From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: QM non-causal?
Organization: ORA Corporation
Date: Tue, 15 Dec 1992 15:04:24 GMT

bhv@areaplg2.corp.mot.com (Bronis Vidugiris) writes:

>In article <mcirvin.724051030@husc8> mcirvin@husc8.harvard.edu (Matt McIrvin)
>writes:
>
>>There is no extra postulate involved at all; the Everett interpretation
>>merely states that the unitary evolution specified by ordinary quantum-
>>mechanical dynamics must be taken seriously at all times.  Thus, when
>>an electron is in a superposition of spin-up and spin-down states and
>>you observe the spin, you end up superposed too, and so does everything
>>that interacts with you, ad infinitum.  There's no added machinery for
>>"world-splitting"-- just QM with no pruning of the wave function's 
>>evolution, arbitrary or otherwise.
>>-- 
>>Matt McIrvin

>This seems to imply half-alive half-dead cats - more formally, Schrodinger's
>cat must also be in a superpostion of alive and dead states when placed
>in the famous schrodinger apparatus, along with the measuring instruments
>(not to mention the physicist/observer).

I think it is wrong to say that the *cat* is in a superposition of
alive and dead states; rather, the *universe* is in a superposition of
states, one in which the cat is dead, and another in which the cat is
alive. This may seem like a petty point, but I think it is important
to remember that the wave function is not a local quantity. There is
no such thing as the value of the wave function here or the value of
the wave function there.

>It seems to me that the much frowned upon view of 'many worlds' as parallel
>worlds is simply an objection to what seems to me to be one valid
>interpretation visualizing what a superposed cat / experimental device /
>experimenter means by reifing the abstract mathematics involved - rather
>like thinking of a 'phase space' as if it were a physical space.

I agree (I think). It seems to me that the most consistent view of the
wave function is by analogy with the probability distributions of
statistical mechanics (such as the Maxwell-Boltzman distribution):

In classical statistical mechanics, one can think of a "possible
world" as determined by an assignment of positions and momenta to each
particle. Statistical mechanics assigns a measure to (some of) the
sets of possible worlds. (I say "some of" because it is conceivable
that some strange sets are unmeasurable.) The measures can be
interpreted as the probability of finding oneself in a particular set
of possible worlds.

Quantum mechanics can be given a similar interpretation, where instead
of assigning probabilities to sets of possible worlds, it assigns
probability amplitudes to sets of possible worlds. The fact that the
statistics is done using amplitudes, rather than probabilities, is
rather strange. However, there is no reason that I know of to abandon
the ensemble point of view of classical statistical mechanics. The
amplitudes given by quantum mechanics can again be interpreted as the
amplitude for finding oneself in one of the sets of possible worlds.
The fact that there are incompatible observables, such as S_x and S_y
(the spin of a particle in the x and y directions), simply means that
some sets of possible worlds, such as the set of all worlds in which
S_x = 1/2 and S_y = 1/2, are not assigned any amplitude whatsoever.
There is no reason that this should be any more upsetting than the
fact that classical measure theory fails to assign measures to some
sets. There are sets that are not assigned a measure in classical
measure theory, and there are sets that are not assigned an amplitude
in quantum theory. In neither case does it mean that the sets (or the
properties used to define them) don't exist.

Daryl McCullough
ORA Corp.
Ithaca, NY

(Note: this view of quantum mechanics is brand-new to me, and I'm not
claiming that I believe it. However, it sounds good.)
Newsgroups: sci.physics