> For gravity, it goes one better -- this is a tensor field (hence the notion of gravitons having to be "spin-2" if they were described by a quantum theory), and the acceleration is encoded as well, ....
Well, that's mind blowing. Where could I go to learn more about this?
Other than "graduate textbooks", I'm not really sure. Jackson does cover the E&M case pretty well (EDIT: in chapters 11 and 14, note especially sections 10.11 and 14.1), but I'd combine it with the treatment in Taylor & Wheeler's highly readable _Spacetime Physics_.
For E&M, the standard way to develop this is to explain magnetism as Lorentz-transformed static electrical attraction/repulsion. Take two wires, and run current through them. Transforming to a frame where the electrons are at rest, but the atoms (and hence protons) are moving, length contraction ends up with the density being different, meaning a net charge in this frame. You then get E&M united as tensor field F, but antisymmetric, meaning the spin-2 components are 0, leaving effectively two spin-1 (vector) components. This lets you do relativistic corrections for a propagating field, and the velocity of the original source gets turned into magnetic effects that act the same as if the source were moving at a constant velocity.
Extremely similar things happen with gravity, if you look at weak-field linearized versions of the Einstein field equations. The actual math ... well, it's rather ugly.
Comments
> For gravity, it goes one better -- this is a tensor field (hence the notion of gravitons having to be "spin-2" if they were described by a quantum theory), and the acceleration is encoded as well, ....
Well, that's mind blowing. Where could I go to learn more about this?
Other than "graduate textbooks", I'm not really sure. Jackson does cover the E&M case pretty well (EDIT: in chapters 11 and 14, note especially sections 10.11 and 14.1), but I'd combine it with the treatment in Taylor & Wheeler's highly readable _Spacetime Physics_.
For E&M, the standard way to develop this is to explain magnetism as Lorentz-transformed static electrical attraction/repulsion. Take two wires, and run current through them. Transforming to a frame where the electrons are at rest, but the atoms (and hence protons) are moving, length contraction ends up with the density being different, meaning a net charge in this frame. You then get E&M united as tensor field F, but antisymmetric, meaning the spin-2 components are 0, leaving effectively two spin-1 (vector) components. This lets you do relativistic corrections for a propagating field, and the velocity of the original source gets turned into magnetic effects that act the same as if the source were moving at a constant velocity.
Extremely similar things happen with gravity, if you look at weak-field linearized versions of the Einstein field equations. The actual math ... well, it's rather ugly.
I think my brain just exploded. Thanks for the references!