- #1
alexh110
- 9
- 0
In Kaluza-Klein theory, the gauge symmetries for all the fundamental
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 gauge 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?
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 gauge 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?