From: Glenn Morton (glennmorton@entouch.net)
Date: Fri Jul 18 2003 - 23:28:12 EDT
I won't respond to replies to this note as it is merely for everyone's info.
When people criticized Tegmark's many world's view applied to a vast
universe beyond the bounds of our visible universe, I had forgotten one
thing, the Bekenstein limit. This is a theorem which seems to limit the
amount of information which can be contained in a volume. and this is where
Tegmark gets his 10(10^118) distinguishable universes. Note Deutsch's use of
this theorem in the many world's discussion from his article:
“The question of whether all finite systems in the physical universe can
likewise be simulated by Q—i.e. whether (1.2) is satisfied in Nature—must
remain open until the state space and dynamics of the universe are
understood better. What little is known seems to bear out the principle. 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 (Bekenstein 1981)
N(A)= exp (Ac3/4hG) 3.15
Of distinguishable accessible states (h is the Planck reduced constant, G is
the gravitational constant and c is the speed of light). That is, in a
suitable basis the system can be perfectly described by using an
N(A)-dimensional state space, and hence perfectly simulated by Q.” David
Deutsch, “Quantum Theory, the Church-Turing principle and the Universal
Quantum Computer,” Proc. Royal Soc., Lond, 400(1985):97-117, p.110-111
Tipler refers to it but apparently has a slightly different radius for our
universe than Tegmark:
"The number of possible visible universes, 10[^10 123] (this number was
first calculated by Penrose), is again 10 raised to the Bekenstein Bound,
with R in this case being the radius of a sphere with radius equal to the
radius of the visible universe, 20 billion light-years, and the mass being
the mass inside that sphere." ~ Frank J. Tipler, The Physics of Immortality,
(New York: Doubleday, 1994), p. 221
See also:
Justin Mullins, “Why black holes put the squeeze on memory,” New Scientist,
Oct. 13, 2001, p. 20-21
Roger Penrose, "The Emperor's New Mind, p. 343-344
If Richard's letter to Scientific American is published and replied to,
anyone want to bet against me that Bekenstein's name will appear in the
reply?
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