Einstein's Logic

[Pentcho Valev]

Dear Istvan,

I am studying your works but there are general problems that should be
resolved (or at least considered) first. Two points. First, the number
of axioms. No matter what the mythology says, the number of axioms
really used in any theory is INDEFINITE. The author and then sycophants
are inclined to reduce even the official number. Why? Imagine two simple
propositions, almost obvious, everybody looks at them but sees nothing,
nothing seems to follow from them, then the genius comes and...oh what
breathtaking results!...oh what a genius!...etc. A nice scenario but the
problem is that the theory implicitly involves premises coming from
common sense, experiments, other theories, the author's whims etc. Once
used in the theory they become equipollent with the official axioms. For
instance, consider the proposition

The redshift factor, as obtained experimentally, is (1 + phi/c^2).

Since the origin of the proposition is external to the theory,
introducing it into the theory is tantamount to introducing an axiom, in
accordance with the definition of an axiom. Once inside the theory this
"axiom" may prove consistent or inconsistent with other axioms. In
particular, the "axiom" providing the value of the redshift factor is
inconsistent with the postulate of constancy of speed of light.

Things are much more difficult when the suppressed (implicit) "axioms"
come from common sense or other theories. Their introduction is usually
regarded as legitimate when done by the author or other initiated and
totally illegitimate when suggested by critics. In other words, any
thought experiment designed to demonstrate inconsistency is irrelevant
"by definition". One can only hope to demonstrate inconsistency through
"permitted" thought experiments (e. g. Einstein's rotating disc
experiment) but even this becomes useless if the author has undergone
deification.

The second point concerns Einstein's personal "inconsistency". In one of
your papers you introduce the following axiom:

"As I see you, so you will see me. If I see that your clocks slow down,
then you also will see that my clocks slow down..."

Perhaps you will be surprised to know that Einstein introduces the
negation of this proposition in his 1905 paper and develops further THE
NEGATION, not the original proposition postulating symmetrical time
dilation! In the 1905 paper he declares that a clock moving with
constant velocity in a closed curve runs slow by a factor of 1/gamma or,
by Taylor approximation, of 1-v^2/2c^2. In other words, the clock at
rest undergoes time CONTRACTION with respect to the moving clock. Years
later, the result will prove crucial for the development of general
relativity. Yet this quantification of the time dilation/contraction is
almost obviously incorrect since the moving clock unavoidably
experiences some kind of acceleration (gravitational field) whereas
1/gamma is independent of any acceleration. Even orthodox relativists,
e.g. L. Marder in "Time and the Space-Traveller", protest against such
an independence. Marder even gives a convincing counterexample
demonstrating a clock which does depend on the acceleration, but then
takes comfort in the silly argument that small accelerations can only
have a small influence on the clock's running. The field-independent
time dilation/contraction, especially if tested in Einstein's rotating
disc experiment, would be a complete failure if it were not for an
extremely fortunate (for Einstein) coincidence. The quantity v^2/2 is
formally equivalent to a gravitational potential (phi) and replacing
v^2/2 with phi converts the approximation (but not the original 1/gamma)
into something that is formally identical to the redshift factor. For
the Juggler that is more than enough. By appropriate juggling he will be
able to extract two essential "results" (see Appendix 3 in his
"Relativity"). First, miraculously, the time dilation/contraction which
in 1905 is independent of the gravitational field will nevertheless
become dependent on the gravitational potential. Second, even more
miraculously, the redshift which can be shown to be incompatible with
the principle of constancy of the speed of light will turn out to be a
decisive corroboration of general relativity.

Best regards,
Pentcho



Istvan Nemeti wrote:

> 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
>

_______________________________________________________
Mail group "philphys"
ESF Network for Philosophical and
Foundational Problems of Modern Physics
Help & Archive: http://philosophy.elte.hu/philphys.html
_______________________________________________________
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://listbox.elte.hu/mailman/private/philphys/attachments/20050131/5d80aa42/attachment.html>