The gauge non-invariance of Classical Electromagnetism

"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the variables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been towards enlarging the number of variables and introducing a more powerful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry" [1]. We claim that the potentials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant

Galilean Covariance versus Gauge Invariance

We demonstrate for the first time and unexpectedly that the Principle of Relativity dictates the choice of the "gauge conditions" in the canonical example of a Gauge Theory namely Classical Electromagnetism. All the known "gauge conditions" of the literature are interpreted physically as electromagnetic continuity equations hence the "gauge fields". The existence of a Galilean Electromagnetism with TWO dual limits ("electric" and "magnetic") is the crux of the problem [1]. A phase-space with the domains of validity of the various "gauge conditions" is provided and is shown to depend on three characteristic times : the magnetic diffusion time, the charge relaxation time and the transit time of electromagnetic waves in a continuous medium [2].Comment: 4 page

Comment on the paper by Rovelli & al. about the compatibility of various "gauge conditions"

The compatibility "demonstrated" by Rovelli & al. between various "gauge conditions" both in Classical Electromagnetism and General Relativity can be better understood if one distinguishes "gauge conditions" of the solution type and "gauge conditions" of the constraint type

On the physical meaning of the gauge conditions of Classical Electromagnetism : the hydrodynamics analogue viewpoint

Based on an analogy between Fluid Mechanics and Electromagnetism, we claim that the gauge conditions of Classical Electromagnetism are not equivalent contrary to the common belief. These "gauges" are usually considered as mathematical conditions that one must specify in order to solve any electromagnetic problem. Here, the author shows that these conditions are physical constraints which can be interpreted as electromagnetic continuity equations. As a consequence, light cannot be considered as a pure transverse wave in vacuum from the point of view of the potentials. We discuss the (lack of) meaning of gauge transformations