# Deterministic quantum mechanics

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?

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Hmm, at least he finally explains his version of "deterministic model" completely clearly. – Ron Maimon Dec 21 '11 at 19:39
– Qmechanic Aug 20 '12 at 18:40

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.

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Greetings Dr. 't Hooft. Perhaps this is a stupid question but it seems to me that finding a deterministic , classical "gears and sprockets" underpinning for QM is only problematic if one demands that it be local, which I think implies that it scales linearly (or sub-exponentially) with the number particles/qubits, whatever. For example, if you wrote down a classical system that reproduces the dynamics of an $N$-level quantum system using $O(N)$, or $O(N^2)$, resources, this wouldn't ruffle anyone's feathers. Would you mind clarifying this for me? (I'd rather not clog your inbox) – lionelbrits Jan 19 '15 at 14:24

It is unpopular among physicists because physicists, by definition, "like" theories and claims that correctly describe our world and Gerard 't Hooft's statements about the nature of the wave function are demonstrably invalid in the world around us, whether or not he may construct a contrived toy model where his claims are right and which has some vague features remotely resembling the real world.

The fact that the basic postulates of quantum mechanics are unavoidable has been known to physics at least from the late 1920s. For example, in his book on principles of quantum mechanics, Paul Dirac disproved all theories of 't Hooft's kind on the first three pages

http://motls.blogspot.com/2011/12/paul-diracs-forgotten-quantum-wisdom.html

and these early stages of the book – explaining that all the concepts and mathematical objects in the quantum theory have a new interpretation, one that doesn't coincide with anything we know in classical physics – are indeed a necessary pre-requisite for the reader to actually understand the rest of the theory.

Many other properties of quantum mechanics that couldn't be obtained from any classical theory compatible with relativity were obtained later, when physicists studied properties of entangled states. Bell's inequalities, Hardy's "paradox", GHZM states, Kochen-Specker theorem, free will theorem, and other results uniformly show that the natural phenomena we observe have features that can't be compatible with any theory of the type that Gerard 't Hooft is discussing. That's another set of rather good reasons for a physicist to treat such alternative theories as unpopular ones.

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-1: Lubos, here you are mistaken. The ideas of 'tHooft are to reproduce quantum mechanics from a stochastic theory which is massively nonlocal. There is no violation of any standard idea, it requires new ideas to rule this out. It is likely that his idea does not work, but you did not demonstrate it. I share your feeling that this is weird, but one must put personal feelings that something does not work to avoid throwing away future string-theory! Remember strings were also dismissed in 1974 as lunatic stuff. – Ron Maimon Dec 21 '11 at 19:41
"I feel there should be an approximation to QM that is nonexponential." John Sidles has a lot to say about this, e.g. faculty.washington.edu/sidles/ENC_2011/index.html#burningArrow – Mitchell Porter Dec 23 '11 at 2:40
Prof. Motl's answer is a mere diatribe without any physics in it. -1 Now, whether Dirac is a demi-god or not, he stated in print that he thought determinism would be restored, that Einstein would eventually be proved right, so your link is not even accurate. – joseph f. johnson Jan 16 '12 at 7:16
The link Prof. Motl provides, as if it were to Dirac's own thoughts, is only to Prof. Motl's own very loose and tendentious interpretation. At the end of his life, at any rate, Dirac said, and this is an exact quote: « And, I think it might turn out that ultimately Einstein will prove to be right, ... – joseph f. johnson Jan 16 '12 at 16:20
« And I think that it is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinisim and which will, therefore, justify the Einstein point of view. But such a return to determinism could only be made at the expense of giving up some other basic idea which we now assume without question.» – joseph f. johnson Jan 16 '12 at 16:20

My understanding is that the Copenhagen intepretation of quantum mechanics (ie. that particles have no definite position/momentum until they are observed) is just one of many interpretations, any one of which could be correct, and that we have no real reason for preferring one to another - they all produce the same results experimentally.

There is, in fact, a semi-popular deterministic interpretation called the De Broglie–Bohm theory. Unfortunately, it relies on an assumption that is even more unintuitive and terrifying (to physicists) than the Copenhagen intepretation: that all particles, everywhere in the universe, are connected by an invisible wave which acts at a distance instantaneously, no matter how large the distance. For obvious reasons, this is called a non-local theory.

Unfortunately, according to Bell's theorem, there can be no explanation of quantum-mechanics which is both local and deterministic. So we must accept that, if there is an underlying explanation for the weirdness of Quantum Mechanics, it must be either non-deterministic (like the Copenhagen Interpretation surmises) or non-local (like the De Broglie-Bohm theory).

