What is the need for KK-theories (and similar)

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Matterwave
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I'm not sure whether this question should go here or in the beyond the standard model forum...but I'll post it here since I think this question mostly pertains to general relativity.

The wikipedia article for Kaluza-Klein theory states: 'In physics, Kaluza–Klein theory (KK theory) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism."

I am no expert in KK-theory (obviously), but I was wondering what's the use for these types of theories?

Einstein's special relativity is fully compatible with E&M since Einstein especially formulated his theory to keep Maxwell's equation the same but modified Newton's equations. General Relativity is an extension of special relativity to non-inertial reference frames.

Is it not logical, then, that GR is fully compatible with E&M (we just take the covariant form of Maxwell's equations and take partial derivatives to covariant derivatives)? Why do we need some other theory to "unify" gravity and E&M then? Why can't we just use GR?
 

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Classical electrodynamics has four parts that I am aware of: Maxwell's equations, the Lorentz force, an orientation on the spacetime manifold, and the assumption that charge is associated with mass. The last is usually implicit, where the author of an article or text assumes the reader knows that electrons and other charged particles must have mass.

KK can associate mass with charged particles but also give mass to some photons. This may not be such a bad a thing, as the weak field bosons are massive.

KK theory attempts to incorporate electromagnetism into general relativity as a curvature in a 5 dimensional spacetime where electromagnetism shows up as curvature in this extra dimension. It's a very nice idea such as Dirac antimatter, but hasn't really delivered.
 
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Matterwave
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So, GR encompasses the first 3 "parts", and KK deals with the last part of how charges "get" mass? o_O

Am I getting the gist?
 
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So, GR encompasses the first 3 "parts", and KK deals with the last part of how charges "get" mass? o_O

Am I getting the gist?
I guess I missed this post for a while.

Kaluza-Klein theory attempts to unit general relativity and gravity by adding an additional row and column to the stress energy tensor. The additional entries to the stress energy tensor are the components of the electromagnetic 4-vector potential.

The new stress energy tensor describes curvature of a 5 dimensional spacetime. This is what Kaluza came up with. Klein asked what would happen if the 5th dimension were rolled-up having some unknown circumference. This way we may not notice it's existence right off if the circumference were very small.

To make things easier to visualize, collapse all 3 spatial dimensions into one, so that for one moment in time, space looks like a tube. 3 space is along the length of the tube. Waves or particles that propagate longitudinally propagate at the natural velocity c. At various angles from longitudinal they spiral. The particles travel less than c, and the group velocity of waves is also less than c, where our measurements for velocity are along the length of the tube.

The phase velocities of spiraling waves are greater than c. This is the case for massive particle fields. Massive particles have phase velocities greater than c.
 
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