Gerard 't Hooft states on his webpage:

I have mathematically sound equations that show how classical models generate quantum mechanics.

Also, there are some interesting discussions here on Physics SE about the question, see for example Discreteness and determinism in superstrings and Deterministic quantum mechanics [or searching for "+hooft +determini*"] and the links therein.

Which of the 't Hooft papers in arXiv should I read in order to grasp the question? Could anybody provide an ordered list? I would like to restrict myself for the moment to those strictly related to quantum mechanics, to grasp the ideas within a known framework. (I have seen that the question extends to the realm of string theory, where I am for the moment nearly ignorant.)

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    $\begingroup$ It's trivial to see that 't Hooft's models can't emulate a single quantum system for various simple reasons. One of them is that 't Hooft's models disagree with the superposition principle, the fact that for any two states $\psi_1,\psi_2$, an arbitrarily complex combination $a\psi_1+b\psi_2$ is an equally allowed state of the system. This principle or postulates underlies all of quantum mechanics and may be verified in as simple systems as 1 qubit. Because 't Hooft constructs "his foundations" to explicitly contradict this postulate, they can't agree with anything in proper quantum mechanics. $\endgroup$ – Luboš Motl Dec 20 '12 at 7:15
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    $\begingroup$ @DavidZaslavsky: I removed the soft-question tag again. $\endgroup$ – Qmechanic Dec 20 '12 at 9:33
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    $\begingroup$ It is absolutely not a soft-question. What I request is that some theoretician selects for me the paper(s) by 't Hooft that contains the essential idea in a more or less advanced stage and (if possible) before he extends the question to strings. If I were a physicist in the 1920s I wouldn't want to struggle against the Einstein paper with the previous, wrong version of the field equations (of 1915 or so?), or study all Einstein papers about inertia, but rather I would want a direct reference to the 1916 paper in Annalen der Physik. I am not asking for any popular description... $\endgroup$ – Eduardo Guerras Valera Dec 20 '12 at 11:31
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    $\begingroup$ I am working in lensed quasar spectra and in large scale structure computer simulations, this 't Hooft question is far from my field, and I don't want to devote days studying all papers that may seem related. I'm simply asking that some of you theoretical physicists select for me which paper I should study to grasp the question. I have a more or less solid background in QM but have not yet studied strings seriously. $\endgroup$ – Eduardo Guerras Valera Dec 20 '12 at 11:32
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    $\begingroup$ There's this little point that @Motl failed to grasp about these models: It's the "ontological, true" events described here that are such that any superposition of such events is NOT an ontological event. That's just like cats: the dead cat is ontological, the live one is, but any superposition of the two isn't, or at least, that's the case in our models. Now the superposition of the two cats DOES obey Schroedinger's equation. What I have done is take all "ontological" states of a system and look at the equations they obey. Now superpositions of ontological states also obey the equations. $\endgroup$ – G. 't Hooft Feb 27 '13 at 22:26

Well since this is a request for a reference to a paper one need not be a theorist.

I would start with the last reference 't Hooft himself gives in the paper found in the link at Physics SE. The last reference there is on the non-string model: "The mathematical basis for deterministic quantum mechanics" (arXiv:quant-ph/0604008).


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.

You could then follow backwards in time the references of this one.

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  • $\begingroup$ thanks very much. I'll have a deeper look at this paper. $\endgroup$ – Eduardo Guerras Valera Dec 22 '12 at 21:47

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