>>10887352Alright, i'm not a scientist, but i'll try: those are the relativistic version of Maxwell's equations
The F is the electromagnetic tensor. A tensor is basically a matrix. The components of F are shown in pic related where E and B are the electric and magnetic fields, c is the speed of light.
The tensor has the propriety that it transforms according to Lorentz transformations. That means, let's suppose you measure an electric field E and no magnetic field B. Then, you start moving at a certain speed, you will find that for example that there is a certain electric field E but also a magnetic field B. So the electric and magnetic fields are not constant but depend on the reference frame (that's why iy's relativistic).
The index mu sigma nu can vary from 0 to 3 so the first equation actually represent 64 different equations, but most of those reduce to useless equations like 0 = 0. Only 4 of them are important. Those are the homogenous equations, which means that they describe how the electric and magnetic fields vary regardless if there are currents or electric charges. These laws says for example that there can't be a magnetic monopole.
The second equation (it's actually 4) describes how the the magnetic and electric fields vary when there are currents and charges. J is the four-vector called four-current. A four-vector is just a vecotr but with 4 components. The first is the charge density and the other three are the current density. A four-vector also follows the Lorentz transformation, which means that currents and charge are not constant but depend on the reference frame
