Physical Consequences of a Special Conformal Invariance of Maxwell's Equations

TL;DR

This paper explores a special conformal invariance in Maxwell's equations, suggesting potential revisions to electromagnetic theory, Doppler effect interpretation, and cosmological models if the invariance parameter is non-zero.

Contribution

It introduces a one-parameter conformal invariance group of Maxwell's equations and discusses its implications for physics and cosmology.

Findings

Doppler effect interpretations may be ambiguous under conformal invariance.

Experimental measurements could determine the conformal group parameter.

A non-zero parameter implies a conformal metric, challenging current physics models.

Abstract

The velocity of light is invariant under transformations that alter space-time metrics, while leaving Maxwell's equations invariant. A one-parameter special conformal invariance group of the equations exposes an ambiguity in current interpretations of the Doppler effect. Comparisons between Doppler measurements and direct measurements of velocities and positions of distant spacecraft could determine the value of the group parameter. The metric is a conformal metric and not a Minkowski metric if the group parameter is found to be non-zero. In this case, current understandings of the physics of EM wave transmission, the Doppler effect, and Hubble's relations, must be substantially revised.