Monday, May 11, 2009

Fine Idea on the Measurement Problem

Following up on the topic of the last post, I found this paper by Arthur Fine, called “Measurement and Quantum Silence”. I found it to be a clearly written summary of Fine’s approach to the quantum measurement problem (which was I was introduced to by the work of Mauricio Suárez.)

The term “quantum silence” refers to the Copenhagen interpretation-motivated suggestion that we just shouldn’t ask about the reality of the quantum system in superposition: there is no need “to talk about the value of an observable unless the state of the system is an eigenstate, or a mixture of eigenstates, of the observable in question.” We prepare a quantum system and calculate that its pure state evolves according to the Schrödinger equation. The problem is that when we measure the system it behaves “as if” what was evolving was only a mixture of the eigenstates of the particular observable we’re measuring. Fine introduces an interesting perspective on this, which is that the measurement process involves an information loss. It certainly seems that the rest of the information contained in the evolving pure state vanishes or becomes irrelevant when a measurement takes place.

Fine reviews other proposals (hidden variable and GRW-type collapse theories) and assesses how they deal with this loss of information, and he finds that while they try to replace the “brute” measurement process with a physical process meant to be more explicable, they don’t really explain the loss of information. And perhaps this can’t be done.

So, Fine makes his own proposal, which I described in the last post (although in this particular paper Fine doesn’t label the idea as “selective interactions”). Since the system behaves “as if” it was an evolving mixture rather than a pure state, why not assumes that it actually what happens. Rather than look to explain the loss of information which takes place in a measurement “farther down the line”, he proposes that the preparation actually replaces the full state with the mixture in advance.

Here’s how he motivates the idea: “There is a physical rationale for this procedure. It is that in making a measurement we do not interact with all the variables of the measured object. We only observe the particular aspect of the object that corresponds to the variable being measured….” The information that is lost pertains to aspects of the object to which the measuring device does not respond. The “aspects” here are what Suarez adopts as “propensities” in his work.

So, what to think? Well, in a nice aside in this paper, Fine credits philosopher of science Heinz Post* for suggesting a “conservation law” for problems in quantum theory: if you resolve one aspect of quantum strangeness, this tends to just shift it elsewhere. In Fine’s case, he addresses the puzzle of the measurement process with an account which says that the way we prepare a system alters the system from a pure state to a mixture prior to evolution. It’s an interesting idea and the pursuit of it offers additional illumination of the landscape of quantum mechanics. But in my case I’m happy to have collapse as an additional natural process which describes physical interactions between systems – I don’t feel a need to shift the strangeness in the way Fine suggests. And I don't think interpreting quantum systems as bearers of propensities turns on whether you adopt Fine's proposal.

*I would provide a link for mentioning Heinz Post, but very little comes up in an internet search. He was a professor at Chelsea College (which later merged into King's College, London). You get the impression he was an influential colleage and mentor, but published hardly at all.


Thoughts said...

Interesting idea but it seems to recast the measurement problem as "the entanglement problem": why and how are the screen and emitters in an interference experiment entangled from the start? The Transactional Interpretation of QM might offer some hints ie: interactions can move back and forth in time. In fact the more I look at this paper the more it seems to be a rephrasing of the transactional interpretation of qm..

Steve said...

That's interesting. You're right that there is a sense of moving back in time with Fine in that the measurement set up seems to reach back and alter the preparation.
It didn't strike me that it otherwise was that similar to the transactional interp. but I would have to go back and look. Thanks.