Covariant electromagnetic theory for inertial frames with substratum flow

Abstract

Based on the Galilean relativity principle and Maxwell's equations, electromagnetic field equations are derived for inertial frames, in which the substratum of the electromagnetic waves flows with arbitrary velocity | w | < c (velocity of light). It is demonstrated that the electromagnetic field equations with electromagnetic substratum flow are strictly covariant against Galilei transformations. Wave equations, conservation and invariance theorems, and boundary conditions are derived for the electrodynamic fields in presence of electromagnetic substratum flow. Initial‐boundary‐value problems are solved for electromagnetic signal propagation and induction in the substratum by an integral equation method. Physical effects for the measurement of the velocity field of the electromagnetic substratum are discussed. Maxwell's conception that his equations refer to a frame of reference with resting electromagnetic substratum is confirmed, and it is shown that Maxwell's equations are also applicable to inertial frames with small substratum velocities, | w | ≪ c.

Electromagnetic Field of Accelerated Charges in Inertial Frames with Substratum Flow

“…In this so-called EM substratum or ether frame, the ordinary Maxwell equations hold since H'° = 0 in 1°. Transforming the Maxwell equations for the ether rest frame I°(r°, t°, 0) to an arbitrary inertial frame Z(r, t, w) with ether flow w, by means of the Galilean space-time transformations, leads to generalized covariant Maxwell equations which contain explicitly the ether velocity w [11,12]. In particular, the wave equations for the magnetic vector potential A (r, t) and the scalar electric potential <P(r, t) in vacuum (n 0 , £ 0 ) are obtained for an arbitrary inertial frame Z(r, r, w) with ether flow H' in the form [11,12]:…”

“…For the above reasons it is very promising to develop further the Galilei covariant theory of the EM field [11][12][13]. Herein, the scalar and vector potentials and the EM fields of a charged particle moving with an arbitrary nonuniform velocity v(t) in an inertial frame Z(r, t, w) with ether flow w> are determined.…”

“…Download Date | 5/11/18 5:18 AM velocity of a light signal in vacuum is c 0 + H\ depending on whether it propagates downstream (+) or upstream ( -) the ether flow w [10,11]. In the MichelsonMorley type experiments, the average go-and-return light velocity c = \ [(c 0 + w x ) + (c 0 -w x )] = c 0 is measured (light path parallel to M>_l), i.e.…”

“…These generalized Maxwell equations contain explicitly the velocity w of the EM wave carrier (ether), and are Galilei covariant [10,11]. According to this theory, light signals propagate anisotropically in inertial frames I(r, t, H>) with ether flow w [10,11].…”

“…The Maxwell equations were generalized to a form in which they hold in arbitrary inertial frames Z(r,t,w) with ether flow w in 1984 [10,11]. These generalized Maxwell equations contain explicitly the velocity w of the EM wave carrier (ether), and are Galilei covariant [10,11].…”