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The Cellular Automaton Interpretation of Quantum Mechanics

Gerard 't Hooft

2014 · arXiv

PhysicsMathematicsBiology & medicine
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From the abstract

When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will always involve states in Hilbert space, controlled by operator equations. Returning to classical, that is, non quantum mechanical, descriptions will be forever impossible, unless one accepts some extremely contrived theoretical constructions that may or may not reproduce the quantum mechanical phenomena observed in experiments. Dissatisfied, this author investigated how one can look at things differently. This book is an overview of older material, but also contains many new observations and calculations. Quantum mechanics is looked upon as a tool, not as a theory. Examples are displayed of models that are classical in essence, but can be analysed by the use of quantum techniques, and we argue that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analyse a system that could be classical at its core. We explain how such thoughts can conceivably be reconciled with Bell's theorem, and how the usual objections voiced against the notion of `superdeterminism' can be overcome, at least in principle. Our proposal would eradicate the collapse problem and the measurement problem. Even the existence of an "arrow of time" can perhaps be explained in a more elegant way than usual. Discussions added in v3: the role of the gravitational force, a mathematical physics definition of free will, and an unconventional view on the arrow of time, amongst others.

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17 selected excerpts · 17 total mentions

miltondts
Neutral mention · rule
Regarding global conspiracy: "Explicit construction of Local Hidden Variables for any quantum theory up to any desired accuracy" https://arxiv.org/abs/2103.04335 Regarding unfalsifiable, from [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." [0] - https://arxiv.org/abs/1405.1548 Now, this does not mean these theories are ready, but they are being worked on.
Original comment Einstein-Bohr debate settled once and for all
T-A
Neutral mention · rule
> Just because he does not say explicitly "[GR and QM] are compatible", does not mean opposite. It also doesn't mean what you are claiming. To have a meaningful discussion about the incompatibility of GR with QM, you first need to know how they are incompatible. Reproducing classical electromagnetism with the Kaluza-Klein trick from 1919 [1] has nothing to do with it. QM deals with unit vectors in a state space, operators acting on those vectors, and observables whose values can not all be known simultaneously [2]. The hole left by the observer's limited knowledge about the state of the system is filled by an intrinsic randomness which does not exist in classical…
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theories. GR and other classical theories have only observables, their evolution is deterministically determined and the state of the system can in principle be fully known at all times. We have known for a long time that nature does not actually work like this [3]. If you want to claim that GR is compatible with QM, you have to resolve the above contradiction. What people who actually understand the problem have been trying to do for a long time is: 1) Quantize GR. This is the obvious first thing to try; you treat the problem as analogous to the quantization of classical electromagnetism and hope to create a quantum version of GR, the gravitational equivalent of QED. When you try that, it turns out you can't make the theory renormalizable - the infinities caused by loops in Feynman diagrams can not be brought under control. Trying to fix that leads to things like loop quantum gravity [4]. Weinberg came up with the alternative idea of asymptotic safety, which tries to neuter the problem with a fixed point in the renormalization group flow [5], but proving that it actually works is another story. 2) Come up with a deterministic (i.e. classical) theory underlying QM. Naive approaches involving hidden variables (i.e. trying to explain away our limited knowledge of quantum states as ignorance rather than truly fundamental) died with Bell's theorem. A few brave souls, notably t'Hooft [6] are still trying more sophisticated approaches (I think it would be nice if superdeterminism [7] got more attention). 3) Write down a more fundamental theory which produces both GR and the other known interactions in the appropriate limits (thermodynamic, large number of quanta). Since the other known interactions are empirically known to be quantum mechanical, it is generally believed that this theory will have to be quantum mechanical too. String theory is the obvious example. In principle, you could also imagine a classical (i.e. deterministic) theory along the lines of (2), but I can't think of any example which comes close to actually doing the job. [1] https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory [2] https://en.wikipedia.org/wiki/Quantum_mechanics#Mathematical... [3] https://en.wikipedia.org/wiki/Bell%27s_theorem [4] https://en.wikipedia.org/wiki/Loop_quantum_gravity [5] https://en.wikipedia.org/wiki/Asymptotic_safety_in_quantum_g... [6] https://arxiv.org/abs/1405.1548 [7] https://en.wikipedia.org/wiki/Superdeterminism
Original comment Einstein's description of gravity just got much harder to beat
zakk
Neutral mention · rule
