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Regarding the debate between quantum mechanics and determinism I have encountered a problem I can't find the answer to. It is my impression that in order to solve Bell's inequality you would have to sacrifice the principle of locality or determinism. This is where most people seem to sacrifice determinism and conclude the world is not deterministic.

However, the principle of locality seems to state that "an object is only directly influenced by its immediate surroundings", and that "for an action at one point to have an influence at another point, something in the space between the points, such as a field, must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, to carry the influence."

So my question then is: Is this not overruled by the proven theory of entanglement? Since entangled particles can alter each other regardless of distance or position, does that not mean the principle of locality is incorrect? If so, does that mean that determinism is the only option left for Bell's inequality and is thus true?

I do realise there are a lot more factors and debates within this, but I have no educational degree in physics and I am therefore asking if any of you can elaborate on the matter.

Conifold
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Torstein Hatlebakk
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In the relevant sense the answer is "no", the appearance of a "yes" is created by projecting classical intuitions about locality onto quantum objects. This is confusing because the definition of locality adopted in classical physics becomes misleading when transplanted into quantum physics. "Quantum non-locality" of entanglement is a misnomer, rather than demonstrate non-locality entanglement demostrates non-classicality, that the language of "objects" and "points" is inappropriate in quantum theory due to indeterminacy. Entangled quantum pair is not two separate objects that "coordinate" across long distances instantaneously, it is a single distributed "quantum object" described by a joint wave function. It can "split" in two when observations are made, which is why we are tempted by classical intuitions to think of it as an interacting pair.

If we imagine it as something like two interacting classical objects then there are restrictions on how much their behaviors can correlate called Bell inequalities. "Quantum non-locality" refers to the fact that they are violated for entangled pairs. What this reflects however is that quantum objects can fuse (entangle) and come apart (decohere) in a way classical objects can not, not non-locality, despite the common phrasing in popular sources. Even in quantum mechanics, which is non-relativistic, entanglement violations of Bell inequalities still do not allow energy, mass or information to travel instantaneously despite the appearances caused by classical anticipations. This is Bohm's no-signalling theorem.

On the other hand, quantum field theory (Standard Model), which is the governing theory in modern physics, is relativistic, which means that it explicitly requires all interactions to spread no faster than the speed of light, or in 4D picture, influence of any event is confined to its future light cone. The same Wikipidea article you linked states in subsection on relativity:"Locality is one of the axioms of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if we have two observables, each localized within two distinct spacetime regions which happen to be at a spacelike separation from each other, the observables must commute". Translation: no interaction is possible between regions of spacetime that can not be connected by trajectory of a photon ("spacelike separated"). So not only does entanglement not contradict the relevant notion of locality, but locality is one of the axioms of the theory that describes it.

For the relation of Bell inequalities to local realism and determinism see Does Einstein's local realism in quantum mechanics imply superdeterminism? Whether we call violations of Bell inequalities non-locality or not, they allow for some remarkable phenomena like sending dense messages over a channel seemingly lacking capacity to carry them ("superdense coding"), or creating "remote copies" of quantum systems, while destroying the originals ("quantum teleportation"). An illuminating philosophical discussion of issues surrounding entanglement, like realism, locality, causality, relativity, etc., in various interpretations of quantum mechanics is Timpson and Brown's Entanglement and Relativity.

