🚀 go-pugleaf

In article <1992Nov17.023054.3771@organpipe.uug.arizona.edu> corleyj@helium.gas.uug.arizona.edu (Jason D Corley ) writes:
>[...]
>However, with the
>extra dimensions being proposed in superstring theory gaining
>more and more acceptance, perhaps a review of Kaluza and Klein
>and their ideas might be in the works!
>
This is almost exactly what has happened, though historically in the
reverse order --- the revival of Kaluza-Klein theories in the 1980's
was one of the main reasons that the extra dimensions of string theory
were considered acceptable a few years later.  

One can actually do a great deal with Kaluza-Klein theories; by letting 
spacetime have more than one "extra" dimension, one can naturally
incorporate non-Abelian gauge theories (strong and weak interactions)
into general relativity.  There was a great deal of work on this topic
a few years ago --- see, for instance, _Modern Kaluza-Klein Theories_,
edited by Appelquist, Chodos, and Freund (Addison-Wesley, 1987).  The
work has slowed down, for two basic reasons:

1. General relativity in four or more spacetime dimensions is not
renormalizable, and we don't know how to quantize the theory.  The
successes of electrodynamics, electroweak theory, and quantum
chromodynamics are all successes as _quantum_ theories; a classical
unification is not nearly enough.

2. As classical models, Kaluza-Klein theories have too much flexibility
to be satisfying.  By appropriately choosing the geometry of the extra
dimensions, you can get just about any gauge theory you want; there is
nothing that picks out the particular interactions we see in the real
world.  The early hope in string theory was that consistency requirements
would pick out a unique model, which would look like a Kaluza-Klein
model at large distances, but with a unique, determined "internal
geometry."  It is now clear that this will not happen classically, but
it is still an open question whether quantum effects will determine a
unique string ground state.  

Steve Carlip
carlip@dirac.ucdavis.edu