HI,
Almost all body of theoretical physics can be generalized to 5D spacetime.But the effects of the 5th dimension cannot be seen or detected by us.However if you, like Klein, assume that the spacetime along the 5th dimension is curled up into a tiny circle (Plank circle),then you have to wait until experimental physicists can probe distances of order of Plank length! This, of course, requires a particle accelerator which operates with Plank energy! I am afraid, building such accelerator, if not impossible, would take a very very long time. I don't know how much you know about 5D physics? Let me tell you, in brief, the story of the subject. First, I should mention that, except for field theory, 5D generalization of physics is trivial.
Soon after the formulation of general relativity(GR) by Einstein, Kaluza(1921) reformulated Einstein's GR in a 5-dimensional Riemann spacetime R(5). He showed that both the gravitational and electromagnetic interactions ( the only two forces known at the time) can emerge as different manifestations of his 5-dimensional GR. Point particles of this theory move along geodesic lines in R(5), and these path are seen, in 4-dimensional Reimann spacetime R(4), as trajectories of particles subject to both gravitational and electromagnetic forces.
In 1926 O. Klein investigated the compatibility of Kaluza's theory with quantum mechanics.By using Bohr-Sommerfeld quantization rule and applying it to the periodic motion along the 5th dimension, Klein deduced that the electric charge is a multiple of the elementary charge (e), i.e. it is QUANTIZED. From the known value of e, he found that the radius of the 5th dimension is of order of Plank length.
Well, things get more surprising, if one analysises the dynamical behaviour of a classical point-particle in 5D gravitational field. One, indeed, can show that THE ELECTRIC CHARGE IS NOTHING BUT A MANIFESTATION OF MOTION IN THE 5th DIMENSION. How about that?
In the orignal work of Kaluza & Klein it is not clear wether the 5th dimension should be considered as physical or just a mathematical device necessary for unification. Nowaday, it is accepted that the 5th dinension should be taken seriously as physical dimension.
As you might know, the ground state (vacuum) is an important concept in studying the physical properties of dynamical system because, the low-energy physics can be obtained by introducing physical fields as excitations around the ground state. It might seem natural to assume that the vacuum of the K-K theory is the 5D Minkowski space M(5). But,this assumption, if true, means that K-K theory is wrong, because we are certain that the space we live in is not M(5). So the vacuum of R(5) has to be different from M(5).As I mentioned before, the way out of this problem is to take the true vacuum of the K-K theory as a product of 4D Minkowsiki space M(4) with a circle S(1) [M(4)XS(1)] and assuming that the circumference of this circle is very small so that the 5th dimension is unobservable in standared experiments.
UNFORTUNATLY, AS IT IS TIME FOR ME TO GO TO BED, I won't be able to mention any thing about the modern K-K theory.
I shall leave you with what
Kaluza said in the 1921 paper;
"it appears hard to believe that those relations,hardly to be surpassed in their formal correspondence, are nothing but an alluring play of whimsical chance"
references;
1. GRAVITATION AND GAUGE SYMMETRIES, BLAGOJEVIC, IoP,2002.
2. THE OSKAR KLEIN MEMORIAL LECTURES, VOL1, WORD SCIENTIFIC, 1991.
REGARDS
SAM