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Conifold
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  • I disagree. What about the experiments where photon pairs were entangled that were literally kilometers apart? How is that different than "classical" non-locality? – Alexander S King Apr 20 '16 at 22:44
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    @Alexander They can be light years apart making the difference starker: violate Bell inequalities all you want you still can't send a superluminal signal. And violation of Bell inequalities is all the experiments measure. It can not imply non-locality in the usual sense of the word simply because QFT, whose predictions experiments confirm, is a local theory. "Quantum non-locality" is an artifact of translating what happens into inadequate language of "objects" and "interactions", but then that's the only way to explain it non-technically. – Conifold Apr 21 '16 at 00:20
  • See How does QFT help with entanglement? on Physics SE http://physics.stackexchange.com/questions/76036/how-does-qft-help-with-entanglement – Conifold Apr 21 '16 at 00:29
  • "that the language of "objects" and "points" is inappropriate in quantum theory due to indeterminacy." do you have any refs on this? – Alexander S King Apr 21 '16 at 18:24
  • So is the language of classical fields, see e.g. Baker http://philsci-archive.pitt.edu/4350/1/AgainstFields.pdf I think he is too harsh, Wallace argues that classical notions can be salvaged approximately as long as we give up bright lines, and accept that in some situations intuitions behind classical meanings are misleading http://arxiv.org/pdf/quant-ph/0107144.pdf – Conifold Apr 21 '16 at 21:34
  • You linked to Motl's answer on physics SE where he says that it is realism that fails, not locality. Can you explain this? how does this local non-realism help with entanglement? and I do not mean how does it help with the math. the fact that Motl or someone else can calculate the results of an experiment is a separate matter. – nir Apr 22 '16 at 07:46
  • @nir He is referring to Einstein's "local realism", not realism broadly construed. You may want to look at Timpson-Brown's paper I added, one of their interpretations is QM having local interactions but non-local states. Quantum Bayesianism is a realist interpretation that avoids any non-locality http://arxiv.org/abs/0804.2047. – Conifold Apr 23 '16 at 21:28
  • There seems to be a confusion between locality and causality here. Entanglement is non-local but also does not allow for superluminal signalling. – AjaxLeung Jan 10 '20 at 08:14
  • As defined here: https://en.m.wikipedia.org/wiki/Principle_of_locality#:~:text=In%20physics%2C%20the%20principle%20of,local%22%20action%20at%20a%20distance. Quantum entanglement does violate this principle. Hence, this answer is simply false, and pretending as if the only definition of non locality involves signaling faster than the speed of light doesn’t change that. –  Nov 22 '23 at 23:47
  • @thinkingman Both Wikipedia article and this post distinguish classical and relativistic principles, and it is not even possible to apply classical one as is to quantum objects. One either has to erroneously "analogize" them to classical ones, or to assume classical hidden variables and apply classical locality principle to them (that is termed "local realism"). As they put it, "the fact that quantum mechanics violates Bell inequalities indicates that any hidden-variable theory underlying quantum mechanics must be non-local". – Conifold Nov 23 '23 at 00:57
  • “it is a single distributed "quantum object" described by a joint wave function” To many, this is enough to stare that the effect is non local. Non factorizability implies non locality unless you question assumptions which are up for debate. “ Following Bell's work, a broad consensus has it that the quantum realm involves some type of non-locality.” See https://plato.stanford.edu/entries/qm-action-distance/#BelTheNonLoc –  Nov 23 '23 at 22:37
  • “ Following Bell's work, a broad consensus has it that the quantum realm involves some type of non-locality (for examples, see Clauser and Horne 1974, Jarrett 1984,1989, Shimony 1984, Redhead 1987, Butterfield 1989, 1992a,b, 1994, Howard 1989, Healey 1991, 1992, 1994, Teller 1989, Clifton, Butterfield and Redhead 1990, Clifton 1991, Maudlin 1994, Berkovitz 1995a,b, 1998a,b, and references therein).” –  Nov 23 '23 at 22:43
  • @thinkingman Sure, non-local correlations are "some type of non-locality", the OP question is about the principle of locality though. – Conifold Nov 23 '23 at 22:48
  • The SEP article mentions how entanglement does violate the principle mentioned in the OP. It is not just referring to the correlation but also influences. “Yet, a common view has it that these influences are due to some type of holism and/or non-separability of states of composite systems, which are characteristic of systems in entangled states (like the spin singlet state)” This is still defined as an influence. What you’re doing is simply defining a joint system separated by light years as one object and then stating there are no non local influences. That’s begging the question. –  Nov 23 '23 at 22:58
  • @thinkingman "Influence" is a vague colloquial word that means different things in different contexts. In the OP it is described as "to exert an influence, something, such as a wave or particle, must travel through the space between the two points, to carry the influence". Whatever "influence" happens in EPR it is not that, and the answer opens with "relevant sense". Your own quote describes the joint system as holistic and non-separable, call it "one object" or not. – Conifold Nov 24 '23 at 01:18
  • @Conifold I mean if it did influence the other particle instantaneously without a medium, the results of the experiment are what they would like. So how can you rule that out? The non local correlation is just as much evidence for no local causality than there is for nonlocal causality. Yes, it is defined as non separable and holistic but the point is those particles are far away from each other and the quote still calls it an influence. –  Nov 24 '23 at 10:14
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Entanglement does not refute the principle of locality. A sketch of the sort of experiment commonly said to refute locality runs as follows. Suppose that you have two electrons with entangled spin. For each electron you can measure the spin along the X, Y or Z direction. If you measure X on both electrons, then you get opposite values, likewise for measuring Y or Z on both electrons. If you measure X on one electron and Y or Z on the other, then you have a 50% probability of a match. And if you measure Y on one and Z on the other, the probability of a match is 50%. The crucial issue is that whether you find a correlation when you do the comparison depends on whether you measure the same quantity on each electron.

