and atoms react like ‘electrical forces’ and thus they can change the ‘form and dimension’ of solid matter as well.

[29] This type of direct physical measurement was later called a ‘proper’ measurement.

[30] This indirect and imprecise relativistic method of measurement by a relatively moving observer (measurer) was later called a ‘non-proper’ measurement.

[31] The greater the magnitude of v the greater will be the coordinate illusion of changed length.

[32] In addition to coordinate measurements, Einstein also measured the length of the distant object using clocks and light signals.  (Einstein, 1905d [Dover, 1952, pp. 41 – 42]; see Chapter 26B)

[33] Again, this artificial measurement of length was merely a result of Einstein’s time delayed coordinate measurements.

[34] Lorentz, in his April 1904 contraction theory, made substantially similar assertions concerning the “dimensions” and “deformation” of moving spheres into “flattened ellipsoids with their smaller axes in the direction of motion.”  (Lorentz, 1904 [Dover, 1952, pp. 21 – 22])  Again, this is another example of Einstein in 1905 using Lorentz’s April 1904 treatise as his guide.

[35] A skeptical reader might assume that Einstein was trying to mislead and fool him.

[36] In other words, such objects have no dimension of length at all.

[37] Both of Einstein’s 1905 ad hoc concepts of the Relativity of Length and Length Contraction were axiomatic, because he did not present any empirical examples as proof that they existed.

[38] For the mathematical method, manipulation or trick (multiplication) by which Einstein turned the expansion of a rod into a contraction, see Figure 28.3.

[39] Whereas, Einstein had previously failed in such attempt using only empirically invalid assumptions and fool’s logic.  (see Chapter 26)

[40] On the other hand, if the body and the stationary observer were moving relatively toward one another, then a priori the length of the moving body should be reciprocally perceived to be expanding in length.  (see Figure 28.6, and compare to Figure 28.3)

[41] One reason is because it theoretically explains the M & M paradox.  Length Contraction is also theoretically useful in particle physics, quantum mechanics, quantum field theories, general relativity, cosmology, and many other relativistic disciplines and concepts.  What do all of these facts tell the reader about the empirical validity of these other relativistic disciplines?

[42] This implied deduction of a length contraction only theoretically occurs because Fitzgerald, Lorentz and Einstein incorrectly asserted that this was the only possible explanation for the M & M null result.  (see Einstein, Relativity, pp. 58 – 59)

[43] We now know the real reasons for Michelson’s null results, and they have nothing to do with any distance contraction or time dilation.  (see Chapters 9 – 12)  For these reasons, Einstein’s longitudinal light clock thought experiment was also based on false premises.

[44] Later this method of measuring a time interval with one clock was called a ‘proper time’ measurement.

[45] This imprecise method of measuring a time interval using two separated non-synchronized clocks was later called a ‘non-proper’ measurement.

[46] Again, this artificial coordinate measurement of the duration of time was merely a result of Einstein’s time delayed coordinate measurements.

[47] Einstein also claimed in 1916 that two simultaneous events (lightning flashes) were not perceived to be simultaneous by a relatively moving observer who was equally separated from such events when they occurred.  (see Chapter 26)

[48] Resnick, of course, makes numerous dubious assumptions, illogical interpretations and algebraic manipulations in order to reach this conclusion.  Notice his qualifying reference of the word ‘measured.’  ‘Measured’ means Einstein’s ridiculous 1905 time-delayed method of measuring moving coordinates.

[49] Resnick asserted that “the phrase ‘moving clocks run slow’ means that a clock moving at a constant velocity relative to an inertial frame containing synchronized clocks will be found to run slow when timed by those clocks.  We compare one moving clock with two synchronized stationary clocks.”  (Resnick, 1968, p. 77 – 78)  This artificial methodology and Einstein’s artificial measurements will always produce the relativists’ desired result.  (see Chapters 25 and 26)

[50] In Figure 28.13, it is asserted that A will assume that the light event occurred at an earlier time than A' and B', and that A' and B' will assume that the light event occurred at an earlier time than B.  So do the disagreements of such observers about the order of occurrence (causation) of the light event have any meaning as to when the light event actually occurred?  Of course not.  It is all a matter of the relative times of causation and observation at different relative positions.  The same results would occur if there was no relative motion and the various observers were stationary at their positions of observation.  To characterize the above disagreements as an example of the Relativity of Simultaneity is an affront to our intelligence.  (see Goldberg, pp. 115 – 116)

[51] Similarly, Einstein’s concepts of the Relativity of Distance and Length Contraction were little more than his ad hoc attempt to keep the changing distances between two inertial frames of reference mathematically consistent with his concept of Time Dilation.

[52] In 1913, von Laue described this paradoxical state of affairs, as follows:  “How could ‘purely kinematical considerations’ distinguish between a moving clock and one at rest?”  (Miller, p. 246)  Von Laue obviously believed that Special Relativity and ‘Time Dilation’ were valid concepts.

[53] Sklar asserts that the ‘clock paradox’ is “not a paradox at all…but simply a surprising result of the theory.”  (Sklar, p. 267)

[54] If this conjecture actually occurs it must happen because of gravity, acceleration, altitude, centrifugal motion, a vacuum or some other empirical reason; not because of relative velocity or Time Dilation.  (see Chapter 38)

[55] In 1911, Einstein explained this phenomenon for the traveling twin’s asymmetric aging:  “the lengthy time of the journey was a mere instant, provided the motion [was]…approximately the speed of light.”  (see Miller, p. 248)  Harrison claims that the ‘twin paradox’ is explained by a Spacetime diagram.  (see Figure 33.4B)

[56] But, again, remember that Einstein’s theory of measurement is artificial and ridiculous, because it depends upon the 1905 time delay of a human observer trying to measure moving coordinates with the laborious and imprecise hand and eye method.