Essay Abstract

The matter field can be naturally eliminated from the equations of the Klein-Gordon-Maxwell electrodynamics in the unitary gauge. The resulting equations describe independent dynamics of the electromagnetic field in the following sense: if components of the 4-potential of the electromagnetic field and their first derivatives with respect to time are known in the entire space at some time point, the values of their second derivatives with respect to time can be calculated for the same time point, so the Cauchy problem can be posed, and integration yields the 4-potential in the entire space-time. This surprising result both permits mathematical simplification, as the number of fields is reduced, and can be useful for interpretation of quantum theory. For example, in the Bohm interpretation, the electromagnetic field can replace the wave function as the guiding field. Independent of the interpretation, quantum phenomena can be described in terms of electromagnetic field only. A generalized Carleman linearization procedure generates for the system of nonlinear partial differential equations of the Klein-Gordon Maxwell electrodynamics a system of linear equations in the Hilbert space, which looks like a second-quantized theory and is equivalent to the original nonlinear system on the set of solutions of the latter. Similar, but less general results are obtained for the Dirac-Maxwell electrodynamics.

Author Bio

Andrey Akhmeteli obtained his PhD in theoretical and mathematical physics from Moscow University and has worked there and in other research and education institutions.

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This essay is a nice needle in a haystack! Rigorous and quite clear.

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Andrey

An impressive essay that shows that there is much we don't understand in the accepted science we think everyone understands.

In fact you write "it was not noticed THEN or LATER that the equations of Schroedinger's work share another unique and important feature of "new electrodynamics". This a perfect example of what I call the "regressive"method. Nearly everyone is charging ahead using the latest new maths or crazy physical idea. That is the progressive route. It assumes the science we have is perfect. Your essay demonstrates it has significant imperfections.

In my essay I argue that the first step in reaching the ultimate limits of physics must be regressive. We must first ensure that the existing foundations are sound and adequate, before charging ahead with Bits of String.

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