Bell's theorem just explains that the extent of this correlation is greater than a local theory would allow if the measured quantities were represented by stochastic variables (i.e. - numbers picked out of a hat).

This fact is often misrepresented as implying that quantum mechanics is non-local. But in quantum mechanics, systems are not characterised by stochastic variables, but, rather, by Hermitian operators. There is an entirely local explanation of how the correlations arise in terms of properties of systems represented by such operators. For an explanation of how the correlations arise, see

http://arxiv.org/abs/quant-ph/9906007

and

http://arxiv.org/abs/1109.6223.

alanf
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  • Given the complete information about a system of two entangled particles before measurement, can one compute the outcome of measurement with certainty? Does such a computation exist in principle? – nir Apr 22 '16 at 09:17
  • That depends on what you mean by outcome. If you mean "is there a complete description of what will happen after the measurement?" then answer is yes. If the question is "what outcome will I see after the measurement?" the answer is no. Before the measurement the system exists in multiple versions that are identical in all their measurable atttributes. After the measurement, there are multiple versions of the system that don't interact with one another. And there is no fact of the matter about which version before the measurement corresponds to a particular version after the measurement. – alanf Apr 23 '16 at 10:06
  • See "The Beginning of Infinity" by David Deutsch, Chapter 11. – alanf Apr 23 '16 at 10:06
  • I have expanded my comment into a question — I hope you can take a look: http://philosophy.stackexchange.com/questions/33819/entanglement-and-the-computability-of-nature – nir Apr 23 '16 at 18:06
  • 'But in QM systems are not characterised by stochastic variables, but by Hermitian operators'; I beg to disagree, in the standard Copenhagen interpretation, on measurement of an observable, the observable takes a value stochastically from the spectrum of the operator representing it. – Mozibur Ullah Apr 23 '16 at 19:14
  • @MoziburUllah I have not yet found a clear discussion of what the CI says about what exists in objective reality. As far as I can tell the CI consists of denying that quantum theory is an accurate description of reality while still using the relevant equation of motion and a set of ad hoc rules of thumb like picking a single value stochastically. What does this imply about reality? Who knows? And in any case if there is a local explanation of what's going on with entanglement then it makes sense to say QM is local. – alanf Apr 24 '16 at 11:31
  • @alanf: the measurement postulate is part of the standard presentation of QM - go look at any undergraduate QM book. Any interpretation of QM will have recreate this whether axiomatically or as a theorem - as it's been experimentally justified. – Mozibur Ullah Apr 24 '16 at 12:10
  • @MoziburUllah The measurement postulate (MP) is part of how QM is usually presented but it is ambiguous. Does it mean that only one outcome takes place? Or is it just intended to be a rule of thumb? You see a single outcome because decoherence prevents interactions between the different outcomes that take place in reality. That is absolutely not the same as only a single outcome taking place. If the MP is a claim about reality, then it is an extremely badly worked out hint at an explanation, and it is unnecessary at best. If the MP is a rule of thumb, then it is untestable. – alanf Apr 24 '16 at 13:18
  • @alanf: yes, there is only one outcome - and it has been tested - inasmuch QM as a scientific theory has been tested; the measurement postulate is as ambiguous as Newtonian gravity, in the sense that a more general theory - general relativity - resolves to it in a certain limit; even no-collapse theories such as Deutchian Many Worlds still have to explain how to find this in some limit; QM has a certain claim on reality, but it isn't a full picture - which is why there are as many ontologies which take this as a point of departure. – Mozibur Ullah Apr 25 '16 at 13:32
  • @MoziburUllah No. There is not only one outcome. First, quantum theory explains why each version of you sees only one outcome despite the existence of the other outcomes. Second, it also explains why you can't account for EPR correlations, single particle interference etc. without invoking multiple outcomes. The reason why many people take the single outcome view is largely bad philosophy, e.g. - instrumentalism. – alanf Apr 25 '16 at 21:09
  • @alanf: I don't understand you - perhaps you should try to study QM to understand what I said, and maybe to understand QM itself? QM, axiomatically formulated as in Diracs textbook or Shankar maintains that there is a single outcome to a measurement, this is what is popularly known as collapse; an interpretation of QM might suppose that the collapse is due to decoherence with the environment; but this is part of interpretation all ontologies and isn't part of the formalism. – Mozibur Ullah May 03 '16 at 01:13
