Kaluza-Klein Theory: Exploring Its Merits & Drawbacks

[El Hombre Invisible]

I'd never heard of Kaluza-Klein theory before today, and from what I've read I think that's rather odd. Taking it from a purely non-quantum, relativistic unification of gravity and electromagnetism, what's wrong with it? I know it has been subsumed into other, more sophisticated theories, but on its own merits, does it work?

 

[robphy]

Possibly interesting reading on this recent thread:
https://www.physicsforums.com/showthread.php?t=101151

 

[El Hombre Invisible]

Thanks robphy. I'll be getting into the ins and outs of Maxwell's equations next year, and of GR... sometime before I have kids, so I'm not too optimistic about actual understanding K-K theory. I was more interested in why, if both EM and GR are derivable from it, it is not covered more in textbooks, or pop sci books come to that.

Everywhere I see a problem with K-K theory it seems to concern either quantization, particle physics or nuclear forces. Those things aside, I'm wondering if there's any historical reason why what appears to be an extention of GR to cover EM in which Maxwell's equations emerge is any less prominent than GR itself. As the advert says, why take two bottles into the shower when you can take one?

I guess this is more of a science history question.

 

[pervect]

I *think* the situation is that KK theory predicts an unobserved scalar field. But I'm not terribly sure I've got this right, so take this with a grain of salt.

 

[El Hombre Invisible]

I *think* the situation is that KK theory predicts an unobserved scalar field. But I'm not terribly sure I've got this right, so take this with a grain of salt.

This is the radion field, right? Isn't this predicted in certain QFTs though? If the radion field was originally predicted by KK theory (which, so far as I can tell, it was), would not a success in these theories (the discovery of the radion particle) prove an equal success for KK theory?? Or are the two fields dissimilar in the two theories?

I know Einstein disproved Weyl's similar unified field theory (in which Einstein's and Maxwell's equations were also derived in a 5D spacetime) and Weyl believed his own work to be superseded by Schrodinger's, but I cannot find any similar disproof of KK theory, or anything that would suggest it suffered from the same problems. The amount of literature outlining the theory, its history and its problems in the net is very slim.

 

[pervect]

I don't know. What I'm basing my statement on is remarks like

With this assumption, each was successful in obtaining the field equations
of both electromagnetism and gravity from a single five-dimensional theory.
Nordstr¨om, working as he was before general relativity, assumed a scalar
gravitational potential; while Kaluza used Einstein’s tensor potential. Specif-
ically, Kaluza demonstrated that general relativity, when interpreted as a
five-dimensional theory in vacuum ... contained four-dimensional general relativity in the presence of an electromagnetic field ...
together with Maxwell’s laws of electromagnetism.

There was also a Klein-Gordon equation for a massless scalar field, but this was not appreciated and was in fact suppressed — by Kaluza at the time.)

from http://arxiv.org/abs/gr-qc/9805018
Unfortnately my understanding of Kaluza-Klein theory remains rather sketchy.

 

[El Hombre Invisible]

I don't know. What I'm basing my statement on is remarks like
from http://arxiv.org/abs/gr-qc/9805018
Unfortnately my understanding of Kaluza-Klein theory remains rather sketchy.

Yes, this is the radion, I think. This seems to pop up in several other theories and seems to be something we're still hunting down.