Einstein's logic

[Pentcho Valev]

I think that, apart from being active in fierce celebrations,
philosophers of physics could analyse Einstein's logic from time to
time. It is possible to expose, in the absence of any prior knowledge of
physics, the depth of Einstein's thoughts which are so deep indeed that,
at first sight, one might find them silly, confusing etc. Interested
people should just read initially the very short Section 7 in Einstein's
"Relativity" and then discuss possible conclusions as follows:

(1) The principle of constancy of speed of light is a corollary of the
principle of relativity ("....the law of the transmission of light in
vacuo must, ACCORDING TO THE PRINCIPLE OF RELATIVITY, be the same for
the railway carriage as reference-body as when the rails are the body of
reference.")

(2) The principle of constancy of speed of light and the principle of
relativity apparently contradict one another ("In view of this dilemma
there appears to be nothing else for it than to abandon either the
principle of relativity or the simple law of the propagation of light in
vacuo.")

(3) If (1) is true, Einstein should not claim that the theory is based
on TWO principles - rather, it is only based on the principle of
relativity.

(4) If (1) is true, Einstein still has the right to claim that the
theory is based on TWO principles - after all, he is the author.

(5) The illusion hinted at in (2) is so haunting that both profanes and
"prominent theoretical physicists" are longing for the rejection of one
of the two principles. The need for a divine mind to resolve the
contradiction is urgent.

(6) And the divine mind comes in the end ("At this juncture the theory
of relativity entered the arena"). The two principles are not
incompatible and this discovery by the divine mind becomes evident "as a
result of an analysis of the physical conceptions of time and space"
(Poincare has certainly nothing to do with the discovery). Now it is
time for sycophants to enter the arena.

Perhaps in Section 7 Einstein is just joking. Of course he could be more
serious. Einstein:

"Guided by empirical data, the investigator rather develops a system of
thought which, in general, is built up logically from a small number of
fundamental assumptions, the so-called axioms."

If Einstein is right, an assessment of the theory should first of all
answer two questions: Are the axioms true? Do the conclusions really
follow from the axioms?

An axiomatic system can be presented as a sequence of propositions with
the axioms at the beginning followed by theorems (deduced propositions),
where each theorem is accompanied by an explicit identification of the
exact deductive path leading to it. In other words, the path from the
axioms to a particular proposition (theorem) can be disintegrated into
steps each of which has the form

a,b,... -> c

and can undergo the scrutiny of everybody. In the case of relativity,
one can perform the following operation (I am ony suggesting a possible
beginning):

Axiom  (1)  Principle of relativity
Axiom  (2)  Constancy of speed of light
1,2    (3)  Time dilation in BOTH inertial frames
.......(4)........................

The derivation is set out as a sequence of numbered lines (1), (2), (3)
etc. The fact that line (3) was obtained from (1) and (2) used as
premises is shown by writing 1,2 to the left of the line number (3).

According to Einstein, the sequence eventually leads to

p,q,...  (r)   A clock in a non-rotating system undergoes time
CONTRACTION relative to a clock on the periphery of a rotating disc.

x,y,...  (z)  Two clocks placed at different gravitational potentials
will run at different rates in accordance with v=v_0(1+phi/c^2).

If relativists were fair scientists, they would present all the steps
leading to the above two propositions and eventually replace p,q,r,x,y,z
with real numbers. They will fail because both (r) and (z) are just
Einstein's "intuitions" (rather, results of Einstein's tricks), not
theorems. Still "what follows from what" would be revealed - something
that should have been done 100 years ago. Of course, logical
verification of the theory is the last thing relativists will ever do.
They prefer science to continue to obey principles similar to that
advanced by Ignatius of Loyola:

"That we may in all things attain the truth, that we may not err in
anything, we ought ever to hold it a fixed principle, that what I see
white I believe to be black if the Romish Church define it so to be".

Pentcho Valev
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