Date: Tue, 30 May 2000 01:33:33 -0700 (PDT) From: Kris Kennaway <kris@FreeBSD.org> To: Tim Vanderhoek <vanderh@ecf.utoronto.ca> Cc: Terry Lambert <tlambert@primenet.com>, Doug Barton <Doug@gorean.org>, Brett Glass <brett@lariat.org>, chat@FreeBSD.ORG, Arun Sharma <adsharma@sharmas.dhs.org>, Rahul Siddharthan <rsidd@physics.iisc.ernet.in> Subject: Re: The Ethics of Free Software Message-ID: <Pine.BSF.4.21.0005300114560.62245-100000@freefall.freebsd.org> In-Reply-To: <20000524222053.A80883@mad>
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On Wed, 24 May 2000, Tim Vanderhoek wrote:
> Is the amount of time that the universe can remember finite?
Depends on which cosmological model you prefer to believe in :-)
> Or, rephrased, the same question: "Are there a finite or an infinite
> number of states in which the universe can be?"
>
> I know of no evidence that space is quantized.
Actually, this is a pretty active area of research (noncommutative
geometry, one of the things I'm doing in my daytime life).
Just like in quantum mechanics you have a non-commuting phase space (in
other words, spatial coordinates and momenta do not commute, generating
the famous Heisenberg algebra [x, p] = i hbar, which is at the heart of
quantum mechanics), in general non-commutative geometry you generalize
this so that even the coordinates (and their conjugate momenta) don't
commute individually (so e.g. x y != y x where x and y are (operators
corresponding to) the coordinates of some particle).
As a consequence there exists a Heisenberg uncertainty relation in
coordinate space, so you lose the physical notion of a 0-dimensional point
in spacetime, and it becomes "smeared out". In other words, space is
quantized. (Of course, as other posters have pointed out it still doesn't
imply that the universe is a finite-state machine :-)
This idea (at least naively) has implications for the nature of
high-energy physics: since it imposes a cutoff on short distance scales it
may help to tame so-called ultraviolet divergences in quantum field theory
and quantum gravity. In practice of course it's not quite so simple :-)
Kris
----
In God we Trust -- all others must submit an X.509 certificate.
-- Charles Forsythe <forsythe@alum.mit.edu>
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