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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Mon, 9 Sep 2002 11:21:39 +0200

Jesse Mazer wrote:

*>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 difference.
*

*>>
*

*>>BM:
*

*>>"decoherence" refers to anything interacting with what you are, as
*

*>>observer, describing by a wave function, and which is not currently described
*

*>>by your wave function. (-> need of a tensor product).
*

*>>IMO, it has been discovered by Everett and it explained why we don't feel the
*

*>>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.
*

*>JM:
*

*>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.
*

BM: I don't see how the internal interaction could leads to decoherence, unless

the information is not available to the observer. If a cat is in the

(a + d) state in the box, and if we know the state of each "air molecules" in

the box, we can in principle observe macro cat interferences.

Obviously we cannot

keep track of all those molecules and that's why in practice, even if the box

completely isolates the cat and the air molecules we will not be able

to see the

interferences. So Brent is practically right, but the we loose the ability

of witnessing interferences just if the cat interact with *any*

particle we didn't

keep track of, whether that particle was inside the box or not.

JM:

*>
*

*>>>
*

*>>>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?
*

Sorry. It is Schroedinger Wave Equation.

*>
*

*>>JM:
*

*>>>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.
*

*>>
*

*>>
*

*>>BM: 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.
*

So we agree completely.

Bruno

Received on Mon Sep 09 2002 - 02:25:04 PDT

Date: Mon, 9 Sep 2002 11:21:39 +0200

Jesse Mazer wrote:

BM: I don't see how the internal interaction could leads to decoherence, unless

the information is not available to the observer. If a cat is in the

(a + d) state in the box, and if we know the state of each "air molecules" in

the box, we can in principle observe macro cat interferences.

Obviously we cannot

keep track of all those molecules and that's why in practice, even if the box

completely isolates the cat and the air molecules we will not be able

to see the

interferences. So Brent is practically right, but the we loose the ability

of witnessing interferences just if the cat interact with *any*

particle we didn't

keep track of, whether that particle was inside the box or not.

JM:

Sorry. It is Schroedinger Wave Equation.

So we agree completely.

Bruno

Received on Mon Sep 09 2002 - 02:25:04 PDT

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