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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.

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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.

  • 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 0:20
  • See How does QFT help with entanglement? on Physics SE physics.stackexchange.com/questions/76036/… – Conifold Apr 21 '16 at 0:29
  • "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 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 arxiv.org/pdf/quant-ph/0107144.pdf – Conifold Apr 21 '16 at 21:34
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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.

  • 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 9:17
  • 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: philosophy.stackexchange.com/questions/33819/… – 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
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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 ."

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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.

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