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. v_{1} + v_{2} = v_{3}. (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 *c*t [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 – v^{2}/*c*^{2},
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 21^{st} 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*.*Id*.

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 – v^{2}/*c*^{2} √1 – v^{2}/*c*^{2},

__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 – v^{2}/*c*^{2} of a meter” in K. (Einstein, *Relativity*, p. 41)
Therefore, if the relative velocity is v = 60% of *c*, then 1 meter times √1 – v^{2}/*c*^{2} = 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 – v^{2}/*c*^{2}
seconds.” Therefore, if the relative
velocity is v = 60% of c, then 1 second divided by √1 – v^{2}/*c*^{2} = 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 = L_{0}√1 – v^{2}/*c*^{2}) and all of the magnitudes
of Time Dilation (expansion of time)

(T
= T_{0} ÷ √1 – v^{2}/*c*^{2})
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 – v^{2}/*c*^{2}
could be interpreted to describe the quarter arc of a circle or the quarter
geodesic distance of a sphere, √1 – x^{2}/y^{2}. (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 – v^{2}/*c*^{2}.”[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 – v^{2}/*c*^{2},
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 – *v*^{2}/*c*^{2} 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 – *v*^{2}/*c*^{2} = 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 – *v*^{2}/*c*^{2}; 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 – v^{2}/c^{2}, 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 [^{2}/*c*^{2}
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 – *v*^{2}/*c*^{2}
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 – v^{2}/*c*^{2}.”[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*.

“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/*c*^{2} by the factor √1 – v^{2}/*c*^{2}. Similarly, in Lorentz’s theory, it results in
the new factor 1/√1 – v^{2}/*c*^{2}. (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*.__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 ½*tv*^{2}/*c*^{2}…” (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-

**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 = L_{0} √1 – v^{2}/*c*^{2}). (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 = T_{0}/√1 – v^{2}/*c*^{2})
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 [

[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)

[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)

[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.