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.
- Faster than light communication or other causal processes
- Isolated action at a distance within an entangled system
- 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?