Re: MWI, Copenhage, Randomness

From: Jesse Mazer <>
Date: Fri, 06 Sep 2002 14:07:14 -0400

Bruno Marchal wrote:

>Jesse Mazer wrote
>>Ok, I think I see where my mistake was. I was thinking that "decoherence"
>>just referred to interactions between a system and the external
>>environment, but what you seem to be saying is that it can also refer to
>>an internal effect where interactions among the components of a system
>>with many degrees of freedom cause interference terms to become
>>negligible. If that's correct, then when Wigner decided that interference
>>would cause the wavefunction of the cat or Wigner's friend to "collapse"
>>even before the box or the room was opened, then he was probably referring
>>to this sort of internal effect, so my argument about using quantum
>>computers to simulate truly impenetrable boxes would not make a
>"decoherence" refers to anything interacting with what you are, as
>observer, describing by a wave function, and which is not currently
>by your wave function. (-> need of a tensor product).
>IMO, it has been discovered by Everett and it explained why we don't feel
>split or the differentiation. Decoherence is just entanglement with the
>the environment, it is the contagion of the superposition state, the
>linearity of the tensor product.

I probably need to read up on the actual mathematics behind decoherence
before I can discuss it very intelligently. Brent Meeker seemed to say that
even in the case of an isolated system whose wavefunction we know
completely, if it has many degrees of freedom there will be an effect which
approximates wavefunction "collapse" in which interference terms become
neglible. Presumably this does not "collapse" the wavefunction onto any one
particular classical state (dead cat vs. live cat), but by eliminating
interference terms you get something similar to classical probabilities,
where you're free to assume the cat is "really" in some state all along and
your measurement just reveals that preexisting state (interference is the
reason you get into trouble thinking that way about the quantum world, as is
shown most clearly by the Bell inequality).

I don't know whether this diagonalization effect in an isolated system would
normally be called "decoherence" or if some other term would be used. I'd
guess that they're two sides of the same coin, since if you knew the
wavefunction for "system + external environment" it would itself have a
large number of degrees of freedom, so the principle is probably the same.
Also, I don't know whether Wigner was referring to an internal
diagonalization effect or to entanglement with the outside environment when
he argued that decoherence shows that the act of opening the box and
observing the cat has no particular importance.

>>But this makes me wonder about the thought-experiment by David Deutsch
>>which Hal Finney brought up, in which interference shows that an isolated
>>A.I. was splitting into multiple versions which experienced different
>>outcomes. Presumably a simulation of an intelligence would have a lot of
>>degrees of freedom too, so why wouldn't decoherence ruin things?
>Ok, but then SWE is wrong at some point. Where do you think?

What does "SWE" stand for?

>>Maybe since this is a computer simulation where we know the dynamical
>>rules and initial state precisely, we would know just where to look for
>>even the smallest interference effects, unlike in an ordinary macroscopic
>>system where we don't have such detailed information. Also, we could run
>>such a simulation over and over again from the same initial conditions,
>>which would also help to detect small statistical deviations from
>>classical predictions. I once read a comment by Deutch about decoherence
>>where he said something like (paraphrasing) "saying the interference terms
>>are 'almost' zero is like saying someone is a little bit pregnant." His
>>argument would probably be that although decoherence may explain why the
>>world looks approximately classical in the many-worlds framework, it
>>doesn't remove to postulate those other worlds in the first place.
>I don't understand your last sentence.

What I meant was although in practice decoherence might seem to solve the
measurement problem and remove the need for other worlds, in principle even
tiny interference effects are just as much in need of an explanation as
large ones, and decoherence will not make interference disappear completely
(as I argued above, we should be able to detect tiny interference effects in
simulations of macroscopic systems on a quantum computer, unlike in ordinary
macroscopic systems where we don't have enough information to know where to
look for such tiny effects). If you view the universe as a giant
computation, the only way to duplicate interference effects precisely is to
compute all those other histories--I think this is the point you were making
about Bohm and his rejection of COMP, since computing the behavior of the
"pilot wave" would probably be equivalent to computing all possible
histories of the system you are considering, and COMP says that observers
within this computation would see their own histories as real.


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Received on Fri Sep 06 2002 - 11:08:52 PDT

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