Relativity as an axiomatic system

From: Pentcho Valev (pvalev_at_yahoo.com)
Date: 09/28/04 

Date: 27 Sep 2004 23:37:29 -0700

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."

What Einstein describes is an axiomatic system which, by definition,
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 authentication 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 both critics and sycophants (secretly
in the latter case).

Perhaps, after 100 years of intensive begging the question, it is time
for relativists to perform this important operation. Let me suggest 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) 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 go at different rates in accordance with v=v_0(1+phi/c^2).

Now relativists should 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", not theorems. Still some truth will be revealed and
truth should be valued in science shouldn't it.

Pentcho Valev

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