## Article for Novices: Kaluza-Klein Theory

electromagnetism. It was discovered by the mathematician Theodor
Kaluza that if general relativity is extended to a five-dimensional
spacetime, the equations can be separated out into ordinary
four-dimensional gravitation plus an extra set, which is equivalent to
Maxwell's equations for the electromagnetic field, plus an extra
scalar field known as the "dilaton". Oskar Klein proposed that the
fourth spatial dimension is curled up with a very small radius, i.e.
that a particle moving a short distance along that axis would return
to where it began. The distance a particle can travel before reaching
its initial position is said to be the size of the dimension. This, in
fact, also gives rise to quantization of charge, as waves directed
along a finite axis can only occupy discrete frequencies.

Kaluza-Klein theory can be extended to cover the other fundamental
forces - namely, the weak and strong nuclear forces - but a
straightforward approach, if done using an odd dimensional manifold
runs into difficulties involving chirality. The problem is that all
neutrinos appear to be left-handed, meaning that they are spinning in
the direction of the fingers of the left hand when they are moving in
the direction of the thumb. All anti-neutrinos appear to be
right-handed. Somehow particle reactions are asymmetric when it comes
to spin and it is not straightforward to build this into a
Kaluza-Klein theory since the extra dimensions of physical space are
symmetric with respect to left-hand spinning and r-hand spinning
particles."

Is this still at the basis of string/Mtheory today?

[Moderator's note: Yes, Kaluza-Klein theory remains one of the essential
paradigms underlying string/M-theory, although its concepts have been
extended enormously. By the way, string theory is able
to obtain the left-right asymmetric (chiral) spectrum of particles very