From: Hal <hfinney@shell.portal.com>
Date: Wed, 30 Mar 94 22:04:59 PST
To: cypherpunks@toad.com
Subject: Bekenstein Bound (was: Crypto and new computing strategies)
Message-ID: <199403310605.WAA22633@jobe.shell.portal.com>
MIME-Version: 1.0
Content-Type: text/plain


The Deutsch paper I quoted before was where I first heard of the Bekenstein
Bound which Eric Hughes mentioned.  According to Deutsch:

"If the theory of the thermodynamics of black holes is trustworthy, no
system enclosed by a surface with an appropriately defined area A can have
more than a finite number

        N(A) = exp(A c^3 / 4 hbar G)

of distinguishable accessible states (hbar is the Planck reduced constant,
G is the gravitational constant, and c is the speed of light.)"

The reference he gives is:

Bekenstein, J.D. 1981 Phys Rev D v23, p287

For those with calculators,  c is approximately 3.00*10^10 cm/s, G is
6.67*10^-8 cm^3/g s^2, and hbar is 1.05*10^-27 g cm^2/s.  N comes out
to be pretty darn big by our standards!

Hal