🚀 go-pugleaf

paul@mtnmath.UUCP (Paul Budnik) writes:

>> [...] Statistical mechanics assigns a measure to (some of) the
>> sets of possible worlds.

>In classical mechanics we understand what the connection is between the
>possible worlds and the actual world. There statistics provide an objective
>measure of our imperfect knowledge of a single physical world.

I'm not sure what you mean by "an objective measure". The statistics
is definitely *not* objective, in that different observers might use
different weights on the possibilities.

>> 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 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. [...]
>
>It may not be upsetting but it is a direct conflict with the classical
>interpretation. It precludes the possibility of there being a single
>objective physical reality that the statistics refer to.

Why does it preclude it? Why isn't it possible to assume that we are
in some definite world, and the wave function measures our lack of
knowledge of which world we are in? Of course, the wave function does
not represent our lack of knowledge in the form of a probability, but
in the form of a probability amplitude.

>Of course you do not need to use the classical interpretation, but if
>you do not you have to replace it with something else. What could that
>be? That there actually exist many different physical worlds or ... ?

I don't know why you think the physical existence of many different
worlds is any more necessary in the quantum case than in the classical
case of statistical mechanics.

>The problem in quantum mechanics has always been how do we connect the
>mathematics of the theory to the observations in experiments. I do not
>think anyone has a resaonable answer to this question. I suspect that
>Everett only succeeds in obscuring the problem with some pointless
>mathematics.

I disagree that Everett was doing "pointless mathematics". What the
mathematics shows is the coherence of quantum theory. Many of the
add-ons to quantum mechanics, such as the assumption that measurements
collapse the wave function, or the distinction between "mixtures" and
"superpositions", are unnecessary, since many of the key features of
these additions are derivable from quantum theory itself. Quantum
theory predicts that the act of partitioning the world into system
and observer will have the result of introducting mixtures into
the description of the system following an observation.

I don't agree that Everett's work has closed the book on
interpretations of quantum mechanics by any means, but I
believe that it is an important contribution.

>Bell had some harsh criticism of Everett in "Measurement theory of
>Everett/de Broigle's pilot wave" (in *Speakable and unspeakable in
>quantum Mechanics*, J. S. Bell, Cambridge). Bell suggests that
>Everett's ideas compare unfavorably with de Broigle's earlier work
>along the same lines. Do any of the supporters of Everett have an
>answer to these objections?

De Broglie's work was not "along the same lines", except in a very
general sense. They both were working on the assumption that the wave
function was a physical quantity, but whereas De Broglie believed that
the wave function was a component of physical reality, Everett
believed that the wave function might be a *complete* description of
physical reality.

I'll have to postpone a rebuttal to Bell until I reread his essay.

Daryl McCullough
ORA Corp.
Ithaca, NY