For more information, see Nick Herbert's excellent book, Quantum Reality: Beyond the New Physics.

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The point is that physics has abandoned locality with holographic principle and string theory, but physics has not come to an end. In fact, the nonlocal theories are more tightly constrained than the local ones. In this atmosphere, it is legitimate to revisit hidden variables, to see if they make sense. t'Hooft is not looking for an interpretation of quantum mechanics, but a new theory, which can replace it. The new theory must have an interpretation as real stuff changing deterministically, and the QM is just informational superstructure on top of this. I don't think his idea works, it might. – Ron Maimon Dec 21 '11 at 23:12
@Ron, is string theory really nonlocal in this sense? Presumably you can't, for example, use a really long string to send a signal faster than light? – Harry Johnston Dec 26 '11 at 5:31
@Harry: String theory is nonlocal, not in the sense of sending signals between two points faster than light, but in the sense that space and time are emergent, so that two nearby points are smeared over a big far-away null surface holographically to big overlapping disks, and even the most local null-surface dynamics are massively nonlocal. This holographic nonlocality is not even describable in terms of 'stuff here' and 'stuff there' so you can't say whether the signal moves faster than light really, because it was always everywhere. – Ron Maimon Dec 26 '11 at 9:44
By the way if you asked a person some centuries ago what would he prefer - undetermined, random fate and unconnected world or underlying connections of the all things with determined fate he would prefere the later. – Anixx Jul 22 '12 at 0:45

Addendum: an other important point of criticism raised (Newman and others): why search for such a theory at all? Its predictions will be nil.

While Maimon thinks that my prediction that true quantum computing will be impossible implies that my theory will deviate from true divine qm. No to both: my theory implies that not all qm models will work for physics. The ones with a deterministic system behind them form a very tiny subset. Such that I predict that there will be obstructions, not deviating from true qm at all, that prohibit quantum calculations outperforming classical computers if you would scale their performance to Planckian dimensions. So yes, quantum computers will be great, but their performance will be limited. The engineers will blame that to problems producing ideal materials, I will blame it to the fact that, in agreement of the Standard Model, ideal materials cannot exist. Most importantly, if the equations could be worked out better than I can at present, they should give important constraints on the parameters of the Standard Model or other theoretical constructs used in fundamental particle physics. That's my real motivation: do good physics.

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thanks for the updates on your work. – anna v Jan 19 '15 at 10:51

Thanks for the great question, I just skimmed the paper. My reaction: it is still a vague proposal, with hand-waving, ill-defined concepts, and not at all axiomatically 'clean'. For example, he never defines «probability.»

Weinberg and others agree with t'Hooft at least in how to pose the problem: derive the probabilities from the deterministic unitary evolution. There have been real physical models done and published with this end in view, and they tend to take a quantum statistical mechanical approach, so there is some point of contact with some of t'Hooft's attitudes. But the valuable work in this way, as I see it, is using Schroedinger's equation to analyse actual physical measuring devices, such as the important work by Balian and two others at

arXiv:cond-mat/0203460 « Curie-Weiss model of the quantum measurement process.»

: See http://arxiv.org/abs/quant-ph/0507017 for a much less realistic toy model, and my axiomatically clean treatment of it's implications for Hilbert's Sixth problem, the axiomatisation of physics, http://arxiv.org/abs/0705.2554 ,

and Prof. t'Hooft is not even attempting to do that. It seems strange to hope to analyse measurement without thinking of the physics of measuring devices, or solve an axiomatic difficulty about probability without giving it a physical definition. I leave aside rival approaches to the problem, such as the decoherence approach, which some physicists are interested in.

Now QM seems to me, and most physicists, correct physically: the measurement problem is merely an axiomatic problem. Most physicists don't believe there is any new physics to be discovered which is relevant to the issue of determinism or the measurement problem, nor do I. (There are important physicists who are an exception, e.g., I suppose, Penrose.) I believe that a careful axiomatic analysis would be interesting, most physicists do not. I do not see one in this paper.

