Finite time and infinite space

From: <hal.domain.name.hidden>
Date: Tue, 15 Jan 2002 11:31:11 -0800

One of the things that strikes me as most peculiar and unexpected about
the universe is this: that it is apparently finite and inhomogeneous in
time, yet infinite and homogeneous in space.

>From what we can tell, the universe began about 13 billion years ago
and has gone through a series of phases or "ages" in which the dominant
physical effects have been strikingly different. And current observations
appear to indicate that the pattern will continue into the future, with
our current era of matter and stars being destined to give way to low
temperature and long-term effects.

However at the large scale the universe shows no evidence of being finite
in size. Some models predict that it should be finite, but these aren't
very strong predictions given the struggles which cosmology is facing
these days. And even if it is finite as inflation models predict, it
is so huge that there is no real hope of distinguishing it from infinite
in size. Likewise the universe appears to be roughly the same everywhere.
Although there is clumpiness at many scales, there is no belief that the
average density or other parameters of the universe will be different
in widely separated regions.

Is this something that might be predicted by a multiverse theory?

It might be argued that the finiteness of (past) time is predicted by
the theory, because it is questionable whether it is meaningful to
have an infinite amount of computation in your past.

The apparent infinitude of the spatial universe however does not fit
too well, for the same reason. If the universe is infinite then it
plausibly carries an infinite amount of information. This would require
an infinite amount of computation. Of course most of it is outside of
the "light cone" imposed by relativity, so perhaps this loophole in some
ways could avoid the need for truly infinite computation.

Even if the universe is finite, it does seem extravagantly large.
It seems hard to justify such a size from anthropic arguments, especially
the sizes predicted by cosmological inflation theories. Surely humans
could have evolved in a much smaller universe, one which contains less
information and requires less computation.

The universe seems to contain a lot more information than is necessary
for minds like ours to exist. Perhaps there are subtle reasons why such a
large size is necessary (for example, perhaps inflation is a side effect
of the simplest set of fundamental particles which would allow atoms to
exist and hence life to form, so we get a big universe as a side effect
of having simple physical laws at the microscale). But unless we can
find such linkages, this appears to count against an ensemble theory.

Put another way, the all-universe model should predict that our universe
is little more complex than it needs to be for us to evolve. In effect
it predicts that such linkages will be found.

Hal
Received on Tue Jan 15 2002 - 11:04:59 PST