From owner-freebsd-chat Tue May 30 1:33:36 2000 Delivered-To: freebsd-chat@freebsd.org Received: from freefall.freebsd.org (freefall.FreeBSD.ORG [204.216.27.21]) by hub.freebsd.org (Postfix) with ESMTP id B224937BD79; Tue, 30 May 2000 01:33:33 -0700 (PDT) (envelope-from kris@FreeBSD.org) Received: from localhost (kris@localhost) by freefall.freebsd.org (8.9.3/8.9.2) with ESMTP id BAA66208; Tue, 30 May 2000 01:33:33 -0700 (PDT) (envelope-from kris@FreeBSD.org) X-Authentication-Warning: freefall.freebsd.org: kris owned process doing -bs Date: Tue, 30 May 2000 01:33:33 -0700 (PDT) From: Kris Kennaway To: Tim Vanderhoek Cc: Terry Lambert , Doug Barton , Brett Glass , chat@FreeBSD.ORG, Arun Sharma , Rahul Siddharthan Subject: Re: The Ethics of Free Software In-Reply-To: <20000524222053.A80883@mad> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: owner-freebsd-chat@FreeBSD.ORG Precedence: bulk X-Loop: FreeBSD.org 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 To Unsubscribe: send mail to majordomo@FreeBSD.org with "unsubscribe freebsd-chat" in the body of the message