On 09-Sep-02, Bruno Marchal wrote:

> 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.

Right. Because we cannot construct an appratus that measures an
operator corresponding to determing the state of the cat and
all the particles the cat interacts with and which constitute
the cat, we cannot observe the interference between the very
complicated dead-subspace and live-subspace.  However while
this is a limitation in practice and not in the mathematics,
it is more than *merely* practical.  We, or anything
exhibiting intelligence, must have memory, i.e. irreversible
encoding of some past events/experience.  This implies that
we, and our instruments, must be macroscopic, quasi-classical
things.  So it is impossible that we, or other intelligent
beings, can experience the interference effects. I suspect
that this is a counter-argument to Deutsche's AI quantum
computer that "experiences" interference, but I haven't worked
it through.

>> 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.

I think there is some confusion here about decoherence. 
Decoherence refers to the approximate diagonalization of the
density matrices *relative to certain bases*.  In theory there
are always other bases in the Hilbert space relative to which
the interference terms are not small. But because we are
necessarily macroscopic beings we cannot construct instruments
that implement measurements relative to those bases. 

Brent Meeker
"Epistimology precedes ontology."
      --- Terry Savage

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