proach caught lightning in a bottle—literally. Not only did this assump-
tion result in Einstein’s equations of general relativity, which wasn’t
surprising, but other equations emerged from this treatment—and these
equations were none other than Maxwell’s equations describing the elec-
tromagnetic field.
Every so often, a bizarre assumption results in something totally won-
derful and unexpected. Max Planck made a similar bizarre assumption
when he postulated that energy came in discrete packets; this assump-
tion resolved many of the existing problems in theoretical physics at the
time, even though it was to be years before the assumption was empiri-
cally validated. Paul Dirac made a similar assumption about the existence
of the antielectron. Kaluza’s assumption, and the almost-miraculous si-
multaneous appearance of the two great theories describing the era’s two
known forces (gravity and electromagnetism), made a great impression
on Einstein. Einstein’s enthusiasm was understandable—he spent much
of his career in search of a unified field theory that would successfully
combine the theories of electromagnetism and gravity. Kaluza’s discovery
looked like the fast track to such a theory.
There was just one problem: Where was the fourth spatial dimension?
Recall Kapitsa asking Dirac, “Paul, where is the antielectron?” The nor-
mal three spatial dimensions (north-south, east-west, up-down) seem to
suffice to locate any point in the universe. We seem stuck with three di-
mensions—as it undoubtedly seemed to Kaluza and Einstein. Then a
suggestion from the mathematician Oskar Klein appeared to present an
attractive possibility for a fourth dimension.
Klein proposed that the fourth dimension was an extremely small one
when compared with the usual three dimensions with which we are fa-
miliar. The page you are now reading appears to be two-dimensional, but
it is in reality three-dimensional; it’s just that the thickness (the third di-
mension) is very small compared with the height and width of the page
that comprise the other two dimensions. This suggestion resurrected, at
least in theory, Kaluza’s four spatial dimensions. However, there still re-
mained the problem that no one had ever seen the fourth spatial dimen-
sion, and the state of the art in both theory and experiment were
insufficient to the task of exposing it, if indeed it did exist. The Kaluza-
Klein theory, as it was called, died a quiet death.
The Standard Model Redux
One of the great discoveries in the last century is the fact that an atom
can change its species. Like the shape-shifters of science fiction, speciesSpace and Time: Is That All There Is? 147