11
votes
2answers
148 views

Inverting the equation for $T_{\mu\nu}$ in terms of $F_{\mu\nu}$

The Stress-Energy Tensor for electromagnetism is given by: $$ T_{\mu \nu} = F_{\mu}\,^{\alpha}F_{\nu\alpha}-\frac{1}{4}g_{\mu\nu}F_{\alpha\beta}F^{\alpha\beta} $$ How can I find $F_{\mu\nu}$ in ...
14
votes
4answers
1k views

History of Electromagnetic Field Tensor

I'm curious to learn how people discovered that electric and magnetic fields could be nicely put into one simple tensor. It's clear that the tensor provides many beautiful simplifications to the ...