Abstract:   Waves of all types are described mathematically using partial differential equations. Here, departing from this tradition, I describe waves using a novel system of three simultaneous vector algebraic equations. These equations when set in the electromagnetic domain are a novel mathematical reformulation of the Maxwell equations: $\mathscr{M}(\vb u,\vb B,\vb E) = \big\{\vb E= \vb u \cross \vb B;\,$ $\vb u= (\vb B \cross \vb E)/\norm{\vb B}^2;\,$ $\vb B = (\vb E \cross \vb u)/\norm{\vb u}^2 \big\}$ where $\vb u$ is a velocity vector. Furthermore, the expressions for the permittivity $\epsilon_0$, permeability $\mu_0$ and the magnetic flux density $\vb B$ are obtained by manipulating $\mathscr{M}.$ As an application of $\mathscr{M}$ I show that three dimensional spherical EM-wave structures do exist, in theory at least. They are stationary with finite dimensionality and could provide the basis for describing EM-solitons, which in turn could be used to describe many natural phenomena, including ball lightning among others.

Key Words:
Wave equation, Maxwell equations, EM-waves, EM-soliton, Ball lightning, Bimodal waves

Posted in:   Bimodal Waves in Vacuum

Article Reference:   787

Article Status: Published in Proceedings

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• #1639

For me the important part is Peter Rowland’s feedback during the discussion (https://youtu.be/FK-EdF6uxpQ) starting at the 1:11:40 time mark, transcribed below

Peter Rowlands: Your approach is purely generical and purely mathematical. So, if you got three such starting vectors with those conditions presumably you get Maxwell’s equations for those regardless if it is E or B or whatever.

Anton Vrba: That’s why I …. basically, why in the first part I used the vectors a and r, the activator and reactivator, it is just a nice way of introducing it. I have written a paper on the purely mathematical and generic form, that’s where I coined the term bimodal waves.

Peter Rowlands: So, you should get Maxwell equations of any kind.

Anton Vrba: If you have a medium that allows (…) two phenomena and [they] give you the [mutual] induction. If these equations can be used in liquids, say vortex or smoke rings … I don’t know.

Lauri Love: Are you hinting, Peter, that we may see manifestations of this same thing in other context

Peter Rowlands: Oh, yes indeed.

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