  • Even there, the interpretation is statistical, it's accounted by the innumerable interactions will have with a system; in the same way Newtonian gravity supposes the influence of gravity is instantaneously transmitted despite how Einstein showed it could not be. But whereas Einstein showed how his theory in a certain limit produced Newtonian gravity, is there one that shows decoherence produces collapse - this is in one manner the question I was asking; it's not clear to me that there is. – Mozibur Ullah May 03 '16 at 01:16
  • Instrumentalism as far as I know, is a variety of positivism; on occasion it has proved useful as in Poincares analysis of Lorentz contraction; it's also immanent in the ontology of QM - as in observables. It's bad philosophy to take this as the only view, it's not clear to me that even the founders of QM did, as opposed to their many excitable disciples; it's only human I suppose to push a successful method to a limit - which on a little reflection shows it may transgress the conditions of its success. – Mozibur Ullah May 03 '16 at 01:22
  • which is why Gadamer was opposed to method in his Truth & Method, and Feyerabend too and probably Kuhn. – Mozibur Ullah May 03 '16 at 01:25
  • @MoziburUllah I do understand QM. And I have read many "axiomatic" accounts of the sort you mention. They just don't make sense. They have two completely different rules for how states evolve and switch between them in an ad hoc way. This is useless for any serious investigation of QM. That's why decoherence papers typically work only with the Schrodinger equation and similar eqs of motion. – alanf May 03 '16 at 09:39
  • @MoziburUllah Instrumentalism is not useful. It is anti-scientific and anti-rational. See, for example, "The Fabric of Reality" by David Deutsch chapters 1 and 2 and "Conjectures and Refutations" by Popper Chapter 3. Instrumentalism amounts in substance to taking measurements as uncriticisable primitives. Denying that anything other than results matters involves ignoring explanations of those results that imply the existence of unobserved entities. This can only be done on an ad hoc basis, and so instrumentalism is just an excuse for ad hoc denial of explanations. – alanf May 03 '16 at 09:43
  • @alanf: the Dirac formalism is standard within QM, and it's what's used in beyond anything like a first introduction; and I suppose by 'two completely different rules for how states evolve' you're referring to the Schrodinger and Heisenberg representations, which were shown to be equivalent by von Neumann; to be accurate, it's only in the Schrodinger picture that states evolve, observables don't; in the Heisenberg picture the opposite is true, it's also the picture that's used in QFT, which is essentially relativistic QM as the Schrodinger picture can't be made to work – Mozibur Ullah May 04 '16 at 16:06
  • It doesn't preserve Lorentz invariance, aka causality; given the importance of QFT in modern physics this makes pretty 'good sense'; can you elaborate a little more on why you think it does not? – Mozibur Ullah May 04 '16 at 16:08
  • Sure, instrumentalism isn't the whole of science - this is why I said 'partial'; it was historically important in both QM & relativity, and it's why it's one point of departure in the philosophy that takes the method of science as it's basis - Positivism; I suggest you take a closer look at the original papers of Einstein on relativity & Poincare to see what it looked like in action. – Mozibur Ullah May 04 '16 at 16:12
  • No. The two different rules are the equation of motion, e.g. - the Schrodinger equation, and the collapse postulate, which contradict one another and can't both be true. As for why collapse doesn't preserve Lorentz invariance, this was shown by Lucien Hardy in his 1992 paper "Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories". The result in that paper applies equally well to all collapse variants of QM, since the key point is that there's a single outcome for each measurement. – alanf May 06 '16 at 12:52
  • A person can claim to use a philosophy, and be wrong about that claim. In Einstein's case, he obviously did not take positivism or instrumentalism completely seriously because his theory uses explanations and no explanation can ever follow from any set of experimental results. In 1935, Einstein acknowledged that positivism was junk in a letter to Popper, see "Logic of Scientific Discovery" Appendix xii, the paragraph starting "Altogether I..." Relativity described measurement as a physical process, which is anti-positivist since it gets measurement from explanation not vice versa. – alanf May 06 '16 at 13:01
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The top answer here simply defines locality to mean not allowing super luminal signaling. But that is not the traditional definition of locality. The fact that there is a joint wave function that describes the probabilities of measurement of particles separated at large distances implies there is non locality to many.

