In Kaluza-Klein theory, the gauge symmetries for all the fundamental(adsbygoogle = window.adsbygoogle || []).push({});

forces are mapped onto the higher spatial dimensions.

So the internal symmetries are now externalised.

Does this imply that you can extend the analogy with gravity further:

so for example, if the 5th dimension contains the guage symmetry of

EM, do electromagnetic charges produce distortions in the 5th

dimension, in the same way that mass produces distortions in 4D

space-time?

If so then presumably you can rewrite Maxwell's equations in a 1D 5th

dimensional sub-space, as the sum of a curvature scalar and a metric

scalar field equals the charge density scalar field, just as the

gravitational field equation is written as a sum of a curvature tensor

and a metric tensor field equals the energy-momentum tensor field?

The relative field strength of electromagnetism, compared with the

much weaker gravitational field, could then explain why the 5th

dimension is compactified; whereas space-time is not.

I don't have enough mathematical tools to understand high powered

string theory; but I'd just be interested to know whether what I've

written is reflected in current theory.

It just seems like common sense to me that the relative

compactification of the spatial dimensions, could be related to the

strength of the fundamental forces with which they are associated by

Kaluza-Klein theory.

Btw, since the compactification of all the spatial dimensions becomes

identical, at energies above the symmetry breaking point between

gravity and the other fundamental forces; I wondered does anything

happen to the time dimension?

If not then you're still left with a rather ugly asymmetry between

space and time.

Would be much nicer if the spatial dimensions became more temporal,

and the time dimension more spatial, until they meet in the middle.

I don't know if such hybrid dimensions are mathematically possible?

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# Kaluza-Klein Theory and spatial curvature

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