This is absolutely fascinating. Even just a demonstration that rule application on hypergraphs is expressive enough to potentially describe (for some rule yet to be found) Quantum Mechanics and General Relativity is incredibly exciting in my opinion. Arguably string theory is in a similar situation: a very powerful framework that could potentially describe reality if accurately utilized. Also, notably Gerard 't Hooft has been working on a very similar topic recently: Quantum Mechanics described in terms of cellular automata [0]. [0] https://arxiv.org/abs/1405.1548
Original comment The Wolfram Physics Project
skosch
Neutral mention · rule
This is very exciting. To a computer scientist, superdeterminism seems like the most elegant solution to most of the current problems in physics. But it has always been firmly out of the mainstream, perhaps because it runs directly counter to our human experience. Gerard t'Hoofts framing of the universe as a cellular automaton (https://arxiv.org/abs/1405.1548) is relatively intuitive, but still only a rough sketch. Hopefully, Hossenfelder and Palmer now publicly arguing for superdeterminism will recruit some more bright minds to fleshing out these models into workable theories.
Original comment Superdeterminism may help us overcome the current crisis in physics
Grieverheart
Neutral mention · rule
Funny, a couple of days ago I googled about superdeterminism again to see if there are any developments and came across Hossenfelder's and Palmer's paper on arxiv https://arxiv.org/abs/1912.06462 . Strangely enough, even though I've studied theoretical Physics, the fact that some of Quantum mechanic's claims are based on assumptions such as the fact we have free will, were never really discussed except in a course in the Philosophy of science I took, which, unfortunately, was not very scientific. I actually never heard about superdeterminism until I read one of Gerard 't Hooft's papers (see e.g. https://arxiv.org/abs/1405.1548 https://arxiv.org/abs/1709.02874). Universities should put more emphasis on teaching the things we take for granted and give students the opportunity to question them, if we want to further our understanding.
Original comment Superdeterminism may help us overcome the current crisis in physics
not_kurt_godel
Neutral mention · rule
I think you'd probably be interested in Gerard 't Hooft's latest work: https://arxiv.org/abs/1405.1548 It's rather, shall we say, controversial (that is: widely rejected by his peers), but it's an attempt to construct a framework through which the laws of the universe can be interpreted as deterministic which leverages the sorts of epistemological concepts you seem to be interested in. (That being said: I personally find "is there an amoeba on Europa?" to be supremely interesting, but to each their own.)
Original comment I’m Convinced We Found Evidence of Life on Mars in the 1970s
mikhailfranco
Neutral mention · rule
I think SW became too obsessed with the mathematical and computational approach to CA, while (as usual) 't Hooft pursued his physics intuitions to create a candidate CA theory: https://arxiv.org/abs/1405.1548 I say as usual, because G'tH had already formulated the holographic principles that would allow space-time (hence GTR) to be encoded non-locally over a graph. https://arxiv.org/abs/gr-qc/9310026 There need not be a preferred reference frame if the space-time events do not occur at individual nodes in the graph, but emerge at scales much larger than the graph, with some holographic or permutation symmetry that can reproduce the diffeomorphism invariance of GTR. It is…
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also plausible that the position-momentum duality of space-time could emerge from such a theory. Space-time would be created by the events that occur, not the other way around, hence the aphorism spooky distance at an action, because the events are primary, and distance is the strange phenomenon that emerges from them. There has been much recent progress in making space emerge from entanglement, which also implies that locality emerges from non-locality: https://arxiv.org/abs/1005.3035 https://phys.org/news/2015-05-spacetime-built-quantum-entang... https://www.scientificamerican.com/article/tangled-up-in-spa... Note that LQG has produced a nice discretization of space, based on graphs that have observable quanta of area and volume, but not length. Directions and lengths are defined as normals to areas, which is reminiscent of Clifford Algebra. Having derived (emergent) lengths also makes diffeomorphism easier. https://arxiv.org/abs/gr-qc/9411005
Original comment Wolfram Rule 30 Prizes
wolfgke
Neutral mention · rule
Then read "The Cellular Automaton Interpretation of Quantum Mechanics" by Gerard 't Hooft (https://en.wikipedia.org/wiki/Gerard_%27t_Hooft), which tries to formulate a superdeterministic version of quantum mechanics based on cellular automata (i.e. much more discrete): > https://arxiv.org/abs/1405.1548 EDIT: also cf. https://link.springer.com/book/10.1007%2F978-3-319-41285-6
Original comment What Is Mathematics and What Should It Be? [pdf]
goldenkey
Neutral mention · rule
That's really cool. I see how you sort of built in decay through age. I think the golden information principles for emergent life are easier to find than biological ones, but of course the requirements of space, time, etc are much larger when ones' simulation is at a lower level of abstraction. It really is a question of level of emergent behavior versus level of base behavior. Even QM can be emergent from deterministic automata. [1] [1] https://arxiv.org/abs/1405.1548
Original comment A Computer Scientist’s View of Life, the Universe, and Everything (1999)
abdullahkhalids
Neutral mention · rule