As per the SEP,

Following Bell's work, a broad consensus has it that the quantum realm involves some type of non-locality (for examples, see Clauser and Horne 1974, Jarrett 1984,1989, Shimony 1984, Redhead 1987, Butterfield 1989, 1992a,b, 1994, Howard 1989, Healey 1991, 1992, 1994, Teller 1989, Clifton, Butterfield and Redhead 1990, Clifton 1991, Maudlin 1994, Berkovitz 1995a,b, 1998a,b, and references therein).

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The short answer is "Yes, unless you get really obsessive about it." It has been formally proven that you can have determinacy in a model of quantum dynamics, or you can have locality, and you cannot have both. (Although you could have neither, answering your followup question.)

If you give up the determinacy of the theory in various ways, you can imagine all kinds of 'planned flukes' like the notion that the experiments that demonstrate entanglement leak information and pre-determine the environment to make the coordinated behavior seem real... E.g. the middle of this: http://www.nytimes.com/2014/11/16/opinion/sunday/is-quantum-entanglement-real.html?_r=0

Since this kind of information shaping through distributed uncertainty remains a possibility, folks can cling to locality until someone actually manages something like what those authors are attempting, or we find it impossible.

If you give up locality instead, entanglement does not present a problem, the theory of relativity does. Because the notion of a frame of reference is local. Experiments on quantum tunneling that violate the constraints of the speed of light have been explained with the idea that probabilistic partial information can 'lead' real information faster than light by pushing at the vacuum underneath via the 'Casimir Effect'. http://www.liquisearch.com/faster-than-light/justifications/faster_light_casimir_vacuum_and_quantum_tunnelling. If so, it is only 'complete information' that can only be gotten at a given speed.

If both of these make sense, then the information carried by the entanglement when it is broken would be limited as the particles get farther apart -- entanglements would have to spontaneously break down over time or distance of separation so that the probabilities line up. This bodes ill for our ability to find entangled particles from the Big Bang, which seems to be the only prospect in progress to debunk the excessively locality-focussed.

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Does Entanglement Disprove The Principle of Locality?

Short answer: Yes. See Quantum Non-Locality.

If so, does that mean that determinism is the only option left for bell's inequality and is thus.... true?

No. Even if entanglement is proven, we can still have non-locality and non-determinism both at the same time. See this paper "An experimental test of non-local realism" . From the paper's abstract:

"Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned."

The relationship between realism and determinism can be clarified by the definition from Wikipedia:

"Local realism is the combination of the principle of locality with the "realistic" assumption that all objects must objectively have a pre-existing value for any possible measurement before the measurement is made ."

Alexander S King
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The point of entangled pairs in the EPR paradox is to demonstrate that standard QM couldn't be complete because it allowed for instantaneous influences to propagate, which had been eliminated from gravity and EM by introducing the concept of a field.

There is however an active research programme into a different interpretation of QM - Bohmian Mechanics which allows for a local but superluminal influence to propagate via the pilot wave; in fact the idea goes back to de Broglie.

Hence entanglement doesn't disprove non-locality.

Mozibur Ullah
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It doesn't violate locality as entanglement happens because the eyes of YHVH sees it. This is the source of entanglement.

The notions of particles changing at a distance is a misguided notion in quantum mechanics philosophy. YHVH is made of symmetries. This is what determines and outcome of things once observed from some other remote point.

BTW: Screw all you HATERS for voting posts down that mention GOD, as it is still a LEGITIMATE part of our world and REASON itself. You should all be ashamed of yourselves and reverse the damage you've done.

Marxos
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  • I don't downvote because of God, we downvote because it's a poor quality answer, not argumented and not referenced. Instead of playing the victim card and feeling entitled, put in the work to provide better quality answers if you dislike being downvoted. – armand Nov 24 '23 at 00:22
  • @armand: Bullshit. You don't even understand my answer, nor did you attempt to find understanding. – Marxos Nov 25 '23 at 01:44
  • Sure honey. You're the victim. Enjoy the downvote, then. – armand Nov 25 '23 at 03:06