arguments (inferences) in physics

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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