a monumental gap, so this is an ultra long shot—more so if the extra spa-
tial dimensions are smaller than 10^18 meter.
The Shadow of the Unknowable
While the physics community is pursuing the ultimate theory of reality
with both enthusiasm and optimism, it is hard not to ref lect on what we
have learned during the last century about the limitation of knowledge in
the physical universe. There are at least two paths by which the ultimate
nature of reality may be something that is forever hidden to us. The first
is that the nature of space-time may be so chaotic at Planck length (the
length of a string) and Planck time (the time it takes light to travel the
length of a string) that we simply cannot measure things accurately
enough to determine some critical features of space and time. The sec-
ond is that the complexity of the axiomatic structure of whatever theory
ultimately describes reality admits undecidable propositions—or some-
thing similar to them. It may be that those undecidable propositions have
no impact on reality—much as the undecidable propositions examined
by Gödel were of meta-mathematical, rather than mathematical, interest.
On the other hand, it may be that a proposition lurks somewhere that says
that the ultimate nature of reality—the “atoms,” as it were, of space, time,
and matter—are forever beyond our reach. The quest for a theory of eve-
rything may well meet the same fate as Hilbert’s desire to prove arithme-
tic consistent. Some mathematician with a solid background in physics,
or some physicist who has studied Gödel’s incompleteness theorem, may
be able to show that a theory of everything cannot exist. Indeed, if some-
one asked me to bet, this is where I’d place my money.
NOTES
- See http:// physicsweb .org/ articles/ world/ 13/ 3/ 2. This site is courtesy of Physics
World, a magazine for physicists and possibly those who are just interested in
physics. At any rate, what I’ve read on the site is quite well written.
- W. Heisenberg, Quantum Mechanics (Chicago: University of Chicago Press, 1930).
- See http:// arxiv .org/ PS _cache/ astro -ph/ pdf/ 0302/ 0302131v1 .pdf. There is a less-
technical version of this (Scientific American, May 2003)—but they’ll try to sell
you a digital subscription. I’ve been a subscriber for thirty years; it’s a great
magazine—but this slightly more technical version is free. It is also one of the
most interesting papers I’ve read in the past decade. Although portions of it are
a little rugged, READ IT, READ IT, READ IT!
- Ibid.
Space and Time: Is That All There Is? 151
