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

Nimish Shah Nimish_Shah at onetel.com
Mon Jun 14 08:47:09 EDT 2004

```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.

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