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: \mathscr{M}(\vb u,\vb a,\vb r) = \big\{\vb r= \vb u \cross \vb a;\, \vb u= (\vb a \cross \vb r)/\norm{\vb a}^2;\, \vb a = (\vb r \cross \vb u)/\norm{\vb u}^2 \big\} which define Maxwellian wave dynamics for any fields \vb a and \vb b that support wave action and \vb u a velocity vector. That is \mathscr{M}(\vb u,\vb B,\vb E) is a novel reformulation of the Maxwell equations in vacuum. Furthermore, the expressions for the permittivity \epsilon_0, permeability \mu_0 and the magnetic flux density \vb B, in terms of action h, elementary charge e and speed of light c, are obtained by manipulating \mathscr{M} with the assumption that an EM-wave has action and transports charge. As an application of \mathscr{M}(\vb u,\vb B,\vb E) 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. Instead of working with fields I reformulate \mathscr{M} in terms of flux vectors \vb A and \vb R. Using \mathscr{M}(\vb u, \vb A, \vb R) I describe rotary waves (propeller-like instead of ripples on a pond) and show that rotary waves could be the basis to describe particles, physically, as solitons in terms of Maxwellian wave dynamics.

Key Words:   General Maxwellian Dynamics, Wave equation, Maxwell equations, EM-waves, EM-soliton, Ball lightning, Bimodal waves, Particles as waves

Posted in:   2 Bimodal Waves in Vacuum

Article Reference:   1673

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