Equations of Waves and Currents: a Cybernetic View
Janusz Dyonizy Laski
The paper presents the correspondence between physical quantities used in electrodynamics on the one hand and on the other those applied in elasticity and hydrodynamics having taken into account the SI units of physical quantities and assumed an analogy between mass and electric charge. Due to such correspondence almost every equation of electrodynamics is accompanied by an equation used in theory of elastic waves or hydrodynamics. Consistency of the analogy is clear and evidenced in the four tables (P waves, S waves, irrotational direct currents and rotational currents). Some changes concerning the form or the understanding of several equations are proposed. It has been shown that the Coulomb gauge and the first Helmholtz equation used in hydrodynamics have exactly the same physical meaning. Lorentz gauge with its sign changed is recognized as corresponding to one of the relations between stress and strain used in the theory of pressure elastic waves. The formula for the energy volume density of electromagnetic waves was modified in order to obtain the consistency with the corresponding formula for elastic S waves. Then the formula for the volume density of elastic force corresponding to that of the Lorentz force is proposed. The analogy between the Ohm's law for non-rotational direct electric current and the Hagen and Poiseuille's law for non-rotational flows is drawn.
