# What are the 't Hooft papers about classical models underlying QM?

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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.)

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user Eduardo Guerras Valera
@David Zaslavsky: thanks very much for the edit (I always welcome corrections to my non-native english), but, could you re-formulate it again in some other way? Because now it seems that 't Hooft models generate the whole foundations of QM, which is not true. As I have so far understood, they are able to reproduce some simple systems. That is why I wrote 'underlying classical models behind QM' instead 'generating QM'.

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user Eduardo Guerras Valera
Ah, I just used the wording from the quote. Anyway I fixed the title, hopefully that's okay. (You can always make such edits yourself, you know.)

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user David Z
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.

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user Luboš Motl
@Qmechanic hm, I wouldn't have thought this needed soft-question. Maybe I'm wrong?

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user David Z
@DavidZaslavsky: I removed the soft-question tag again.

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user Qmechanic
except that it raises the suspicion that what's really happening in this world might be just these ontological states, and the rest is due to our limited understanding, somewhat contaminated with some sort of religious feeling that God likes to superimpose. So, the answer to @Motl's objection is that it's our equations used to describe observed reality that allow for superpositions, not reality itself. I thought that this statement would be trivial and unimportant, but if not understanding it causes someone to reject the models first-hand, apparently the statement is important after all.

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user G. 't Hooft
I don't know if it helps you but here is a list of his papers: staff.science.uu.nl/~hooft101/gthpub.html

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user kaj dijkstra

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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).

Abstract:

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.

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user anna v
answered Dec 20, 2012 by (1,995 points)
thanks very much. I'll have a deeper look at this paper.

This post imported from StackExchange Physics at 2014-06-14 12:53 (UCT), posted by SE-user Eduardo Guerras Valera

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