Einstein believes that synchronization cannot be divorced from communication. It is by separating these processes that synchronization becomes possible. None of his arguments - about simultaneity, about the Michelson-Morley Experiment, about the Lorentz Transformation, and about the 'red shift' is free of ambiguities and false inferences.
This much is certain: His two basic principle of Special Relativity Theory (SRT) are contradictory. The result of the Michelson-Morley experiment contradicts his second principle, the assertion that the speed of light is independent of the motion of the source.
There is no such evidence against Einstein's first principle. The first principle implies the symmetry of source and receiver as far as movement is concerned in two inertial systems. For the Doppler effect this is shown to yield a formula that depends only on the separation rate of source and receiver. While this is true as well under SRT, the formula under Newtonian thinking yields a dramatically different result for velocities approaching the speed of light.
The important consequence of this for cosmology is that our inferences about the age and size of the universe, based on Einstein's thinking, are about a factor of two too large. This in turn means that the density of the universe is almost a factor 10 greater than currently estimated.
There are contradictions, false inferences, imprecise thought experiments, ambiguous concepts, and questionable reasoning sprinkled throughout the two books on relativity that Einstein published. The mathematics is not in question, only the relation of the mathematical models to physical reality. The main points that should be noted are listed below:
It is shown that the principle that underlies General Relativity is contrary to the fact that the laws of motion are different for a body accelerated by a specific force, as opposed to a general force (gravity).
The concept 'simultaneity' has two distinct and separate meanings that Einstein did not perceive. There is event simultaneity and observer simultaneity. The former is relative, but it is the latter that is required for SRT. It was shown that using the Doppler effect in two directions allows for synchronization after communication. His errors in reasoning led him to the erroneous conclusion that time is relative.
The Lorentz Transformation was derived using both Einstein's assumptions as well as those of Lorentz. The transformation is shown to be correct only for a 'round trip', not for a single direct path as is required for Special Relativity.
The theory of relativity leads to an interpretation of recent astronomical data that puts the age of the universe at over 12 billion years. This is based on an interpretation of the Doppler shift based on SRT. Without SRT, a reasonable interpretation of type 1A supernovae is obtained by adding the age when these stars were formed, (near the beginning of time), to the life time of stars whose supernovae are now visible, (about three billion years), and adding the time for the light to reach us (based on the minimum red shift, also about three billion years).
This gives us an estimate about half that age. That is the estimate we get if we take 'time' as universal, and the speed of light as constant, only as measured by an observer at rest with respect to the source. The Doppler effect, under Newtonian thinking, related to the data of type 1A supernovae, suggests that the initial expansion velocity of the universe at the time of the 'big bang' was nearer to half the velocity of light, c/2, than to c.
There have been numerous attempts to justify Special Relativity using experimental results in atomic physics. Here are my thoughts about a meson experiment, that can be found on page 103 of a basic textbook "Raum - Zeit - Relativitaet" by Prof. Roman Sexl and Prof. Herbert Schmidt published in 1978.
The experiment conducted at CERN by T.Alvaeger, et,al. [published in Phys. Lett. 12, 260 (1964)] describes how an energetically accelerated proton produced a pi meson traveling at almost the speed of light. This meson vanishes after less than a thousand trillionth of a second, and is then succeeded by two gamma rays. They assume that the resulting photons are propagated at the speed c in the inertial system defined by the disappearing meson, but were, in fact, observed to travel at speed c in the inertial system defined by the cloud chamber.
I have no qualms at all about the result of the experiment only with the way it is used. Let me explain: the mathematics is so basic that it is painful to have to attack it. But even addition in a mathematical context does not necessarily make sense in a physical context. For example, I can certainly add the speed of a water skier to the speed of the boat that is towing him, or I can, in the case of a relay race, add the speed of the first runner to the one that takes his place, but neither of these additions makes much sense physically.
In the case of the experiment cited here, we have a meson that has an ultra short lifetime, and in expiring, produces photons that take its place. The meson is not an enduring platform, such as a train, on which a source is located that emits light. It resembles more the case of the relay runners. So adding these two velocities is comparable to adding the two speeds of the relay runners. The ballistic model of light propagation envisions an enduring platform in motion with respect to an underlying coordinate system and a source of light on this platform, not a hand-off, from a transient signal.
It appears that what we have here is a case of an erroneous addition in the numerator, which is than corrected by an erroneous 'relativistic correction' (the gamma factor!) in the denominator. A case of two wrongs that cancel each other to produce the empirical result that was observed. Thus, the experiment in no way confirms SRT.