Does the Electrostatic Force Originate from Curvature? An Explanation

[soumyajitnag]

einstein explained the origin of gravitational force from the concept of space time curvature.but what about the electrostatic force...does it also originate from some sort of curvature.please explain...

 

[Simon Bridge]

That's a yes and no - all the conservative forces can be described as the gradient of a potential.

Modern ideas about fundamental forces are in QFT - and particle physics - so that is where you want to look for your answers.

 

[VantagePoint72]

einstein explained the origin of gravitational force from the concept of spacetime curvature.but what about the electrostatic force...does it also originate from some sort of curvature.please explain...

There was an early attempt at doing this called Kaluza-Klein theory, in which spacetime was treated as five dimensional instead of four (four spatial dimensions and one of time). The equations governing the curvature in this 5D spacetime could be split into a set of equations equivalent to Einstein's equations for gravity in 4D spacetime, a set equivalent to Maxwell's equations, and a third (extra) piece. The fourth spatial dimension could be assumed to be very small ("compactified"), explaining why we don't notice it.

Impressive sounding as it is, there are a few problems with Kaluza-Klein theory. The extra piece of the equations left over after pulling out those for gravity and EM is one, along with a number of other issues in making the theory consistent with known physics. A bigger problem is the fact that—as was understood well after Kaluza-Klein theory was first published—it turns out Maxwell's equations aren't really the whole story for electromagnetism. The EM field is actually a quantum object, and any attempt at uniting gravity and electromagnetism should reproduce quantum electrodynamics, not classical electrodynamics (and, ideally, quantum gravity too—but that's a whole other story!)

That said, a number of the core ideas of Kaluza-Klein theory, including compactified extra dimensions, have made their way into string theory. So, while the original theory is more or less dead, it's basic elements aren't (at least, not yet).

 

[bapowell]

Interestingly, the mathematics of the electromagnetic force (as well as other so-called gauge forces) has some deep similarities with that of general relativity. Just as the Riemann tensor describes the curvature of physical spacetime, the electromagnetic field strength tensor describes "curvatures" of a space as well. Except it's not physical space, but an abstract "internal" space associated with the U(1) symmetry of the electromagnetic interaction (if that sounds like gibberish, it's language from QFT and gauge theory). So you can imagine that in addition to real space, there is this other space "laid down" on top of it, which has it's own values at each point. The geometry of this space determines the electromagnetic interactions in physical spacetime. So, I'd say the answer is "yes" but the space of relevance is abstract and probably doesn't yield any new physical insights.

 

[TrickyDicky]

Interestingly, the mathematics of the electromagnetic force (as well as other so-called gauge forces) has some deep similarities with that of general relativity. Just as the Riemann tensor describes the curvature of physical spacetime, the electromagnetic field strength tensor describes "curvatures" of a space as well. Except it's not physical space, but an abstract "internal" space associated with the U(1) symmetry of the electromagnetic interaction (if that sounds like gibberish, it's language from QFT and gauge theory). So you can imagine that in addition to real space, there is this other space "laid down" on top of it, which has it's own values at each point. The geometry of this space determines the electromagnetic interactions in physical spacetime. So, I'd say the answer is "yes" but the space of relevance is abstract and probably doesn't yield any new physical insights.

This abstract space corresponds in the*bundles mathematical context to the total space E of a principal bundle, right?
With the 4-potential A being the connection form of this principle bundle and the EM strength tensor F=dA being the curvature 2-form of the bundle.

 

[bapowell]

This abstract space corresponds in the*bundles mathematical context to the total space E of a principal bundle, right?
With the 4-potential A being the connection form of this principle bundle and the EM strength tensor F=dA being the curvature 2-form of the bundle.

Yes, exactly!

 

[WannabeNewton]

Well there is a beautifully simple reason why gravitation can be so elegantly and, more importantly, successfully described entirely in terms of the geometry of a 4 dimensional space-time manifold: the strong equivalence principle.

 

[TrickyDicky]

[Mentor's note: I edited out the part that quoted the deleted post]

Certainly the OP was not simple and mentioned a comparison with GR that is usually considered a fairly complex subject (except for guys like WN :tongue2:), QFT was mentioned in the firs reply and the Kaluza-Klein model in the second, those are also not usually considered simple.
In fact without knowing the OP background which he didn't provide is hard to know what is complex or simple for him.
Actually I thought I was simplifying the issue with my comment, maybe fiber bundles is not something to discuss in the general physics thread but I don't think general physics is meant to be a subforum to dumb down discussions.

 

[Fredrik]

I deleted the the troll post and most of the replies to it.