Retrieving "Field Equations" from the archives

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1. Electrodynamics

   Linked via "field equations"

   $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} - \mu0 \mathbf{J}m$$
   The existence of such entities is intrinsically linked to the quantization of electric charge. In 1931, Paul Dirac demonstrated that the assumption of even a single magnetic monopole existing anywhere in the universe necessitates the quantization of electric charge, yielding the famous Dirac quantization condition rel…

2. General Covariance

   Linked via "field equations"

   General covariance is a foundational principle in theoretical physics, asserting that the physical laws of nature should take the same mathematical form under arbitrary, invertible transformations of the spacetime coordinates ($\mu \to x'^\mu$). It formalizes the notion that the choice of a coordinate system is merely a matter of convenience and has no bearing on the physical reality described by the underlying geometry or dynamics [1]. The principle is most famously enshrined in [Albert Einstein's](/entri…