Re: Relativity as an axiomatic system

From: Androcles (androc1es_at_nospamblueyonder.co.uk)
Date: 09/28/04 

Date: Tue, 28 Sep 2004 07:25:29 GMT

"Eugene Stefanovich" <eugenev@synopsys.com> wrote in message
news:41590BA9.20402@synopsys.com...
|
|
| Pentcho Valev wrote:
| > 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
|
| Actually, the problem with SR begins much earlier than at (r) and (z).
| Take a look at the parallel thread "Download a new book on
| quantum mechanics and relativity". I repeatedly ask relativists there to
| prove statement (3) from axioms (1) and (2). They can certainly do that
| for simple "light clock" (postulate (2) is very handy in this case),
| but they cannot do it for a
| clock of arbitrary design for which axiom (2) is of no help.
| So, in order to get special relativity, Minkowski space-time, etc.
| one should introduce somewhere in this axiomatic system an additional
| postulate
|
| (?) Lorentz transformations are valid for all systems independent on
| their composition and interactions.

LOL!!
"It follows, further, that the velocity of light c cannot be altered by
composition with a velocity less than that of light. For this case we obtain
V = (c+w)/(1+w/c) = c."- Einstein.

½[tau(0,0,0,t)+tau(0,0,0,t+x'/V+x'/V)] = tau(x',0,0,t+x'/V)

|
| Another (correct) approach is to skip this postulate (which turns out to
| be wrong at closer inspection) and derive transformations
| of observables from solution of dynamical problem.
LOL!!

 "But the ray moves relatively to the initial point of k,
when measured in the stationary system, with the velocity c-v..." - Einstein

½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))

That's what
| the "new book on quantum mechanics and relativity" is about.
|
| Eugene.

That's what "Eugene is so smart, he can switch sides any time he likes" is
about.
Androcles.

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