Do quantum correlations violate special relativity?
It turns out that quantum information and foundations researchers tend to disagree on the answer to that question. I’m at the APS March Meeting in Boston and have had a number of stimulating discussions with people, this being one of them. I was surprised by some of the reactions I got when I said quantum mechanics violates axioms of special relativity and/or was non-local.
Bell’s inequalities include locality in their derivation. There are a few different ways one can express this, but, for example, Sakurai says that locality is represented in the fact that Alice’s “result is predetermined independently of [Bob's] choice as to what to measure” [J.J. Sakurai, Modern Quantum Mechanics, (Addison-Wesley-Longman: Reading, 1994), p. 228]. Bell himself noted this in several places. Violations of Bell inequalities would, therefore, seem to imply that quantum mechanics is non-local. Outside of the more fringe interpretations, I did not think this point was under dispute. It seems I was wrong. It also seems that there might be a difference between something being non-local and something truly violating special relativity.
The more I thought about it today, the more I think the debate is really over how to interpret special relativity and not how to interpret quantum mechanics (I think that, in itself, is interesting). Consider the two independent measurement events. Those two events, each represented by some action on one-half of an entangled particle pair, must be correlated in some way. As such, their past lightcones must overlap (technically, the past lightcones of everything overlaps at some point, but what we could say is that they share a common event in their past). However, the crucial point is that the events that represent the choices that Alice and Bob make regarding which basis to measure, are completely independent in that they do not share some common “origin” event (or, since the Big Bang, is a common “origin” event for everything, we could say instead “the chain of events leading to a common origin is too long for them to be correlated”). As such, they are (or can be) spacelike separated and yet a correlation will be found.
One (dare I say incorrect?) response to this could be that the freedom to choose a measurement basis doesn’t actually do anything actively to the particles. For example, if Alice chooses to measure spin along the z-axis, her result will be correlated with Bob’s only if he chooses to measure along the same axis. If he measures, say, along the y-axis he gets a random result but crucially doesn’t know it is random until he talks to Alice and compares notes.
But we know that choosing a measurement basis physically alters the state of the particle being measured. This is the heart of quantum mechanics – you must interact with the particle in order to measure it and it is very difficult to do so without altering the particle’s state! In special relativistic terms, changing some object’s state involves the action of a force (defined relativistically to be dP/dt where P is the relativistic momentum). Thus, from the standpoint of special relativity, a measurement by Alice should produce a force on the particle she is measuring while another force produced by Bob’s measurement (assuming their measurements are roughly at the same time) must produce something else instantaneously. These forces cannot be causally linked and yet they are somehow correlated. This is a fundamental violation of special relativity!
One counter-argument that has been put forward this week by a couple of people is that there’s no violation of special relativity because nothing propagates between the two events. The two events are quantum correlated, so it’s still a non-classical phenomenon, but it doesn’t violate relativity. But what does it mean to be quantum correlated versus classically correlated? It is my contention – and that of others – that the very definition of quantum correlations are that they’re non-local and thus in violation of special relativity! From an empirical/operational viewpoint, I really see no other way to explain this. As I have noted before, citing a mathematical result (e.g. a non-factorable state) as evidence for something physical, has serious interpretational problems.
So, my conclusion is (and always has been) that quantum correlations do, indeed, violate special relativity.