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Magnetic fields are obvious distortions.. of.. something, but what exactly are they distortions of? Massive objects produce curvatures/gradients in space-time resulting in what we observe as gravity.. what is the equivalent explanation for magnetic/electric fields?

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"Magnetic fields are obvious distortions.. of.. something" Some gentlemen from the Naval observatory are here---Michealson and Morley, I think---they beg to differ. – dmckee Feb 21 '11 at 3:57
Care to elaborate? – Alex C Feb 21 '11 at 4:02
Surely the answer is just gauge theory? Weyl came up with the damned things with direct inspiration from GR... @Alex C: gauge theory adds internal dimensions to spacetime, and describes all known forces as the curvature of this internal space. – genneth Feb 22 '11 at 16:26

The short answer is nothing at all - fields are a fundamental part of the universe.

What dmckee is teasing you about in the comments is that your intuition saying that there must be a luminiferous aether, which is an idea that was actually conclusively disproven in the late 19th century by Michelson and Morley in one of the most famous experiments of all time. The fact that fields don't need to be permeating through any material was very disturbing to physicists at the time, because it seems so intuitively bizarre, but that's the way it is - fields just are. They don't exist "in" or "through" anything.

Some famous physicist - Gell-Mann or someone like that - has a quip about how fields are more real than particles; the idea of a "single electron" should be the idea that's abhorrent to our common sense.

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I down-voted this because of the implicit claim that fields are real, where the aether is not. It might be so, but the conventional view at least used to be that there is no matter, just equations that describe or model our experience. Using field in a humpty-dumptyish way (see the comments on Gordon's Answer) as a place-holder for aether is problematic. Convince me that the realist turn of the last few decades justifies saying that the conventional view is that the (quantum) field is real, and I'll remove my down-vote. – Peter Morgan Feb 22 '11 at 13:54
@Peter Morgan I wouldn't agree that the "conventional view" is that reality is just a set of equations and that matter doesn't exist. That sounds like an incredibly strong form of Pythagoreanism which ventures into mysticism. No, physics is based on empiricism: we make observations and then seek to explain them. It's not a deductive process, it's inductive. This foundation implies a belief that the ultimate judge of your theory is not your equations but your experience interacting with matter. The free-standing world outside of human equations is the only reality. – spencer nelson Feb 22 '11 at 17:50
Either way, your objection sounds epistemological, not physical, and I'm not sure I am well-read enough in epistemology to go through a complete debate on this. – spencer nelson Feb 22 '11 at 17:51
SE won't let me remove the down-vote. I wanted to not because you convinced me but because I like the tone of your response. To me, it's not that reality is a set of equations (I didn't see that my comment might be seen that way), but that the equations are associated with "reality" slightly loosely, as a model or description. Empiricism, sure! But, Map is not the Territory. "The free-standing world outside of human equations is the only reality" seems good to me. I suppose the idea in my head (in the world, I hope) of a field is established by its role in the equations. – Peter Morgan Feb 23 '11 at 4:42

I think that the answer depends on which type of physicist you ask. First, if you Lorentz transform the ether, then you would expect the Michelson-Morley result and that would not by itself rule out an "ether". Condensed matter physicists have theories about a medium called a spin net liquid and Xiao-Gang Wen (M.I.T) thinks that the vacuum is a quantum liquid of string nets. I don't know much condensed matter physics, but this looks interesting. He has posted the introduction of his book, Quantum Field Theory of Many Body Systems. Wen studied string theory at Princeton with Ed Witten and then changed fields to condensed matter theory. I don't know enough to make intelligent comments about this theory, but perhaps some string or condensed matter theorists will. This seems to provide the medium you are asking about. I put this answer out there more as what is being suggested by spin networks approach.

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The "ether" seems to be one of those Humpty-Dumpty words of Lewis Carrol--"When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.' 'The question is,' said Alice, 'whether you can make words mean so many different things.' 'The question is,' said Humpty Dumpty, 'which is to be master — that's all.' -Through the Looking Glass – Gordon Feb 21 '11 at 16:02
The present-day quantum vacuum has a suspicious resemblance to the 19th century ether. Xiao-Gang also certainly has a point in that a quantum liquid of string nets behaves quite similarly to the vacuum. (I don't think you can say "is" without venturing into philosophy, which I don't want to do.) – Peter Shor Feb 21 '11 at 16:08

Well, one should maybe separate the idea of "ether" from the vacuum of field theory. The vacuum of field theory is there and fields move over it with the appropriate creation and annihilation operators, but it is a relative frame . So if somebody really wants to hang on to a "medium" picture one can have the vacuum. It just does not have the properties assigned to ether: a universal rest frame.

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Ahem, “conclusive disproof” is perhaps too strong. I think it's worth pointing out that the reason I wouldn't say you've asked a "good question" is that your question seems not to have focused on the general understanding amongst Physicists that Michelson-Morlety was conclusive. The conventional position is that there is no aether. To question this is possible, but it has to be done with care, and, significantly, no-one has managed to make an argument for why it might be helpful when doing Physics to think and do mathematics in terms of an aether. One has to say, for example, that to be compatible with experiment the equations of motion of the aether and of everything else must be Lorentz invariant to quite a high degree of accuracy. That would seem awkward to classical physicists of the late 19th Century, but the advent of liquid Helium experiments makes such an idea seem at least somewhat more commonplace. Grigori Volovich, for example, has constructed a fairly extended discussion of this analogy (published by OUP, a final draft is available here). [I haven't looked at the book cited by Gordon, but his description makes it sound comparable, albeit not similar.] Harvey Brown has a fairly detailed discussion that takes a comparable point of view from the philosophical side in "Physical Relativity. Space-time structure from a dynamical perspective (Oxford University Press), 2005", although this is an entirely classical discussion.

The other problem is, as always, how to accommodate quantum mechanics, and quantum field theory in particular. That's much more difficult. The Helium example is certainly not enough to support talking about an analogous aether without far more care than anyone has so far managed to put together in one place (no-one has come very close at all).

Your secondary question, "Massive objects produce curvatures/gradients in space-time resulting in what we observe as gravity.. what is the equivalent explanation for magnetic/electric fields?", does point, loosely, to a mathematical relationship that is much more often given houseroom by Physicists. That is, GR can be constructed in terms of the mathematics of connections, and so can electromagnetism. This response is, however, at a rather different level from the way in which you have phrased your primary question, and, as just noted, the details of quantum field theory really gets in the way of any simple understanding.

All that said, with apologies for being so direct, WELCOME to Physics SE! I've learned a lot that would have taken me much longer to learn in other contexts, and I hope you have as good an experience.

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I've had good experiences with all other stackexchange sites so I trust that I will, and so far, I have. As for the rest of your post, if you'd care to expand on the quantum aspects of such a discussion, I have somewhat more than an elementary knowledge of quantum principles and could appreciate that discussion. – Alex C Feb 22 '11 at 5:37
At first glance, I ca/won't expand on the quantum aspects. I've built many different mathematical models over the last 20 years that don't work. I have a current "maybe a model like this can be built", but most likely it'll fall apart as well. Maneuvering constructively around the many no-go theorems in a way that we can all agree is sensible and useful is difficult --needless to say, because it would have been done if it was easy. Spencer Nelson said most of the conventional view already. No material, just equations. Saying that fields are real is questionable, however. – Peter Morgan Feb 22 '11 at 13:56

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