The nature of quantum nonlocality

Quantum physics has been on my mind again lately, somewhat triggered by a recent conversation with Wyrd Smythe on his blog. I’ve always known quantum nonlocality has nuances, but stuff I read this week revealed some wrinkles I wasn’t aware of. (Well, I was aware of them, but wasn’t aware they pertained to nonlocality.)

A quick reminder, the principle of locality is that a system can only be influenced by its immediate surroundings. Any influence from further away has to propagate through the intervening distance to influence the system. Einstein’s special theory of relativity mandates that these effects can travel no faster than the speed of light.

But as Albert Einstein and collaborators pointed out in 1935, quantum mechanics seems to allow action at a distance on entangled particles. Take a pair of particles entangled on a particular property, say spin. Measuring that property of one of the particles appears to set the corresponding value of the other particle instantly, even if they’re separated by light years.

Einstein saw this as a problem for quantum theory. However, John Stuart Bell later pointed out a way to test whether the identified effect happens. The test has been done numerous times, and every time, the effect has been confirmed.

However, the nature of nonlocality varies according to which interpretation of quantum mechanics we use. Most of the articles in the news about these experimental results report them under the “standard” Copenhagen interpretation and its cousins.

But before getting into differences, it’s worth clarifying at least three different meanings to “nonlocality” that often come up in discussions of quantum physics.

1. Faster than light communication or other causal processes
2. Isolated action at a distance within an entangled system
3. Nonseparability, that is, nonlocal states that can only be accounted for by considering the system as a whole, not just the individual parts

Note that although Einstein reportedly had issues with all three, only type 1 actually violates relativity. All contemporary physicists seem to agree that this type of nonlocality doesn’t happen in quantum mechanics, no matter which interpretation we use. I explained why in a post last year.

In summary, there’s nothing we can do to one of the particles to affect the state of the other, aside from, under Copenhagen, performing a measurement. This does set the values of both particles. However, there is no way to know ahead of time what the value will be, whether the value was already set by a measurement on the other side, or when the other measurement might have happened. The only way the correlated outcomes can be verified is by slower than light transmission and comparison of results after the fact, which under Copenhagen is a classical event.

In other words, under Copenhagen and similar interpretations, we have type 2 nonlocality, not type 1. So Einstein had nothing to worry about? Brian Greene, in his book The Fabric of the Cosmos, notes that many physicists are uneasy about how close this comes to breaking special relativity. Relativity seems to come out intact, but just barely.

However, even nonlocality type 2 is specific to Copenhagen and similar interpretations, ones with a wave function collapse that is an absolute event, that is, one that everyone agrees has happened. But there are interpretations where absolute collapses do not happen.

One is relational quantum mechanics (RQM), which has collapses, but they are relative to a specific observer, where an “observer” can be any other physical system, including another particle. This means two things. First, any collapse is relative and local. So measuring one of the entangled particles only leads to a local collapse.

Second, under RQM, it’s meaningless to talk about states without reference to an observer. So the correlation between the particles only becomes relevant when the results are compared. Unlike in Copenhagen, where quantum physics doesn’t apply to macroscopic systems, in RQM this is just as much a quantum event as a classical one, involving its own collapse from multiple possibilities.

What I’m not sure about is what keeps the three RQM collapses (the two measurements and comparison event) in sync. An early paper simply asserted that a discrepancy can’t happen, which seems insufficient. A more recent paper asserts that it comes down to common causal factors, which is more plausible, but doesn’t seem to get any more specific. (Maybe an RQM enthusiast can weigh in with an answer?)

Another interpretation without the second type of nonlocality is our old friend, the many-worlds interpretation (MWI). Under the MWI, there is no collapse of the wave function at all. Similar to RQM, measuring one particle has no immediate effect on the other one, but being the MWI, every possible outcome is realized. So there is local branching of “worlds” at the site of both measurements which spread out from those locations.

Like RQM, the comparison event is also a quantum one, but in this case it’s a matter of the correlated branches meeting up with each other, and not the uncorrelated ones. A frequently asked question is, what enables each corresponding branch to find each other? And what stops incompatible branches from matching up with each other?

Which brings us to the third form of nonlocality, non-separability. When particles are entangled, they are not only in superpositions of their own states, but in composite superpositions of all their combined states. This effect is used in quantum computing to produce the massive parallel processing it’s known for. This means a full accounting of the entangled system requires considering it as a whole, rather than looking at each individual part and adding those states together.

In collapse interpretations, if I understand correctly, this relationship ends with the collapse. But under the MWI, while it can be mixed up with other entanglements, it never goes away completely. Inside a quantum computer, these relationships enable the parallel computations to remain distinct (albeit with interference). The same relationship allows different measurement outcomes of distantly entangled particles to match up with each other in the comparison event.

