3 ms·
Very belated reply: I don't consider a magnetic field to be an "action at a distance" explanation at all, so I'm not sure how to answer your first question. In
by Steuard 8y ago
Very belated reply:
I don't consider a magnetic field to be an "action at a distance" explanation at all, so I'm not sure how to answer your first question. In classical E&M, a magnetic field is a local property of space at every point. Moving electric charges affect and are affected by the magnetic field at their location in a specific way, and disturbances or changes in that field propagate outward in accordance with a local wave equation. Nothing is ever "action at a distance", because the field itself carries influences and signals from point to point. (I suppose it could look like "action at a distance" if you pretended that the field was just a made-up theoretical construct that wasn't really there. But that's very much contrary to the accepted perspective on fields at least as I understand it. Things like "fields carrying energy density" and "finite-speed propagation of field changes through empty space" seem to argue strongly for taking fields seriously.)
So I guess I'd say that the "fabric of spacetime" explanation is on roughly the same footing, though my own intuition feels like the spacetime variant is a bit more concrete, somehow. (I suspect a fair number of people would lean the other way, mind you.) Spacetime is very clearly here and real, and Einstein taught us that its structure is definitely dynamical. Adding a magnetic field is, mathematically, basically arbitrarily stapling a gauge bundle onto that spacetime manifold: it's one step more abstract and arbitrary.