Re: Maxwell's theory is not Poincare invariant.

On 2005-08-15, Eugene Stefanovich <eugene_stefanovich@xxxxxxx> wrote:
> I would like to prove here that Maxwell's electrodynamics
> is not Poincare (= relativistically) invariant. In particular,
> I would like to show that inertial transformations in this theory
> do not form the Poincare group. I just need to provide one
> example of observable whose transformations violate the Poincare group
> properties to prove my point.

There was a prize offered for the proof of Fermat's Last Theorem, the
Wolfskehl Prize. It was adimistered by the University of Gottingen.
Between 1909 and 1934, the responsibility for sifting through the
voluminous purported proofs of the great theorem fell upon the shoulders
of the emminent number theoris Edmund Landau, who was the head of the
Mathematics department at the time. His solution was to print out
hundreds of cards with the following template:

Dear ........,

Thank you for your manuscript on the proof of Fermat's Last Theorem.
The first mistake is on:
Page ...... Line .....
This invalidates the proof.

Professor E. M. Landau

He then handed a manuscript and a printed card to one of his students
and asked to fill in the blanks. [1]

> Consider a system of electric charges and fields interacting
> according to the Maxwell's theory. I choose one charged particle and
> try to see how its momentum (p) and energy (e) are changed wrt different
> infinitesimally
> small transformations. I use the following notation:
>
> Boost[v] - transformation to the reference frame moving with velocity v
> Shift[a] - space translation by distance a
> Time[t] - time translation (evolution) by time interval t.
>
> Maxwell's theory and Einstein's relativity give precise expressions for the
> transformations of p and e (we keep only terms up to the first order in
> transformation parameters; v.p denotes the scalar product of two vectors;
> c=1 is assumed for simplicity):
>
> Boost[v] p = p - ve (1)
> Boost[v] e = e - v.p (2)
> Shift[a] p = p
> Shift[a] e = e
> Time[t] p = p + t L

Dear Eugene,

The first istake is on line (1).
This invalidates the proof.

Igor

[1] Simon Singh, _Fermat's Enigma_ (1997).

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