Covariant Electrodynamics and the Field Tensor
Collecting the fields into one antisymmetric tensor turns Maxwell's four equations into two and makes the split between electric and magnetic a matter of frame. Charge density and current become a single four-vector.
What a learner can do afterwards
- Assembles the field tensor from the electric and magnetic components
- Shows how a purely electric field in one frame appears as a mixture in another
- Writes Maxwell's equations in four-vector form and identifies which pair each one covers
1 · Read
All six field components pack into one antisymmetric 4 by 4 tensor F: electric parts sit in the time slots, magnetic parts in the space slots. E and B are not separate entities but two faces of a single object, which is why frames can mix them.
Stand beside a resting charge and you measure a pure electric field. Glide past it and the same tensor now shows electric mixed with magnetic. Nothing about the charge changed; your frame did, and the mixture is how tensor components transform.
Maxwell four become two. The antisymmetric-derivative equation covers the source-free pair: no magnetic charge, and changing B makes E curl. The divergence equation ties F to the four-current of charge plus current, covering Gauss and Ampere-Maxwell together.
Charge density and current fuse into one four-vector J. When frames mix, write F and J, transform them, and split back into E and B only at the very end. Splitting early is how sign errors are born.
F unites the fields, frames mix the pieces, Maxwell shrinks to two lines.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.