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no probability no – propaganda Jan 26 '12 at 3:56

This is a very heuristic argument, but here goes. I believe it is wise to search for determinism in physics, simply because although the physical world we measure appears to contain some elements of indeterminism, the ability to measure anything would not be possible without some degree of placing determinism in our logic. If we measure the position of a particle in the past, the very belief that our memory is even accurate depends upon our reliance on a strong macroscopic deterministic set of assumptions. I believe Bohr thought there was a special relationship between the classic (deterministic) and quantum laws that was not trivial, and one played off the other (and used to restrict and fashion problems) with the other. Perhaps, by investigating this relationship further as tHooft is attempting is very important. There is a second reason which may sound a bit more hoaky, but here goes again. I speculate that all "conscious" thoughts are essentially deterministic and finite, and hence any theory of physics must bow to this prinicple, and that what we see with quantum mechnics is the "maximal" possible violation of this in a presumed exterior world (which also doesn't really exist). In essence, the world seems quantum not because it is, but rather because we have not measured it yet and it is undetermined until we do. The knowledge that we hold and see with our eyes and ears is always deterministic however, it is only the uncertain part. We see similar things in various proofs in mathematics and Goedel's paradox. Our realities (or consciounsness) are a set of deterministic laws meant to be born and to die by their own idiosyncratic laws and can exist independent of any physics. What we call "physics" is are those laws or principles which happen to be in common between different conscious entities and measuring devices. To the extent this is undetermined (as it always is within any finite axiomatic system) is exactly the extent to which we see uncertainty in the world. It is similar to trying to prove the parallel postulate with an incomplete set of axioms. Everything you can say about those laws and think about those laws is deterministic, but you can ask some questions which cannot be determined by those laws...that is the "quantum" part. Once the measurement is made, you have a new axiom...and can go on like this until things get end...though mathematical inconsistency, and death. Of course this whole thing seems hopeless philosophical, but actually I do not think so in reality. Finite laws can be simulated and investigated...as they are with automata, game of life etc...so there is real research that can be done in this area. Perhaps we could create consciousness in our computers using a much smaller set of information than we would normally assume to be the case if we held the classical viewpoint that information exists in outside of our ability to measure it. That would be a strange day indeed if we someday found a mouse could create the (its) universe.

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Possibly interesting, but does this answer "why this view seems to unpopular?" (i.e. the question)? – Kinnisal Mountain Chicken Jul 17 '15 at 13:50
I was going to add some paragraph breaks to this wall of text, but then I realized that this doesn't actually answer the question asked and appears to mostly be nonsense. – Kyle Kanos Jul 17 '15 at 14:08
Certainly the bottom 2/3s really goes off the rails. It does serve to demonstrate that many people really really really want the universe to be fully deterministic (or at least conform to their idea of determinism). – Jon Custer Jul 17 '15 at 14:17

One place to look is the homepage of Antony Valentini now at Clemson University. He claims that Born's probability rule is only an approximation. David Bohm first made this claim. One can show that entanglement can be used for faster-than-light and even retro-causal back-from-the-future delayed choice signaling once the shackles of Born's rule are cast away.

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Even great physicists sometimes write weak paper, and this is the case. Any attempt to find some classical deterministic theory behind quantum mechanics failed, so far. And that is because there is not any.

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I am not sure if there is one, but how would you know that there isn't? For sure Bohmian mechanics works, but the question is if there isn't a reasonable one. No one has argued well that it is impossible, so why should 'tHooft not look? – Ron Maimon Dec 21 '11 at 19:39
If there would be something underneath, it would not be Quantum Mechanics, but some different theory, just like Bohmian QM is different theory, but the problem is that this "different theory" does not give anything new. (or it might give some wrong predictions). Quantum mechanics works perfectly and it is free of paradoxes, and in my opinion, all theories to deal with "something underneath quantum mechanics" are motivated by people who do not like Quantum mechanics. – Newman Dec 21 '11 at 20:39
-1 this is not true, see my answer. – BlueRaja - Danny Pflughoeft Dec 21 '11 at 20:57
@newman: Bohm's theory is logically fine, it is just too big and implausible and contrived. t'Hooft is not looking for a theory which reproduces quantum mechanics. He is looking for a theory which is different from QM in a measurable way, ruling out exponentially faster quantum computation for one. Not all people who look for a different theory do not like Quantum Mechanics philosophically. I personally find the quantum philosophy incredible and profound, and it is my first love. But that doesn't make it the final answer, so it is irresponsible not to dig deeper. – Ron Maimon Dec 21 '11 at 23:05
@Newman: quantum mechanics is a non-probability calculus, because it deals with probability amplitudes which only become probabilities during the act of measurement. A probability amplitude is not a probability, because there is no good way to put together answers to the questions "probability of what?" It is much more physical than probability, because of interference effects. But it is not quite as physical as a separate universe, because you can't solve NP complete problems. So it is intermediate between ignorance and many-worlds, how far it goes this way or that, you decide. – Ron Maimon Dec 22 '11 at 19:06

## protected by Qmechanic♦Jul 17 '15 at 13:47

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