From: daryl@oracorp.com (Daryl McCullough)
Subject: Re:  Simple observation about Quantum Kitty Cats
Organization: ORA Corporation
Date: Mon, 28 Sep 1992 13:48:25 GMT

In article <1992Sep27.073401.3486@asl.dl.nec.com>,
terry@aslws01.asl.dl.nec.com (Terry Bollinger) writes:

>Again my question to MWI advocates: Does MWI say *anything* at all
>that has the courtesy of being testable in *any* conceivable fashion?
>If not, how can you seriously claim the MWI to have any meaning?

I agree completely! (Well, almost completely.) It certainly is not
clear in what way MWI says anything testable. However, the reasoning
process leading to MWI is compelling: 1. QM, with its quaint axioms
about measurement processes is an enormously successful theory; there
are absolutely no hints to the limitations to its applicability. 2.
Since QM seems universally applicable, there is no reason not to apply
it to observers and measurement devices as physical systems. 3. Having
done so, there is no reason to believe in wave-function collapse or in
a measurement nondeterministically selecting one eigenstate out of a
superposition.  4. There you are, at MWI.

I try to alternate between defending MWI to its detractors and
attacking MWI to its advocates, in the hope that someone brighter than
I will solve its problems for me.

It seems to me that the only hope for empirical content from MWI is in
giving us a testable, *subjective* physics. I think it would something
along the lines of Von Neumann's interpretation of quantum mechanics,
with the ugly wave function collapse, except the collapse would be
personal and subjective, rather than objective. The wave function for
a system (such as the correlated pairs of EPR) could simultaneously be
collapsed for one observer and uncollapsed for another. This has, to
an extent, already been worked out by Everett with his
relative-states, but in my opinion he has not satisfactorily addressed
(1) the origin of probabilities in his theory, (I think his derivation
of probabilities is circular), and (2) the origin of a preferred basis
for observers.

The need for a preferred basis can be seen from the very simplest
model of an observation process. Assume that we have a system with a
spin-1/2 particle and an observer measuring its spin in the z
direction. For simplicity, we will assume that there are three
possible states of the observer: |?> the state before observing the
spin, |UP> for observing spin-up, and |DOWN> for observing spin-down.
The spin-1/2 particle can be in two possible states, |+> (spin-up) or
|-> (spin-down). Suppose that the particle starts in a superposition
1/sqrt(2) (|+> + |->).

Then, the evolution of the entire system (particle plus observer)
proceeds as follows:

   1/sqrt(2) |?>(|+> + |->) ==> 1/sqrt(2) (|UP>|+> + |DOWN>|->)

So this is usually considered to be an instance of a measurement,
where the state of the observer becomes correlated with the state of
the particle. Subjectively, it seems that the observer either goes
into state |UP> (with probability 1/2) or into state |DOWN> (also with
probability 1/2).

However, there is nothing in the mathematics of this situation that
says that a measurement of spin in the z-direction has taken place.
We can just as legitimately write the final state as

1/sqrt(8) ((|UP> + |DOWN>)(|+> + |->)
          + (|UP> - |DOWN>)(|+> - |->))

In this way of writing it, it looks as if the measurement were not of
the operator sigma_z, but the operator sigma_x, (which has eigenstates
1/sqrt(2) (|+> +/- |->)).

To interpret the process as a measurement of sigma_z, it is necessary
to have a preferred basis for observers. For some reason, it must be
that describing the observer as being in the state "observing spin-up"
or "observing spin-down" must be more natural somehow than describing
the observer as being in a superposition. This preferred basis doesn't
come from quantum mechanics, so if it is there at all, it must arise
from the details of describing macroscopic objects such as observers.
(Presumably, the preferred basis will always be the one in which
macroscopic observables have definite values.)

While I believe that the MWI program could work, I don't think it is
anywhere close to being sorted out.

>One last note: Yeah, "intermediate versions of MWI..."  Follow them up
>rigorously and I stick with my postion that what you will find is
>going to end up looking an awful lot like a fancy pilot wave model.

I have read Bell's essay in _Speakable and Unspeakable_, and as much
as I admire him, I disagree with him on this point. Everett's MWI, as
I understand it, is an attempt to do QM with no hidden variables. The
pilot wave approach explicitly inserts hidden variables, namely the
positions of particles. (The pilot wave theory solves the problem
mentioned above, a preferred basis, by simply asserting that position
is the preferred basis. While this is a way out, it seems extremely
artificial; there is nothing in the mathematics of QM that makes
position special.)

The two approaches are similar in that they both take seriously the
idea of a universal wave function, but the pilot wave theory uses this
wave function not as the complete description of the universe, but as
an auxiliary field providing a quantum potential affecting particles
with well-defined positions. While this approach has a certain appeal
(it seems to be a minimal departure from classical physics), I find it
completely implausible when doing the quantum mechanics of multiple
particles. For one thing, the quantum potential is completely
nonlocal; the force on a particle here depends on the positions of all
other particles in the universe (in a way that does not fall off with
distance). While this may be acceptable in a nonrelativistic model, it
makes no sense relativistically.

A second problem with the pilot wave idea is the dynamics of the pilot
wave. Does it collapse on measurement of particle position? If not,
then it seems that there is a testable difference between the pilot
wave interpretation and Von Neumann's collapse interpretation. If so,
then the pilot wave interpretation has not accomplished anything,
since the weirdness of quantum mechanics is simply shuffled from
particle dynamics to pilot wave dynamics.

Daryl McCullough
ORA Corp.
Ithaca, NY