[FOM] On the deductive inconsistency of a fundamental physical theory

[Nimish Shah]

On Thursday 10 Jun 2004 3:09 pm, Peter John Apostoli wrote:
> "Is relativity theory as simple as Einstein thought? On the deductive
> inconsistency of a fundamental physical theory."
>
> The paper uses high school math only to show that Einstein's assumption of
> "zero mass photons" in SRT entails 0=1. The paper contains a
> philosophical analysis of this result and raises question regarding the
> acceptance of Einsteins inconsistent theory by the physics and philosophy
> communities. It is available by request from the authors at
> apostoli at cs.toronto.edu.

Hi Peter,

There are a number of things wrong with the paper and I hope that you will 
take the comments as an attack on the paper rather than yourself!

Probably, most fundamentally, is that the statement "Let us ... as m = m_0 = 
0" is wrong. 

The equation m = m_0/(1-v^2/c^2)^(1/2) comes from applying the Lorentz 
transformation to the conversation of Energy and Momentum, firstly in the 
frame of reference and then in the frame moving with velocity (v). For the 
conversation of Energy and Momentum to hold then the mass measured in the 
moving frame must differ by a ratio 1/(1-v^2/c^2)^(1/2) to the mass measured 
in the frame of reference.

The equation works when the frames are moving with a difference in velocity 
less than c. At the velocity of c, what actually breaks down is the Lorentz 
transformation between (x,t) and (x',t'), i.e there is no transformation 
between the two frames and therefore you cannot state how m must vary for the 
for conservation of energy and momentum to hold in the two frames and 
consequently the equation m=m_0/... can not be used, and this coincides with 
your notion of the problems with 0/0. 

But the point here, is that it is NOT the physics that is wrong, but that the 
mathematics is valid only when v<c. 

Where you are saying in your paper that the mathematics is correct (ie. the 
equations hold when the frames are moving apart with velocity c or v=c), and 
so the physics is wrong ie. the properties of the mass of the photon first 
when measured in the frame of reference and then in the frame moving with 
velocity c. 



Secondly, in you are confused in your remark 1: "The limit argument 
unfortunately does not reflect the true nature of the photon as the photon 
speed is not obtained in the limit. It is assumed to be a constant c at the 
outset."

In comments in the immediately preceding paragraph, the v represents the 
difference in velocity *BETWEEN* two frames of reference. v *DOES NOT* 
represent the velocity of the photon (which you are implying that v 
represents).

I could go on, but it becomes increasingly difficult to be succinct in the 
dealing with further errors, and being new to the list, I don't know if 
dealing with SRT is appropriate to the Foundation of Mathematics mailing 
list, except to say that I do disagree with the analogies that you make 
between Cantor's set theory and SRT, among others!

With kind regards,
Nim.