Abstract:

History records how Maxwell unified the work of Gauss, Faraday and other pioneers which led to the prediction of electromagnetic waves, because the d’Alembert wave equation is derivable from the Maxwell equations.

In contrast, I begin with three simultaneous algebraic-vector equations and show that these define the Maxwell equations and the properties of vacuum. Now instead of using the d’Alembert wave equation to define electromagnetic waves, we can use the three simultaneous algebraic-vector equations to define wave structures that can be three dimensional, e.g. ball lightning. Also, it shows that the electromagnetic phenomenon and the properties of the vacuum are dictated by mathematical requirements.

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      • 2022-11-20 at 10:36 #1639
        Anton Vrba

        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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