From: scerir (scerir@libero.it)
Date: Wed Feb 12 2003 - 15:15:11 MST
[Rafal]
> ### But I thought that as the entropy of the universe increases, the
> amount of information needed to describe it also increases.
I did not read Tegmark's paper. But, yes, if by entropy you mean a
measure of irreversibility, then in MWI entropy increases for sure.
We can see it in many ways. The branching structure, i.e., is,
itself, irreversibility. Or, if you prefer, it is asymmetry
between past and future. So we can also say that MWI broke its
own and unique law: the time symmetrical Schroedinger equation.
We can also put it in different terms. MWI supposes there is no
communication between different worlds. Hence, imo, it supposes
there is no 'interference' between different components of the
wave function (at least after the splitting occurs). But having
no 'interference' means a transition from an original 'pure' state
to a 'mixture'. And we know, from a Von Neumann theorem, that in
the change from a 'pure' state to a 'mixture' the entropy increases.
(On the contrary the evolution described by the Schroedinger equation
is unitary and the entropy is invariant).
I do not know if MWI 'maximize', globally or locally, the entropy
increase. And, perhaps, a 'comparative' calculation is not easy.
Because there are many different theoretical models of measurement
or 'collapse'.
In any case it is possible, in general, to link the effective gain
of information to the difference betwwen the initial entropy and
the final one (Brillouin rule).
s.
"This approach has several variations which are called
the 'relative state interpretation' and the 'many worlds
interpretation'. None is satisfactory because they
merely replace the arbitrariness of the collapse postulate
by that of the no-communication hypothesis."
- Asher Peres, 'Quantum THeory: Concepts and Methods',
Kluwer Ac. Press, 1998, p. 374.
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