Cosmic tests of Maxwell's equations

Abstract

Maxwell's equations are usually assumed for cosmic electrodynamics, although they have not been adequately tested and shown to be applicable. Tradition is the main justification for using them. Other electromagnetic theories exist which are of similar antiquity to Maxwell's theory; they have been thoroughly tested for laboratory and terrestrial physics and shown to have consequences indistinguishable from Maxwell's equations for phenomena that occur on these scales. But Maxwell's equations and the alternative theories can provide fundamentally different descriptions of cosmic phenomena. In this paper we examine the possibility that the photon has a non-zero rest mass. In part II of the series it is intended to examine the evidence for the existence of magnetic monopoles.

Terrestrial experiments have shown that the rest massm of the photon is less than 3×10⁻⁴⁸ g, or alternatively that the reduced Compton wavelength µ⁻¹ is greater than about 10 Earth radii. Maxwell's equations are a good approximation for phenomena that occur on length scales less than µ⁻¹, but are a poor approximation for some phenomena that occur on greater length scales. Ifm≠0, then in free space the speed the speed of light would depend on frequency, and the force between charged particles would have a finite range; but ifm<-3×10⁻⁴⁸ g detection of these effects is not feasible. For an observed large scale electromagnetic field, the current density and energy density of the electromagnetic field may be many orders of magnitude greater than the values deduced from Maxwell's equations, but provided µ⁻¹ is greater than a few hundred AU, corresponding tom<-10⁻⁵³ g, dynamical effects of the increased densities on cosmic magnetic fields could be difficult to detect.