From: Hal Finney (hal@finney.org)
Date: Wed Feb 12 2003 - 15:43:00 MST
Scerir writes:
> 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.
I don't believe this is the case. MWI is a fully deterministic theory.
You can evolve the wave function arbitrarily far backwards or forwards
in time by the Schrodinger equation. Therefore information is neither
created nor destroyed, and the total entropy of the multiverse never
changes. I believe this is equivalent to saying that the time evolution
is unitary.
> 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.
Tegmark argues that universes join as well as branch. We may have
multiple pasts as well as multiple futures.
> 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).
Perhaps we mean different things by MWI? In my view the MWI is simply
the position that Schroedinger evolution is the only thing that happens,
there is no state function reduction.
> 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).
Of course, from the local perspective of any one branch of the MWI,
entropy does increase, as we gain information about where we are in
the multiverse.
Hal
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