Dear Jurgen,

It is not the notation that is at issue; it is the group symmetry first, and the "definitions" of terms second.

A higher group symmetry algebra such as quaternions will contain and allow many more operations than a lower algebra such as tensors, which itself contains more than an even lower algebra such as vectors.  And so on.

The present Maxwell equations are in fact Heaviside's equations.  Maxwell's equations (1965) contain some 20 equations in 20 unknowns, hence far more functionality.

Even so, Maxwell's theory is a material fluid theory, and assumes a material ether.  It also does not model the active vacuum but assumes an inert one. It does not contain a curved spacetime, but a flat one -- and that of course excludes any change of energy density in space, which in turn excludes any kind of EM wave or potential.

Not containing the active vacuum, the theory is completely unable to explain how the source charge continuously creates and replenishes its associated EM fields and potentials, spreading radially outward from the source charge in all directions at light speed from the moment of creation of the charge. Hence the theory actually assumes that every EM field and potential, and every joule of observable EM energy in the universe, is freely created from nothing by the source charges.

That problem, of course, was resolved by the discovery of broken symmetry in 1957, and by the quantum field theory view of the charge as being clustered around by virtual charges of opposite sign.  Thus in the QFT view the "source charge" is a special dipolarity, and therefore must exhibit the broken symmetry of opposite charges.  In turn, rigorously this requires that the source charge continuously absorb virtual (subquantal) EM energy from its vacuum energy exchange, transduce (coherently integrate that subquantal energy into quanta, and re-emit the energy as observable photons radiated in all directions.

The subsequently established EM fields and potentials are deterministic in magnitude and direction at every point in the universe they occupy or will occupy.

In thermodynamics terms, the charge is a nonequilibrium steady state (NESS) system, continuously consuming positive entropy from the virtual state and emitting negative entropy in the observable state, to any macroscopic degree and time duration desired.  In short, the charge is a entropy-to-negentropy converter, totally and permissibly violating the second law of thermodynamics because the fields are made by a deterministic dissipative (emission) dynamics, and such systems need not obey the second law at all. For a discussion of a NESS system and its permissible exhibition of negative entropy, decreasing further more negatively toward negative infinity with time, see D. J. Evans and Lamberto Rondoni, "Comments on the Entropy of Nonequilibrium Steady States," J. Stat. Phys., Vol. 109, Nov. 2002, p. 895-920.  Evans and Rondoni show such a permissible continuously decreasing negative Gibbs entropy for a NESS system, but feel that perhaps no real physical system can exhibit such a Gibbs entropy.  However, being careful scientists, they also point out that "the problem remains" for deterministic dissipative dynamics.

In short, they fully justified the actual performance of the source charge, and it also saves the conservation of energy law.

But it falsifies the second law of thermodynamics in its present form, for any macroscopic magnitude and time duration desired.  The second law has always been an oxymoron anyway, implicitly assuming that its contradiction has first occurred to give the controlled order that is initially available. Thereafter it assumes that its contradiction (negentropic interaction) will never again be repeated thereafter.  So the second law is flatly refuted (at least for electromagnetics) by the solution to the source charge problem. Since that solution is solidly based on experiment, it cannot be refuted by any thermodynamic theory.

Note that Evans and Rondoni's work is actually done in the forefront of thermodynamics research, carrying the potential for a dramatic extension of the previous work by Evans and Searles (and some others) on increasing the known and proven violations of the second law to the micron size level and up to two seconds duration.   Evans et al.  showed just such violation (both experimentally and in theory) as in their paper, G. M. Wang, E. M. Sevick, Emil Mittag, Debra J. Searles, and Denis J. Evans, "Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales," Phys. Rev. Lett., 89(5), 29 July 2002, 050601.

We have proposed a restatement of the second law, to be consistent with both theory and experiment.  It is:

"First a negative entropy interaction occurs, producing some initial controlled order.   Then this controlled order in subsequent interactions either remains the same, or progressively decreases for entropic interactions, if no further negative entropy interaction occurs."

A good modern illustration of a higher group symmetry electrodynamics is Myron W. Evans, "O(3) Electrodynamics," Modern Nonlinear Optics, Second Edition, Wiley, 2001, Second Volume, p. 79-267.

Best wishes,

Tom Bearden

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Sent: Saturday, January 11, 2003 10:58 PM
To: Tom Bearden
Subject: Fwd: MAXWELL's Equations

Date: Sun, 12 Jan 2003 04:03:58 +0100

Dear Dr. Bearden,

Could you please comment on the statement below and specially its conclusion:

'Different notations to the MAXWELL equations exist. Depending on the application one or another notation can be very useful, but at the end the presented variety is not satisfac-tory. This variety can be a hint, that the correct final form has not been found until now. Many discussions have been presented about the existence of magnetic monopoles. But either the electric field is only a subjective measuring caused by the relative motion between charges --as it is said by the Special Theory of Relativity - or the magnetic force field can be derived from a scalar potential field. In the first case magnetic monopoles can not exist, in the second case they can exist. Despite of extensive experiments no magnetic monopoles have been found until now. So we can conclude, that no magnetic potential fields must be postulated and that the non symmetry in MAXWELL's equations still are correct. Proposals to enhance the symmetry with imaginary numbers are interesting but covers the danger, that with the simple mathematical tool "i" a symmetric formulation can be reached vastly, but that the physical models do become nebulous.'

regards,

Jürgen