From today's perspective, the crucial thing about electromagnetism is that it is a theory in which the dynamics (i.e. the behaviour of the forces) is intimately related to a symmetry principle. In the everyday world, a symmetry operation is something that can be done to an object that leaves the object looking the same after the operation as before. By extension, we may consider mathematical operations--or 'transformations'--applied to the objects in our theory such that the physical laws look the same after the operations as they did before. Such transformations are usually called invariances of the laws. Familiar examples are, for instance, the translation and rotation invariance of all fundamental laws: Newton's laws of motion remain valid whether or not we translate or rotate a system of interacting particles. But, of course--precisely because they do apply to all laws, classical or quantum--these two invariances have no special connection with any particular force law. Instead, they constrain the the form of the allowed laws to a considerable extent, but by no means uniquely determine them. Nevertheless, this line of argument leads one to speculate whether it might in fact be possible to impose further types of symmetry constraints so that the forms of the force laws are essentially determined. This would then be one possible answer to the question: why are the force laws the way they are? (Ultimately of course this only replaces one question by another!)
-- I. J. R. Aitchison and A. J. G. Hey, Gauge Theories of Particle Physics, 2nd ed., 1989, p. 42.
This is a good summation of the entirely pervasive idea that symmetry constraints (also called invariance principles) are behind the "behaviour of the forces" as we now understand them. Exactly how you get a force field out of a symmetry principle is also discussed by A & H, but we'll have to come back to that later. Shades of Larry's visit with Rabi Nachtner here... questions that result in more questions.
I should add that there's the rather contradictory idea, one that I'm in agreement with, that gravity is not a force. Yes, this most noticeable and inescapable presence is a different animal from, say, electromagnetism. Objects responding only to gravity, like a satellite in orbit or (neglecting air's influence, which you really can't) a tossed basketball, are following their simplest paths in spacetime. (Yes, spacetime, not just space.) It takes a force of some kind to knock them into or onto some other path. Or to hold them in one position, as you and I are being held in position now by electromagnetic forces keeping us from falling further toward the center of Earth.
This is a good summation of the entirely pervasive idea that symmetry constraints (also called invariance principles) are behind the "behaviour of the forces" as we now understand them. Exactly how you get a force field out of a symmetry principle is also discussed by A & H, but we'll have to come back to that later. Shades of Larry's visit with Rabi Nachtner here... questions that result in more questions.
I should add that there's the rather contradictory idea, one that I'm in agreement with, that gravity is not a force. Yes, this most noticeable and inescapable presence is a different animal from, say, electromagnetism. Objects responding only to gravity, like a satellite in orbit or (neglecting air's influence, which you really can't) a tossed basketball, are following their simplest paths in spacetime. (Yes, spacetime, not just space.) It takes a force of some kind to knock them into or onto some other path. Or to hold them in one position, as you and I are being held in position now by electromagnetic forces keeping us from falling further toward the center of Earth.