I agree that progress in experimental abilities and QC is really forcing physicists to think carefully about what QM means. In fact the month of May saw three papers by major physicists about these deeper issues in QM [1,2,3] In my own humble capacity as a graduate student in physics, my research is about clearly understanding the divide between classical and quantum physics. On the rewriting of theory, I should have been clearer. I meant that when you rewrite the theory you should think about ontology. Differences in ontology between different rewrites, as well as interpretations of those rewrites, will point to how quantum theory can be generalized. I agree completely…
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that quantum mechanics is taught horribly. Strangest of all are introductory quantum/modern physics courses that are meant to give students an intuition of quantum theory use the Copanhagen interpretation -the one that says the least about ontology and emphasizes calculations and empiricism. I still stand behind my central claim. Let me be clearer. The mathematical model of classical physics says something about physical reality. The mathematical model of quantum mechanics says something very different about reality. Even if there are disagreements, we all agree that the ontology of classical physics is very much incorrect. Extrapolating from this I claim that the next theory of physics will have an ontology that will look nothing like that of quantum theory. As I have said previously, the ontology of quantum theory can be a means to an end (the next theory), but not the end itself. [1] http://arxiv.org/abs/1405.1548 [2] http://arxiv.org/abs/1405.3483 [3] http://arxiv.org/abs/1405.7577
Original comment Fluid Tests Hint at Concrete Quantum Reality
miltondts
Neutral mention · rule
I'm not sure if that is the case or not but if that is the prediction then they are in good company. Nobel laureate Gerard 't Hooft also has a cellular automaton theory and one of his conclusions is: "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." https://arxiv.org/abs/1405.1548
Original comment The Wolfram Physics Project
miltondts
Neutral mention · rule
The kind of superdeterministic theories proposed by t'Hooft are falsifiable. From [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." As for the author of the article I've never seen a clear proposal but it appears the idea is to do repeated measurements that display quantum effects while reducing noise as much as possible and check if there are deviations from quantum theory. EDIT: found a more concrete proposal http://backreaction.blogspot.com/2013/10/testing-conspiracy-... [0] - https://arxiv.org/abs/1405.1548
Original comment Superdeterminism may help us overcome the current crisis in physics
miltondts
Neutral mention · rule
From [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." by Gerard 't Hooft - Nobel Prize in Physics [0] - https://arxiv.org/abs/1405.1548 EDIT: See page 79 of the referenced paper for the detailed argument.
Original comment Arrow of time and its reversal on IBM quantum computer (2018)
wolfgke
Neutral mention · rule
> With quantum computing there are also no real signs that a quantum computer will beat a "classical" computer at anything any time soon. It always was and still is very difficult to get quantum systems to scale and you need a large enough system to make a difference and it may be impossible to do so. Again a lot of this is more of an engineering problem though admittedly the line between physics and engineering can be blurry since it's not always clear whether something can't be done because you've reached a fundamental limitation vs. having a clever enough design. The mentioning of quantum computers is very interesting in the following sense: If one were able to build a…
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sufficiently large quantum computer, this would provide strong evidence that the (at the moment rather hypothetical) theory whether quantum mechanics is rather an emergent phenomen by a deterministic process (cellular automaton) > https://arxiv.org/abs/1405.1548 which the Nobel laureate Gerard 't Hooft worked on for the last years is probably wrong. To quote p. 79-80: "Such scaled classical computers can of course not be built, so that this quantum computer will still be allowed to perform computational miracles, but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist. If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." On the other hand, if we seriously get into trouble building a sufficiently large quantum computer (despite our best efforts), this would at least to me provide evidence that 't Hooft is on something - since that this is a prediction that his Cellular Automaton Interpretation of Quantum Mechanics provides.
Original comment Fake Physics
miltondts
Neutral mention · rule
Actually the kind of superdeterministic theories proposed by t'Hooft are falsifiable. From [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." [0] - https://arxiv.org/abs/1405.1548
Original comment The Trouble with Quantum Mechanics
wolfgke
Neutral mention · rule
Relevant for those who are interested in the topic: Two rather unusual interpretations if quantum mechanics: - De Brogle-Bohm theory: https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory - Gerard 't Hooft - The Cellular Automaton Interpretation of Quantum Mechanics: https://arxiv.org/abs/1405.1548 (see also https://en.wikipedia.org/wiki/Superdeterminism)
Original comment The Trouble with Quantum Mechanics

Keep following the thread.

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