Crazy Talk

Some of you are familiar with my fondness for fringe science. My latest infatuation is this new paper:
quant-ph/0604008


Unlike many of my enthusiasms, this one has impeccable bloodlines. The author, Gerard 't Hooft, is a Nobel Prizewinner and one of the deepest thinkers in Physics. The subject, although somewhat disreputable, also has excellent heritage, having been championed in one form or another by Planck, Einstein, Schroedinger, and Bell. In The mathematical basis for deterministic quantum mechanics, 't Hooft takes a shot at a hidden variables theory of quantum mechanics.

Many physicists have been bothered by the paradoxical seeming qualities of quantum mechanics, and a lot of prominent ones have tried to fix it up. Even Feynman, who didn't believe in trying to fix up quantum, said something like If quantum mechanics doesn't bother you, you're crazy.

't Hooft's idea is that information loss can make an honest quantum theory out of a deterministic one:
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes.
The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
The paper is only slightly technical. I predict that Luboš will hate it, partly because t' Hooft likes discrete time.

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