Let me follow up on the previous post with a few comments on the interpretation of quantum mechanics.
First of all, I do agree that there is a problem still to be solved in the foundations of quantum mechanics.
Not everybody agrees on this. Quantum mechanics works extremely well in all situations, so far as we know, which leads to people adopting the shut-up-and-calculate interpretation of quantum mechanics. In 99 percent of my professional work, I adopt that interpretation myself, sometimes quite explicitly – probably the single most frequent complaint I’ve heard about my book with Ike Chuang is that we take too pragmatic an approach to the foundations. (I suspect part of the problem is that we’re rather brazenly pragmatic, stating upfront that we’re not going to talk about foundations at all.)
However, it being a Saturday, I’ll let my hair down and admit that yes, I think there is a problem in the foundations.
Part of the difficulty is deciding what exactly is the nature of that problem. Is it an interpretational problem? Is the problem in the physics?
My own belief is that the problem is in the physics, and that if that problem can be solved, then there won’t be any interpretational problem.
So what is the physical problem?
Quantum mechanics as presented in many textbooks usually has postulates telling you that (a) a closed quantum system evolves according to unitary dynamics, i.e., Schroedinger’s equation, and (b) a quantum system that is measured evolves according to the so-called “projection postulate”, or something similar. Part (a) is completely deterministic, while part (b) is the part where probabilities enter quantum mechanics.
Now, of course, a measuring device is itself a quantum system. Furthermore, the quantum system being measured and the measuring device are both parts of larger closed systems (e.g., the Universe). That larger system should therefore be describable by a unitary evolution, if we believe the postulates of quantum mechanics.
Naively, then, one might think that it ought to be possible to derive the projection postulate from the postulate that closed systems evolve unitarily. Certainly, such a derivation ought to be possible if quantum mechanics is to be put on a single unified dynamical foundation.
The physical problem, in my opinion, is that no one has ever succeeded in carrying out such a deriviation.
There have, of course, been many attempts to put quantum mechanics on such a unified dynamical foundation. Perhaps the most fashionable in recent years has been the so-called “decoherence program”. Unfortunately, so far as I can determine, although the decoherence program has contributed substantially to our understanding of how classical physics arises from quantum, I still know of no convincing derivation of the projection postulate from unitary dynamics.
What are the prospects for carrying out such a derivation in the near future?
Not good, in my opinion, without the injection of some major new ideas, and quite possibly some experimental input. (Indeed, the possibility of experimental input into this issue is one reason for finding mesoscopic physics and quantum computing interesting.) This problem has simply been beating around for too long to be solved without some significant new ideas.
My own favourite crazy idea for resolution of the problem is that, in fact, the projection postulate will not be derived from unitary dynamics. Instead, unitary dynamics will be derived from the projection postulate. One of the insights to come out of quantuum computing in the past few years is that any unitary dynamics can be simulated by measurements alone. Perhaps, then, measurement is the underlying basis for all physical dynamics.