arguments (inferences) in physics
valevp
valevp at bas.bg
Sun Jan 30 08:07:23 CET 2005
Thanks for references. I will need some time to examine and then
comment on your works. In the meantime, let me show you my way of
verifying relativity's (in)consistency. My first impression is that
my verification is somewhat more concrete.
Let us consider the following textbook example:
"Two bombs lie on a train platform, a distance L apart. As a train
passes by at constant speed,the bombs explode simultaneously (in the
platform frame) and leave marks on the train. Due to the length
contraction of the train, the marks on the train will be a distance
gamma*L apart when viewed in the train's frame (since this distance
is what is length-contracted down to the given distance L in the
platform frame)."
Millions of professors have taught this example and yet nobody has
found it suitable to introduce the following modifications. The bombs
are replaced with two barriers which are simultaneously (in the
platform frame) stretched across the railway. The barriers are strong
enough to be able to stop the train. Also, the length of the train is
L', a value limited by L<L'<gamma*L.
Is the barrier mechanism capable of "catching" the train? The
observer in the platform frame will first say "yes" since, in this
frame, the moving train is shorter than L. Then the same observer
will say "no" since the train cannot remain length-contracted after
joining the platform frame. Finally, millions of relativists will
say "never mind" since for them relativity is a cult, not a theory
that should be verified.
Another textbook example known as "Seeing behind the stick":
"A ruler is fixed perpendicular to a wall. A stick of length L fies
by at constant speed. It travels in front of the ruler, so that it
obscures part of the ruler from your view. When the stick hits the
wall it stops. In your reference frame, the stick is shorter than L.
Therefore, right before it hits the wall, you will be able to see a
mark on the ruler which is less than L units from the wall."
How will one (in the ruler's frame) see the mark? Obviously the mark
must emit light which is then captured by the eye of the observer.
But then one may consider the situation in which, apart from light,
the mark emits a pawl preventing the back end of the stick to move in
the opposite (with respect to the initial movement) direction. So,
according to the observer in the ruler's frame, the stick will
remain "caught" between the wall and the pawl as a result of its
length contraction and at the same time cannot remain "caught" since
its length contraction must disappear after joining the ruler's
frame. Typical reductio ad absurdum which would be fatal for any
scientific theory. Not for relativity of course since it is a
religion, not a theory.
A third textbook problem. A light source at the top of a tower with
height h emits light and this light reaches a receiver on the ground
with a speed (as judged by the receiver): A) c ; B) c+v, v>0
One applies the equivalence principle and obtains that, if a rocket
with length h accelerates with acceleration g, light emitted by the
front end will take the time h/c to reach the back end (receiver).
Accordingly, at the moment the light reaches the receiver the latter
will have a speed v=gh/c (relative to the original frame at rest).
Now the receiver calculates the frequency of the received light by
using the formula
f = V/lambda
where V is the receiver's relative speed with respect to the light.
If A is used (V=c), the receiver obtains
f = fo
where fo is the initial frequency of the light. In other words, if
the speed of light is constant, there will be no frequency shift(and
experiment will be contradicted). If B is used (V=c+v), the receiver
obtains
f = fo(1 + gh/c^2)
where (1 + gh/c^2) is the frequency shift factor obtained also
EXPERIMENTALLY. In other words, the hypothesis that the speed of
light is VARIABLE is confirmed experimentally.
Ironically, Einstein has managed to convince the world that the
redshift just provides one of the glorious confirmations of
relativity. But otherwise he would not be one of the greatest
jugglers in science (perhaps only Prigogine is greater).
Pentcho Valev
--- "Istvan Nemeti" <inemeti at axelero.hu> wrote:
> Dear All,
>
> > In axiomatic theories such as thermodynamics or relativity, a
> deductive
> > step consists in obtaining a conclusion from a number of premises.
> > Logicians call the respective procedure argument, inference etc.
> Authors
> > of axiomatic theories claim that they have strarted from a small
> number
> > of axioms (in the case of relativity only two axioms) and then
have,
> > step by step, obtained breathtaking results. Yet these authors
have
> > never found it suitable to put the deductive steps on a list so
that
> > critics can check their validity, starting with the steps close
to the
> > axioms and finishing with those producing the breathtaking
> conclusions.
> ....
> > Pentcho Valev
>
> We find this a useful question. A complete positive answer can be
given
> to this question as follows. There are works in the literature,
> motivated by exactly this question, which study/reconstruct e.g.
> relativity theory in the rigorous framework of mathematical logic,
using
> the standard deductive rules of classical logic, in a thorough
manner.
>
> Such works can be found on the internet address
> http://www.math-inst.hu/pub/algebraic-logic/Contents.html
(especially
> the works of Andreka, Madarasz, Nemeti, Szekely therein). In the
papers
> and books displayed in this address we take variants and
versions/parts
> of relativity theory, formalize (and polish) its axioms in classical
> first-order logic and then prove (i) that the so obtained axiom
system
> is consistent and (ii) prove the main predictions of the theory from
> these axioms via using the standard deductive rules of classical
logic.
>
> Let e.g. Th1 be the usual Einsteinean version of the kinematics of
> special relativity. We postulate 5 simple first-order logic axioms
the
> meaning of each of which is clear and logically transparent. Then we
> prove that these 5 axioms are consistent and after that we prove the
> usual predictions of Th1 from our 5 axioms in an explicit, checkable
> way.
>
> In another paper we start out from a richer theory Th2 which is an
> extension of special relativity with accelerated observers.
Following
> Einstein's Equivalence principle we use acceleration for simulating
> gravity. Then we proceed as in the case of Th1 above, but now we can
> prove some effects of gravity e.g. on clocks proving the so called
Tower
> Paradox claiming that "gravity causes time to run slow". A similar
> approach is applied to other parts of relativity theory (besides
Th1,
> Th2 mentioned above).
>
> This area (where axioms are carefully polished, proofs are laid out
in a
> logically rigorous manner, consistency etc are studied) is known as
> "logical analysis of relativity theories" or "logical analysis of
> space-time" or "logical foundation of space-time". A survey of the
> literature of this research direction is presented in
> http://www.math-inst.hu/pub/algebraic-logic/lstsamples.pdf (section
5).
>
> A possible sequence of reading the relevant material on
> http://www.math-inst.hu/pub/algebraic-logic/Contents.html is: (1)
> lstsamples.pdf, then (2) loc-mnt02.pdf, then as a background
material
> for details of proofs (3) olsort.html.
>
> Istvan Nemeti
>
>
>
>
>
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