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Asymmetry in Special Relativity

Just as we did in RT, with our perpendicular and parallel ray photon 
clock, Einstein considers the round trip of the light beam for the purposes 
of learning what the time and length contractions must be.  It is the round 
trip consideration that addresses the synchronicity aspect of the Principle
of Relativity.

In his derivation, Einstein proceeds to relate k's coordinates and times to 
K's by regarding each of them as obtaining  the same measured speed of 
light, in both positive and negative directions.

In the course of his treatment, Einstein concludes that a clock that 
changes inertial frames, though once synchronized with its mate, will 
show a lesser time reading than the other clock upon reuniting. This 
should indicate to him an asymmetry of an absolute nature, since such an 
absolute difference can come about only with an absolute difference of 
clock rates.  Thus he ought to regard mu and lambda, which are identically our 
t1 and t2, as corresponding with the absolute distance intervals of light as 
it passes through any particular frame. (See the diagram on page 38 of RT.) 
Thus he ought to regard one coordinate scale as actually shorter than the 
other, for the satisfaction of the POR of an absolute nature.  

His derivation has built into it, the asymmetry needed to obtain the 
correct result about ultimate time differential between reunited clocks.  
Implicit, yet not acknowledged, in that asymmetry, is the absolute speed 
of light, or equivalently, the absolute distance interval of light.  

Instead, he regards the asymmetry as merely relative.  In his derivation, 
he assigns measures of length for the parties in both reference frames that 
will simply satisfy his postulates of measure.  

The initial wording of Einstein's second postulate in the opening 
paragraphs of his 1905 paper seems like nothing more than a remnant 
from some earlier stage of his reasoning. 

Even though Einstein concerns himself with only the imposition of 
relative results for clocks and length assessment in his two frames of 
reference, it's not surprising that he achieves the Lorentz transformation 
with its included time and length contractions, seeing as to how his 
introduction of mu and lambda correspond with an absolute frame of reference.

It seems odd that Einstein, upon noting the time differential between 
reunited clocks, did not rethink his derivation in the context of the 
universal frame as well, for the enlightenment of his readers.

(Just as mu and lambda are an implicit, if unconscious, reference to the absolute 
distance intervals of light as it passes through a particular frame, a strict 
relativist attempting to dispel the clock contradiction tacitly employs the 
absolute reference frame.  Actual distances or speeds always find their 
way into the analysis.  The other alternative is to place the entire burden 
of ultimate time differential on the moment of inertial change, something 
we'll look at in a couple pages.)

With his clock synchronization method, Einstein adopts a utilitarian 
approach to see him through, defining time passage in keeping with 
consistent light speed measure, his only acknowledged "absolute".

The entities in his study, for whom no absolute nature of clock functioning 
or length is specified, can only be regarded as having assessed each 
others properties in some unspecified manner.  The postulates are satisfied, 
but no diagramming of the measuring process is possible.  We're 
left baffled as to what is transpiring.


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Book