Put another way, each “world” in the MWI is, to use Matt O’Dowd’s phrase, an entanglement network, a nonseparable system. Decoherence is essentially a quantum system becoming massively entangled with its environment. Similar to the circuits in a quantum computer, each portion of an MWI “world”, each portion of an entanglement network, is coherent enough with other portions of the same network to interact. But unlike in the quantum computer, a “world” is decohered enough from the other branches, the other entanglement networks, to not to be affected by them. (At least not in any fashion currently detectable.) (As it turns out, this paragraph is wrong. Please see the correction post. MS 12-27-20)

It’s worth noting that not all MWI advocates agree it has nonseparable states. David Deutsch uses the Heisenberg picture (essentially Heisenberg’s version of the quantum formalism) to argue that it doesn’t, in a technical paper I haven’t tried too hard to parse. However, other MWI advocates, such as David Wallace and Lev Vaidman, disagree.

I’m not sure whether nonseparability really amounts to nonlocality. On the one hand, it could be considered just what’s necessary to account for nonlocal relations. On the other, what entanglement enables in quantum computing circuits and beyond could be argued to be much more than just a matter of correlations. And Einstein in 1935 apparently stipulated separability as a necessary condition for “local realism”.

By that standard, quantum mechanics is unavoidably nonlocal. No interpretation is nonlocal enough to break special relativity, but most collapse interpretations have isolated action at a distance and nonseparable states, and all interpretations seems to have at least nonseparable states. We can say RQM and MWI are local in the sense of local dynamics, but not in the sense of being separable.

Unless of course I’m missing something?

16 thoughts on “The nature of quantum nonlocality”

1. Interesting take on it by Lee Smolin.

https://blogs.scientificamerican.com/observations/space-the-final-illusion/

Basically spacetime isn’t fundamental and there is nothing that stops an event on Proxima Centauri being the cause of an event on Earth. Locality is somewhat an illusion because “locality, and space itself, emerges from averaging over fundamental processes involving a myriad of individual events … Mostly, influences will be local because most of the time, causally related events will end up close to each other in the emergent rough description we call space. But there will be many pairs of events that are causally related, that will end up far from each other—thus disordering space and locality”.

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1. Thanks. An interesting article. Interestingly enough, Sean Carroll, in a recent AMA podcast, actually expresses a similar expectation, that space and locality are emergent. Although I think the theoretical logic he takes to get there is very different from Smolin’s. (I really need to reread the section of his latest book that covers spacetime. I kind of plowed through it last time and didn’t really grasp it.)

But if they are emergent, that could open up all kinds of possibilities. I hope they’re able to make progress on this sometime soon, ideally in our lifetimes.

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2. Stephen Wysong says:

Silberstein, Stuckey and Cifone explain the block universe’s explanation of entanglement and non-locality in “An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics”, PDF available here:

http://philsci-archive.pitt.edu/3214/

Lots of maths, but also readable explanation, as in:

Entanglement & Non-locality. On our geometric view of NRQM [non-relativistic quantum mechanics] we explain entanglement as a feature of the spacetime geometry24 as follows. Each detection event, which evidences a spacetime relation, selects a trajectory from a family of possible trajectories (one family per entangled ‘particle’). In the language of detection events qua relations, it follows that correlations are correlations between the members of the families of trajectories and these correlations are the result of the relevant spacetime symmetries for the experimental configuration. And, since an experiment’s spacetime symmetries are manifested in the Hamilton-Jacobi families of trajectories throughout the relevant spacetime region D, there is no reason to expect entanglement to diminish with distance from the source. Thus, the entanglement of families of trajectories is spatiotemporally global, i.e., non-local. That is, there is no reason to expect entanglement geometrically construed to respect any kind of common cause principle.

We understand quantum facts to be facts about the spatiotemporal relations of a given physical system, not facts about the behavior of particles, or the interactions of measurement devices with wave-functions, or the like. Entanglement and non-locality are built into the structure of spacetime itself via relations. Correlations between space-like separated events that violate Bell’s inequalities are of no concern as long as spacetime
symmetries instantiated by the experimental apparatus warrant the correlated spacetime relations. Since the non-local correlations derive from the spatiotemporal relations per the spacetime symmetries of the experiment, satisfaction of any common-cause principle is superfluous. To sloganize: ours is a purely geometric/spacetime interpretation of non-relativistic quantum mechanics.”

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1. Thanks Stephen. I’ve only read the first couple of sections so far. Two things stand out. One is that it’s a hidden variable theory. The other is that it’s focused on non-relativistic QM.

