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kdv
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In the Kaluza-Klein approach, 4-D electromagnetism is explained in terms of the curvature of a 5D space.
But I am bothered by an obvious question: what are the sources of the em field?
In GR, matter and energy curve spacetime. Now, if we assume a 5 dimensional version of of GR, it seems as if any matter/energy distribution would curve 5D spacetime.
So how could the theory accounts for the fact that charged matter "curves 5D spacetime" whereas neutral matter curves only the 4D submanifold (so that there is no electromagnetic force observed).
Whenever I have seen derivations of KK, it has always been with the metric only, not the metric coupled to sources. And one indeed ends up with 4D GR plus electromagnetism. But it seems to me that the question of sources is an obvious question.
Anybody can shed some light on this?
But I am bothered by an obvious question: what are the sources of the em field?
In GR, matter and energy curve spacetime. Now, if we assume a 5 dimensional version of of GR, it seems as if any matter/energy distribution would curve 5D spacetime.
So how could the theory accounts for the fact that charged matter "curves 5D spacetime" whereas neutral matter curves only the 4D submanifold (so that there is no electromagnetic force observed).
Whenever I have seen derivations of KK, it has always been with the metric only, not the metric coupled to sources. And one indeed ends up with 4D GR plus electromagnetism. But it seems to me that the question of sources is an obvious question.
Anybody can shed some light on this?