Tuesday, November 18, 2008

The Scandal of Quantum Mechanics

I've came across this letter to the editor for about a month, but only now remember to make a comment on this, so it's a bit "stale". But what the hey....

This letter was published in the Nov. 2008 issue of AJP, written by N. G. van Kampen of Utrecht University in the Netherlands. He was responding to an article published earlier in the same journal by Hrvoje Nikolić titled "Would Bohr be born if
Bohm were born before Born?".

I wouldn't say that van Kampen's views on this is exactly like mine, but I think I can concur with him at the minor annoyance at the continued problems among physicists at reconciling that the "quantum world" may not be anywhere similar to the "classical world", and that all of these conceptual difficulties could be entirely due to us using classical concepts and forcing it to work in the quantum regime. For example, he wrote this:

The difficulty is that the authors are unable to adjust their way of thinking—and speaking—to the fact that phenomena on the microscopic scale look different from what we are accustomed to in ordinary life. That two electrons far apart may be entangled seems strange to someone who still thinks of electrons as individual particles rather than as manifestations of a wave function.

This is what I mean by forcing our classical concepts into the quantum world. There's nothing a priori that indicates that such an exercise is meaningful, or even valid. We simply do it because we are familiar with the classical world, not that we know the classical concept works in the quantum regime. Thus, we still use the concepts of classical particle, energy, position, momentum, etc... in extracting information from the classical regime, mainly because we don't have anything else to use, but we shouldn't fool ourselves that these concepts are meaningful there.

van Kempen went on to tackle quickly the issue of the double-slit experiment, the "measurement problem", and possibly the "Schrodinger Cat".

If you access to AJP, this might be something you want to read.



Peter Morgan said...

Art Hobson has a response to the van Kampen accepted for AJP, which is available on the web-page you cite in your links: http://physics.uark.edu/hobson/papers.html

Peter Morgan said...

My annoyance at this kind of dismissal of Classical modeling is that there are logical problems as much with the theory of measurement in QM as with classical theory of measurement.

The first problem is that instead of talking about preparation apparatus and measurement apparatus, which is moderately justifiable in instrumental or positivist terms (a mode of discussion that is perhaps particularly associated with Margenau), Physicists generally talk in terms of "quantum systems" and a measurement apparatus, which is hardly justifiable by empirical data at all. This is old, of course. The problem here is the desire to understand the causes of phenomena; Physicists consider nothing less than a causal account to be sufficiently explanatory. This is not about visualization, and it is as endemic amongst quantum theorists as amongst classical visualizers. Causality is essentially metaphysical, in contrast to empirically verifiable statistics and correlations of events.

More seriously, preparation apparatus (or an ensemble of quantum systems if one absolutely must) and measurement apparatus have to be perfectly separable in order for us to write expected values of measurement results as the trace of a product of
[a density operator that represents a given preparation apparatus (or ensemble of quantum systems) in every experimental setting, regardless of what measurement apparatus is used] and
[a measurement operator that represents a given measurement apparatus in every experimental setting, regardless of what preparation device is used]
= Tr[rho.O].

The trouble with this is that the Reeh-Schlieder theorem shows that (for quantum fields at least, if we accept the Wightman axiomatization of our best theories) idealized local measurements are enough to tell us the state of the whole apparatus to arbitrary accuracy, so that idealized local measurements can tell us everything about all the experimental apparatus, so we cannot suppose preparation apparatus and measurement apparatus to be perfectly separable. The only way to model an experiment is as a whole, not separated into a part that is represented by a density operator and a part that is represented by a measurement operator. Bell is eloquent on this in his article "Against `measurement'" (though I think with different intentions that I have here).

Note that it's common to say that the Reeh-Schlieder theorem is problematic in its relationship to causality, whereas I take an essentially different conclusion from it here: Experimental apparatus is not separable.

If we can in principle only model a whole experiment, indeed the whole universe, quantum measurement becomes empirically indistinguishable from classical measurement, because looking at a meter or reading a computer printout does not affect such effectively classical objects. Now, the point is not that classical measurement theory is better than quantum measurement theory, merely that they are different, and that we can understand Physics better if we know how to model experiments using both formalisms.

Before you say "Bell's theorem", please read and be able to destroy my "Bell inequalities for random fields" in detail (that's J. Phys. A 39 (2006) 7441-7455). Since no-one has yet decided to comment formally on this paper, you'll have to figure out whether it's wrong all by yourself.

Of course there's a lot more to say, understanding the relationship between classical and quantum models is not an overnight thing, but whether a classical model can be visualized is not the point.

It's quite amusing that van Kampen says that "phenomena on the microscopic scale look different from what we are accustomed to in ordinary life" (my emphasis), since we don't look at microscopic phenomena at all.