I came across a very recent paper by Gerard 't Hooft
The abstract says:
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show that this is not true in certain models where quantum behavior can be attributed to underlying deterministic equations. It is argued that indeed the apparent spontaneous collapse of wave functions and Born's rule are features that strongly point towards determinism underlying quantum mechanics.
http://de.arxiv.org/abs/1112.1811
I am wondering why this view seems to unpopular?
Best Answer
I'm working on a new, much improved version of my paper. Please note that I am not a fundamentalist, like, as it seems, some of my critics. I don't have an open telephone line with God, like Einstein on one side, and Motl on the other. So what I am doing in my paper (which will come out as a book, eventually), is I simply explore the idea that the usual counter arguments against a simple, deterministic interpretation of qm can be ignored, and I ask what you may get. The answer is quite interesting, but yes, one does encounter some interesting problems. The most severe, technical problems one gets are totally unrelated to the usual emotional arguments against deterministic qm, so I ask: are these totally prohibitive then, or is there a way out? Would that also answer the usual Motl-like objections? The most obnoxious problem I get: how does one arrive at an effective Hamiltonian that is both bounded from below and locally defined (or: extensive) ? There may be very interesting answers; one of them says that yes, the entire theory obeys complete locality - all physics is local - but the ultimate Hamiltonian of qm is non-local. This means that the phases of wave functions of far-away particles enter in the physics equations in a non-trivial way, while nothing of this has effects on the predictions of qm, which, in the usual qm way, are local.
But that does not have to be the answer. An other possible answer I find much more interesting and natural. You know that there are lots of crackpots who claim that you can "disprove the Bell theorem". Most of those totally miss the point, but there is a way. Bell assumes that in the initial state, the entangled particles just separating from one another, and Bob and Alice, who did not yet make their decisions, are fundamentally uncorrelated. That's because Alice and Bob must have "free will". There are two points to be considered to see why this may well be wrong. One is, that correlation functions do not have to vanish outside the light cone (look at QFT, but also look at simple classical systems such as liquids showing critical opalescence near the critical point); the other is directed to those who believe that only "conspiracy" can force Bob and Alice then the mike the "right" decisions. No, there can be something else. If you have a deterministic underlying theory, then there are two kinds of states: the truly `ontological' ones, and the templates, which are quantum superpositions. In ordinary qm, we do not distinguish between the two, but when it comes to the question of realism, you must. Then we note that there is a simple conservation law of nature: once a state is ontological, it will stay that way forever. A template will forever be a template. This means that, no matter what Alice and Bob decide, they will not be able to rotate their polarisers in such a way that the photons come out as superpositions of the other choices they wanted to make. They will have to rotate objects in their environment as well, so that, after changing their minds, they will again work with an ontological state.
Of course, Alice and Bob cannot change their settings without essential changes in their past, and, in probability terms, they might change their state into a much less (or more) likely one.
By the way, the notion of probability enters into my theory in a very simple way: it exactly corresponds to the uncertainties in the initial state, which are reflected in the use of the templates. This leads to the (EXACT) Born rule. Please wait until the improved version of my paper comes out.