Introduction
instein's
"theory" of relativity is invalid in its entirety because of reasons
inherent in it. It is destroyed at once by the very formulae which
Einstein derives in the stationary system K when discussing the
thought experimenthe
has presented in §2 of [1],
pivotal for that theory.
These formulae are naively aimed at proving the crucial claim, which
the entire theory [1]
is based on, namely, that the same two clocks which are synchronous
for the observers at rest with these clocks in the stationary system
K are nonsynchronous (which according to the theory is a judgement
of the observers in K) for the observers at rest with these same
clocks in the moving system k. That claim Einstein has clothed in
words in the following general way:
"So we see that we cannot attach any absolute signification
to the concept of simultaneity, but that two events which, viewed
from a system of coordinates, are simultaneous, can no longer be
looked upon as simultaneous events when envisaged from a system
which is in motion relatively to that system." The above
claim, later called "relativity
of simultaneity" by Einstein, which is the very heart of
the theory, is untenable. This causes the collapse of Einstein's
theory of relativity altogether. There is nothing in Einstein's
theory of relativity, once "relativity of simultaneity"
is proven invalid, which would remain or would be of any use for
physics or science in general.
Prerequisites
To understand the failure to prove "relativity
of simultaneity" it should first be clear that the
claim mentioned in [1]
is based solely on the derivations carried out by the observers
in the stationary system K. These observers have at their disposal
only the parameters in their own system K. Therefore, the conclusions,
both in what we denote here as the first part of the claim, referring
to the stationary system K, and in the second part of the claim,
referring to the moving system k, stem only from these parameters
in K.
Further, to aid in achieving the goal of the theory in [1],
namely, to enable the observers in K make a conclusion as to what
the observers in k see, which the conclusionmaking observers
in K have no way to know directly, Einstein assumes and expresses
explicitly the obvious fact that spatially coinciding clocks are
synchronous in the stationary system K:
"We imagine further that at the two ends A and B of the
rod, clocks are placed which synchronize with the clocks of the
stationary system, that is to say that their indications correspond
at any instant to the "time of the stationary system'' at the
places where they happen to be. These clocks are therefore "synchronous
in the stationary system"."
In this way the observers in the stationary system K can conveniently
tell what the readings are of any clock which happens to coincide
spatially with a clock of known reading in their system K since
these coinciding clocks will show the same time equal to the known
time.
Theory
Once the above is understood well, one is ready
to proceed with the analysis, which reveals conclusively that the
attempt to prove the claim
for "relativity of simultaneity"is a failed attempt.
In ruminating about the failure of the mentioned claim
one should not be mislead by the fact that what we denoted here
as its first part, stating that
"observers in the stationary
system would declare the clocks to be synchronous"
is certainly confirmed by the mentioned formulae for completeness
shown below in a general form), derived in K  it is seen that
the clocks positioned in the stationary system K, where the ends
A and B of the moving rod happen to be in K, are synchronous; the
formulae show that both clocks in K read the same time
on their faces which means, in agreement with the abovequoted first
part of the claim, that these
clocks are synchronous in K:
and
where (…) denotes either ,
or .
Disappointingly, however, the second part of the claim,
which, recall, is a claim by the conclusionmaking observers
in K, stating that
"Observers moving with the
moving rod would thus find that the two clocks were not synchronous"
is incorrect because the clocks discussed in
the quote, moving with the moving rod (the clocks in the moving
system k, that is), coincide spatially with the same clocks in K
which, as just discussed, the above formulae show are synchronous
in K, both showing time
on their faces. Therefore, the clocks placed at end A and at end
B of the rod, moving with the moving rod, also both show time
on their faces, that is, they are synchronous. Therefore, contrary
to the statement in the above quote, observers moving with the moving
rod would thus necessarily find that the two clocks were synchronous.
In summary, the truth is that two synchronous clocks in K remain
synchronous also in k which means that, contrary to Einstein's impression,
simultaneity is absolute.
As seen, this truth is confirmed by the formulae given by Einstein
in §2 of [1],
even if they are presented in most general form, as is done above,
independent of whether or not the second postulate is considered
as valid or independent of whether or not the source of light is
at rest with respect to the stationary system (that is, is immovably
attached to the moving rod).
Thus, purportedly one of the greatest discoveries of all time called
"relativity of simultaneity" turns out to be no
discovery at all but a most trivial mistake due to incorrect analysis
of elementary formulae from Newton's mechanics. As seen, the truth
these formulae contain, which can be revealed when said formulae
are properly analyzed, is that simultaneity is absolute. The conclusion
contradicting absoluteness of simultaneity, that is, the conclusion
for the "relativity of simultaneity", is arrived
at only if the mentioned truth following from the mentioned initial
condition, namely, that the valid mechanics in K is the Newton's
mechanics, is deliberately "forgotten" and the analysis
is based solely on another initial condition, postulating that
is the universal velocity of light. Thus, by postulating an initial
condition such as the ubiquitous
Einstein reaches a conclusion in contradiction with a conclusion
following from another, inevitable at that, initial condition, namely,
the obvious validity of Newton's mechanics in K. Clearly, it is
utterly unacceptable to postulate anything that would lead to a
contradiction with elementary truths about a system of reference.
