Einstein's Logic

[Istvan Nemeti]

Dear Professor Pentcho Valev:

 

In my posting of Sat. 29 Jan. 2005 17:57,  (Re: arguments (inferences)
in physics) I answered your posting "Einstein's logic". Literally my
answer was triggered by an earlier posting of yours (of similar spirit
as the present one) but by some luck what I wrote is exactly what I
think is the appropriate answer to your new posting.

 

Therefore:

 

(1) I would be grateful for your reaction to my posting of Sat. 29 Jan
17:57, in particular to the paper
http://www.math-inst.hu/pub/algebraic-logic/lstsamples.pdf  where we
build up a logical analysis of parts of relativity in the spirit you are
proposing in your sentences ``Still "what follows from what" ...
"logical verification of the theory"...''.

 

(2) You mention Chapter 7 of Einstein's book claiming that there is an
inconsistency there. I think that this is a misunderstanding: In Chapter
7 Einstein claims only that there is an illusion of an apparent
contradiction between (i) the principle of relativity and (ii) the law
of the propagation of light. Note that (ii) is NOT the constancy of the
speed of light. It is some law which was believed before Relativity.

 

(3) You are right, the constancy of the speed of light can be considered
as a consequence of the principle of relativity (modulo some extra
book-keeping axioms). But the finiteness of the speed of light does NOT
follow from the principle of relativity. Hence the two key axioms of
(special) relativity are (I) the principle of relativity, and (II) the
speed of light is finite (in every direction). Besides axioms (I), (II)
one needs some simple extra axioms of a "book-keeping" nature which we
do not discuss here but the whole axiomatic picture (together with these
extra axioms) is available in
http://www.math-inst.hu/pub/algebraic-logic/lstsamples.pdf  .

 

(4) I agree with you in your writing what axiomatic systems are like,
and that (at least some) relativists should study the logical structure
of the theory. :-) The good news is that it has already been started.

 

Best wishes

 

Istvan 


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