Tuesday, August 10, 2004

Quantum mechanics interpreted

I've long been one of those folks just not satisfied with the Copenhagen interpretation of quantum mechanics. It's too positivist; essentially claiming that all there is is correlations of measurements. I can't accept that. There is something out there, whether it be particles, waves, or very tiny gnomes. The other thing I don't like about it is the postulated mysterious "collapse" of wave functions, which I have never found more plausible than saying, "It's magic."

What stands between me and a better interpretation? Bell's inequality, and the experimentally verified violations thereof. I won't go into the definition of Bell's inequality here. The violations of Bell's prove that the two following principles cannot simultaneously be true.

(1) Locality. Nothing physical can propagate faster than speed of light. Using a little bit of relativity, one can show locality is equivalent to the even more plausible principle that all observers agree that cause always precedes effect.

(2) Realism. There is a meaningful answer to the counterfactual question, "What would have been the result of performing measurement X?" It's okay if the answer is a probability distribution, but there has to be an answer.

Faced with this dilemma, my response is and always has been, "Okay, (1) has got to go." (Note: denying (1) doesn't necessarily entail the possibility superluminal communication or time-travel, a subtlety I don't wish to go into here.) This has led me to embrace the existence of non-local hidden variables, particularly as expressed in Bohmian mechanics. A particularly appealing aspect of Bohmian mechanics is that it explains the ubiquitous probabilities in quantum physics in terms of a deterministic process, rather than treating the probabilities as fundamental. My biggest problem with Bohmian mechanics is that, as its own supporters admit, they haven't quite worked out a way to make it compatible with relativity. I also have a small problem with what I consider its mathematical inelegance.

But last week Geekpress made me aware of a new experiment. Reading about the experiment, and the experimenter Afshar's claim of falsifying the Copenhagen interpretation, I regret to say that I'm not sure if I agree with his claim or not, as I'm not exactly sure what the Copenhagen interpretation would predict the result to be. At issue are subtle distinctions about exactly what the Copenhagen interpretation says and how to interpret that in terms of Afshar's experiment. Even if the Copenhagen interpretation has been falsified (that's an extraordinary claim requiring extraordinary evidence), I've no idea whether the wound is fatal or treatable by a minor tweak.

As a side effect of following Geekpress's link, I was introduced to the apparently rather obscure transactional interpretation of quantum mechanics by John Cramer. I find this interpretation to be very elegant, especially in comparison to all the additional mathematic structure Bohmian mechanics adds on to the usual, beautiful quantum mathematical formalism. Crucially, the transactional interpretation embraces relativity. For me, the only drawback is that it is inherently probabilistic, unlike Bohmian mechanics.

The approach of the transactional interpretation is to explain things completely atemporally. One looks at the whole of space-time: past, present, and future. One then uses boundary conditions to determine what is possible. The fact that time moves forward (e.g. Second Law of Thermodynamics) is explained by a boundary condition on the universe! (For what is probably the simplest example of the use of boundary conditions in quantum physics, see the particle in a box.) For the next step, one uses Cramer's concept of transaction to calculate the probability distribution of the possible events. These probability distributions mathematically must agree with the usual probability distributions predicted by quantum physics. (If the probability distributions disagreed, then the transactional interpretation would be a new physical theory, not an interpretation of an existing one.)

Thus, my new dilemma is, do I embrace the nice probabilistic theory, or do I hold out for a relativistic theory in which "God does not play dice"?

Links to this post:

Create a Link

<< Home