Electrical storms in the center of the Milky Way do not affect us, but the
gravity that emanates from the black hole at its center most certainly
does.
Above all, is there a deeper level to reality than the one shown by the
Standard Model? We have already seen that the Aspect experiments
have confirmed that there are no hidden variables underlying quantum-
mechanical properties, but that merely eliminates a deeper reality in
one specific situation.
Beyond the Standard Model
Physics at the moment is awash with myriad variations of Dirac’s antie-
lectron. There are numerous attempts to go beyond the Standard Model
(which categorizes the array of particles and forces now thought to com-
prise our universe) by answering the question, Why these particles and
forces? The quest for an elegant theory of everything will undoubtedly
continue, because only the discovery of such a theory or a proof that no
such theory is possible can derail the quest. As a result, mathematical
descriptions that extend the Standard Model are currently abundant. We
shall examine some of the consequences of these models—the particles,
structures, and dimensions whose existence might possibly never be
known.
The Other Side of Infinity
There is probably only one thing on which every mathematical model for
physics agrees—in this universe, there is no such thing as infinity.
That’s not to say that there is no such thing as infinity in any universe.
In an intriguing and provocative article^3 (which initially appeared in
Scientific American), the physicist Max Tegmark classified four differ-
ent types of “parallel universes” that could be explored. His Level IV
classification consisted of mathematical structures. Tegmark argues
cogently, if not necessarily persuasively, for a concept he calls “mathe-
matical democracy.” The multiverse (which is the collection of all pos-
sible universes) consists of every possible physical realization of a
mathematical model.
There is certainly good reason to consider this possibility. The Nobel
Prize–winning physicist Leo Szilard, ref lecting on the “unreasonable ef-
fectiveness” of mathematics in physics, declaring that he could see no ra-
tional reason for it. John Archibald Wheeler, whom we encountered in a
discussion on the physical utility of the continuum, wondered, “Why these
138 How Math Explains the World