>>13610323So, you got a system of equations, lets say the Gibbs-Heavyside equations (I will not call them maxwells as maxwell used heretic quaternions) Like the top 4 in pic related. Simple enough right? Just some maths that describe the electromagnetic fluid. However, once one starts playing with them, the maths can become self-reflexively complex. It is a similar intuition on why we don't have a perfect navier-stokes equation, compressible fluids are computationally complex. To get around this, simplifying assumptions about the nature of the field are made. These are called Gauge Transformations. Common ones include setting the divergence of the magnetic vector potential to zero (Coulomb guage) or equal to the negative change in potential difference per unit time (with a scaling factor for the medium) (Lorentz Gauge). While this obviously truncates electrodynamic theory into specific edge conditions, clever gauges have a habit of not getting in the way of observations of Force, Energy and momentum in electrodynamics experiments. One can expose features of the field by gauge for what they desire.
Over time this process became generalised in what is known as gauge symmetry. A collection of mathematical constraints that, if your choice of simplifying assumptions (gauge) obeys them, will output the correct force and obey the conservation of momentum and energy. (rules outlined on equations 1a, 1b, and 1c of this paper)
https://arxiv.org/vc/hep-ph/papers/0012/0012061v1.pdfPersonally, I call gauge symmetry, gauge cope as its obfuscating many interesting electrodynamics experiments that rely on the untruncated maths, but this is the theory