The truth cannot be overruled by deciding to postulate something
which would lead to overruling that truth.
Summary
The above concludes the analysis  Einstein's
theory of relativity has been definitively proven to be invalid
in its entirety due to reasons internal to it. Thus, any further
discussion of that theory is superfluous and will bring nothing
new to the above categorical proof for its invalidity.
Any further considerations of that theory would be reasonable for
educational purposes only and/or for examining the ramifications
of its invalidity  the invalidity of Einstein's theory of relativity
also causes any other theory or theories such as string theories,
cosmology etc. which are based on it to be invalid.
The above also proves that Einstein's theory
of relativity could have never possibly been nor can ever be shown
experimentally or otherwise to be valid. All claims to
the opposite are either due to undetected errors or are due to unscrupulous
manipulation of the public opinion.
Further Educational Exercises
In the spirit of exercise one may further want
to analyze the abovementioned internal contradiction between the
two initial conditions, one inevitable (Newton's mechanics valid
in K), the other postulated (velocity of light
"independent of the state of motion of the emitting body".
That internal contradiction expresses itself further in obviously
unacceptable contradictiory statements about the same objects in
one and the same system. Those contradictory statements, following
from Einstein's theory of relativity, about the same objects in
the same system, can serve as yet another, although redundant, proof
for the invalidity of said theory.
The culprit in question leading to the discussed internal contradiction,
namely, the postulated velocity of light
"independent of the state of motion of the emitting body",
has enabled Einstein to carry out his manipulation, as said, by
seemingly forgetting the fact shown above that his very formulae
prove persistent synchronicity in all systems of two clocks synchronous
in a given system. Recall, this directly follows from the fact explicitly
acknowledged as well by Einstein himself [1]
that the valid mechanics in the stationary system K where the derivations
are carried out is the Newtonian mechanics.
Before giving links to arguments regarding the culprit in question,
notice a more than telling fact which in itself can bring understanding
as to why the second postulate is unacceptable. The culprit (the
discussed second postulate) is the reason that the relationship
derived in K between
and
can only be the inequality
and can never be an equality. Therefore, because of the synchronicity
in K of spatially coinciding clocks, the only conclusion the observers
in K can arrive at is that the only relationship between
and
in k can also only be the inequality
and can never be an equality in k.
However, for a light source moving with the rod, although the condition
is obeyed, the inequality
is not possible to be true in k. Indeed, recall from the
above that the clocks at A and B in k are synchronous which
makes it impossible for the inequality
to be true in k when
(synchronous clocks can only exhibit the equality
when the velocity of light is
)
On the other hand, for a light source at rest with K the relationship
derived in K between
and
is indeed the inequality
and therefore, because of the synchronicity in K of spatially coinciding
clocks, the relationship between
and
in k is indeed the inequality .
Recall again from the above, however, that the clocks at A and B
in k are synchronous, which makes it impossible for
to be the velocity of light in k when the true relationship
in k, as is in this case, between
and
is the inequality
(velocity of light cannot be
when synchronous clocks exhibit the inequality
).
Therefore, because of the aboveproven persistent synchronicity
in all systems of two clocks synchronous in a given system, following
from Newton's mechanics valid in K, joint validity of the
inequality ,
which Einstein's theory of relativity always inevitably derives
in k and the equality
in k can never be achieved. As seen above, for a light source
at rest with k, whereby ,
the relationship between the time intervals
and
read from the faces of synchronous clocks in k must necessarily
be the equality ,
which Einstein's "theory" of relativity can never derive for k.
On the contrary, for a light source moving with respect to k synchronous
clocks in k can exhibit the inequality
in k if and only if the velocity of light is expressed by the inequality
.
It may be more convenient for some to understand the untenability
of the second postulate by following the links given below, presenting
arguments which are essentially variations of the same abovediscussed
arguments:
The second postulate leads to contradictory
statements about the synchronicity of two clocks in the same system
(moving system k).
The formula
(respectively )
from §2 of
Einstein's 1905 paper violates directly
the second postulate.
One should note also that the failure of Einstein's "theory" of
relativity is only indirectly connected with the nonphysicality
of the Lorentz transformations. Einstein's theory of relativity
cannot derive these transformations despite the impression created
that it does. Also, the Lorentz transformations are by no means
synonymous with Einstein's theory of relativity as is often presented
to be the case. It should be noted that unlike Einstein's theory
of relativity, no parts of which make any sense, Lorentz transformations
are perfectly mathematically consistent. The problem is that they
lack physical meaning, which can be proved by arguments only tangentially
similar to the arguments invalidating Einstein's theory of relativity.
Further, as can be
seen at once, Einstein's theory of relativity, specifically
its first postulate, is in an unresolvable conflict with the Lorentz
transformations. As a detail, the latter means that Einstein's theory
of relativity cannot derive the massenergy relationship, popularly
known as E = mc^{2},
despite the vigorous propaganda insisting that it is Einstein's
theory of relativity that has derived that massenergy relationship.
References
1.
Einstein A., The Principle of Relativity, Dover, 3765, 1952  English
translation of the original: Einstein A., Annalen der Physik, 17,
891921 (1905).