I’m wondering if it bypasses quantum field theory. That’s not unusual for hidden variable theories. Such theories have to add to the QM formalism, and doing so in a manner that stays consistent with QFT and its reconciliation with relativity and classic field theory has proven to be a common obstacle. (Apparently no one has yet succeeded in mapping deBroglie-Bohm theory to QFT.)

Searching, I do see some mentions of “RQFT” coming up in the paper with a footnote about not yet having found the right spacetime structure for it.

Anyway, I might have more to say when I read the rest, which may not be tonight.

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2. Okay, ran aground on the mathematics and so switched to skimming mode, eventually landing in section 5. I can’t say I fully understand their idea. I think we’ve discussed this before, that it seems to be saying that the various events just are. It seems to be relying heavily on the blockworld concept at a scope and layer I’m not sure I buy it’s applicable. But it’s entirely possible I’m just not getting it. 🙂

Anyway, related to this post, this snippet from the Conclusion section covers their interpretation’s local / nonlocal aspects.

” And there is also no “Einstein separability” between the system being measured and the system doing the measuring on our interpretation. Our view respects the causal structure of Minkowski spacetime in the sense that there are no faster than light “influences” or “productive” causes between space-like separated events as there are in Bohm for example. So our view is not non-local in any robustly dynamical sense. However our view does violate Einstein separability and it does have static “correlations” outside the lightcone as determined acausally and globally by the spacetime symmetries.

So their interpretation has roughly the same level of nonlocality as RQM and MWI. It has local dynamics (well, to the extent it recognizes dynamics), but is nonlocal in terms of nonseparability. That seems right. I’m not sure we can escape nonseparable states in any quantum theory and still have it be quantum.

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1. Stephen Wysong says:

Mike, QM isn’t one of my interests so I have nothing to add. I pointed to the BlockWorld folks’ paper because their viewpoint hadn’t been mentioned but seems to deserve consideration.

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3. I think it’s natural and important to draw a line between a nonlocality of influence and something lesser such as nonseparability. I would be reluctant to call it “causal influence” in some of these quantum experiments though, because we’re in a regime where the intuitive idea of causality breaks down. Intuitively, causality is a one-way action, while for quantum states with few degrees of freedom we have either mutual influence, or even simply correlation.

I don’t know whether nonseparability counts as a kind of “nonlocality”, but if it does we need a new word for nonlocal influence.

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1. I see the word “dynamics” often used to refer to influence, although I’ve often seen “influence” itself. The Wikipedia comparison table labels the column for Locality “Local Dynamics”. I understand why now. They’re focusing on the action at a distance aspect, the influence outside of light cones. When those are absent, then we can say a theory has local dynamics.

Nonseparable states seem equivalent to entanglement, which itself seems inseparable from quantum mechanics. I wish I understood the math behind it better.

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1. “Nonseparable states seem equivalent to entanglement,…”

By definition and by the math. Which in this case isn’t too bad:

$\mid\Psi\rangle=\frac{\mid00\rangle+\mid11\rangle}{\sqrt{2}}$

This is called a Bell Pair or EPR Pair. (See the Scott Aaronson PDF about QC; Section 5.3.2 Entanglement; Equation 5.7) The characteristic aspect is that there are only two states that can be measured on the standard basis (which gives a |0⟩ or |1⟩ outcome).

As Aaronson writes:

This state is particularly interesting because measuring the first qubit collapses the state of the second qubit. The state can’t be factored into a tensor product of the first qubit’s state and the second qubit’s state. Such a state is called entangled, which for pure states simply means: not decomposable into a tensor product.

It would require some matrix math to demonstrate, but he’s saying the state shown Equation 5.8 mathematically cannot be decomposed into distinct wave-function matrices without violating the rules for such matrices. Thus the state of the qubits is inseparable.

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1. Thanks! This matches my previous understanding, and maybe I understood more than I thought, because I was expecting there to be…more, even for simple pure states. Part of this was driven by the Wikipedia article on entanglement’s dense treatment of the formalism. But maybe I’m just overthinking it.

I really need to spend more time in that Aaronson PDF.

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1. I still think nonlocal dynamics is a strike against most collapse interpretations.

I was fine with nonseparable states before and remain so. If we classify that, in and of itself, as nonlocal, then QM is unavoidably nonlocal.

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2. “I still think nonlocal dynamics is a strike against most collapse interpretations.”

How so?

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3. It’s still action at a distance, something that doesn’t seem to have withstood the test of time anywhere else in physics. It’s causally isolated nature ensures it meets the letter of special relativity, but that same causal isolation seems to make its existence completely contingent on a postulate. Maybe the evidence will eventually bear it out, but for now there are alternatives without it.

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