One of the things that has always bothered me is the apparent absence of a tested classical (ie, not quantum) theory unifying electromagnetism and general relativity. Maxwell's equations and special relativity combine well (Maxwell's equations actually imply special relativity). Looking through the literature, I find that the most credible combination appears to be Kaluza Klein (http://www-th.phys.rug.nl/~schaar/htmlreport/node12.html) theory. Namely, that gravity and electromagnetism are combined on a 5-dimensional manifold so that charge, mass, and laws of physics (including motion, gravity, and electromagnetism) are expressed as the geometry over this manifold.

Another approach which has some promise (but dips into quantum mechanics) is to combine the two forces into a single force for particles of a given mass/charge. Hence, we would have a manifold shape for the universe's proton field and another for the universe's electron field. Then we somehow need to calculate the interactions of these fields with each. We already know that there's (apparently) only a finite number of elementary particles, hence we need consider the interactions of a finite number of such fields. Seems pretty clumsy to me though.

So in any case, anyone have ideas about how these two forces go together? Thanks!

I am under the impression that electromagnetism fits nicely into the general relativistic framework, as long as you're only talking about the classical theory rather than the quantum one.

Originally posted by James R
I am under the impression that electromagnetism fits nicely into the general relativistic framework, as long as you're only talking about the classical theory rather than the quantum one.

yup, this is so. in fact, you can even fit the quantum theory of electrodynamics on top of a classical theory of gravitation. the so-called semi-classical approach. this is the theory in which hawking radiation was predicted.

note, this isn t really a "unification" as the term is usually used. to unify gravity and electrodynamics really means to realize both forces as different aspects of a cohesive whole. kaluza-klein theory is an excellent example of a unification of gravity and electrodynamics, if you restrict yourself to a classical theory.

string theory promises to be a unifying theory as well.

Originally posted by James R
I am under the impression that electromagnetism fits nicely into the general relativistic framework, as long as you're only talking about the classical theory rather than the quantum one.

Well, what got me thinking differently about that was a couple of observations (old and recent). First, charged particles always have mass. Hence, at the quantum level, there's some coupling between mass and charge. Theories like Kaluza Klein and superstring theories often predict interactions between gravity and electromagnetism. In particular, does the presence of electromagnetic fields curve space?

Hmm, that does remind me, the way you're probably talking about to combine GR and EM is to find the energy-momentum tensor of EM fields and add that as a corrective term to the GR equation which determines an aspect of the curvature of space in terms of the energy-momentum tensor of space. If someone knows work on that, I'd love to see it.

Anyway, the second observation is that some cosmologists are claiming "concensus" on the nature of expansion and dark matter in the universe. These claims occasionally involve "anti-gravity" which is merely a repulsive force and despite the name doesn't necessarily have anything to do with gravity though it probably would if it exists. Another indication that perhaps the interactions between gravity and EM aren't straightforward.