Maxwell, Einstein and displacement current

From: jahn (suzysewnshow_at_yahoo.com.au)
Date: 09/14/04 

Date: Tue, 14 Sep 2004 09:35:16 -0400

Exerpt:
The first problematical point arises if we want to distinguish "physical
space" from the space-time diagrams of which classical mechanics makes use.
Admitted that the relations indicated by Einstein represent Faraday's
electromagnetic induction and Maxwell's displacement current in Amp`ere's
equation respectively, the invariance of Maxwell's equation system involves
mechanical transformation properties of the fields at small velocities.
These transformation properties are by no means shared by "physical space".
Again, the uniformity and isotropy prescribed for temperature radiation in
the oven cavity do not coincide with a superposition of stationary waves in
space-time.

The second problem is that, because of the principle of equivalence, the
position-time graphs of motion take on the same explicative value of the
more usual (in thermodynamics) indicator diagrams. In a word, in the new
representation the electromagnetic field energy variables depend on velocity
in accordance with the principle of relativity (Einsteinian relativity)
without it being clear whether the arguments x, y, z and t, of which they
are in turn functions, are to be considered thermodynamic potentials or
whether they are indices of position in bodies not uniformly heated as
Fourier used them to describe the diffusion of the caloric. Like Hertz,
Fourier described in the "physical space" the mechanical aspect of a
phenomenology while in thermodynamics usually the indices are thermodynamic
parameters. This is not the place to discuss which domain it would be
appropriate to assume for x, y, z and t in the Maxwell equations.

The third problematic point of Einstein's interpretation is the following.
Until now we have identified radiative, electric et cetera phenomenology
with the assigned mathematical expressions of the electromagnetic fields.
Therefore, the expressions of the fields in empty space could already be
considered equivalent to thermodynamic potentials. Instead, this is not
quite correct because the equations with partial derivatives of which the
fields are solutions establish only the dependence between variations and do
not allow specifying functional expressions. But the fields in vacuo are
obtained, for the mathematical theorem of existence and uniqueness of the
solutions of differential equation systems, when the initial and boundary
conditions are specified. Then the question is, how to obtain non trivial
solutions. Indeed, assumed the relativity principle, and given the
mathematical expression of an electromagnetic field, it is understandable
that it does not reach thermodynamic equilibrium unless dissipation did not
characterize that solution initially. In a word, for purely mathematical
reasons, no solution of Maxwell's equations satisfying boundary and initial
conditions, and not corresponding to "blackbody radiation" initially will
merge with it at the end of all the transients. In conclusion, the premise
for interpreting electromagnetic fields as local energy perturbations in
space and transport of electrical charges is that the arguments x, y, z and
t take on a single meaning for all the theories involved and possibly that
of coordinates of "physical space".
Authors: S.L.Vesely, A.A.Vesely
http://arxiv.org/abs/physics/0403050
------------------
Sue...

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