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.
February 29, 2012 at 1:22 am
You haven’t successfully ruled out counterfactual definiteness (ie the multiple universe hypothesis).
February 29, 2012 at 1:30 am
Sorry, misspoke. You haven’t ruled out the possibility that counterfactual definiteness what is violated instead of locality.
February 29, 2012 at 3:21 am
“The spooky effect at a distance is a process outside time and space that even I can’t really imagine.” — A. Zeilinger, interview “Spooky Action and Beyond” …
http://www.signandsight.com/features/614.html
One could argue that if it lies outside of space and time it doesn’t violate SR which is only about what’s inside space and time, but that could be overly Jesuitical?
Another argument — which you’ve noted — is that the superluminal signalling interdict only refers to transfer of classical information. That ban you’ll never get around. Quantum Information remains inferential anyway. Myrvold says it’s fallacious to think in terms of separability. And so on.
February 29, 2012 at 11:34 pm
” You haven’t ruled out the possibility that counterfactual definiteness what is violated instead of locality.”
It’s not mandatory that only one of the parameters — realism (counterfactual definiteness) or locality — is violated. Both could be.
Leggett-Garg, an arguable advance on Bell, takes nonlocality as read and drills down on counterfactual definite realism. If requested I can cite papers by both the Zeilinger and Gisin groups experimentally demonstrating violation of Leggett-Garg inequalities in the spirit of the Aspect group’s (and others’) experimental violation of Bell. Charles Tresser has two or three interesting papers seemingly demonstrating that the locality assumption isn’t needed for Bell tests.
March 1, 2012 at 4:26 pm
So, regarding counter factual definiteness, until someone proves the existence of the multiverse, I will assume it is a convenient fiction.
I am aware of Leggett-Garg (in fact, as I type this, I am sitting in a session in which several presenters discussed experimental violations of them including some of Anton’s students). However, I disagree that they are in some sense “better” or more general than Bell’s inequalities. I see them as complementary – Bell’s are for spatially separated states while the LG ones are for temporally separated states. So I don’t think they are necessarily relevant to whether SR is violated or not in the above argument (it would be a different argument).
March 1, 2012 at 4:27 pm
Oh, and I LOVED the “overly Jesuitical” comment (I am a product of a Jesuit education…)
March 2, 2012 at 1:59 am
I tried to cover my ass by saying “an arguable advance” over Bell. It couldn’t exist without Bell and it doesn’t dispute all nonlocal realistic theories — Bohm being a notable and serious exception. Suarez along with Gisin address that with before-before (arguably).
I meant “Jesuitical” not unadmiringly, certainly not pejoratively. A good Jesuit (I’ve met a few really neat ones) is sincere first and slick second. But they appear to be a dying breed.
March 2, 2012 at 6:49 pm
I loved my Jesuit education. The Jesuits taught me how to learn almost anything in about 48 hours.
March 5, 2012 at 1:56 am
Quantum correlations violate special relativity only if there are elements of reality that specify the measurement outcomes.
I usually talk about an “underlying realist model”, other people use terms like counterfactual definiteness or local causality. To talk about locality in the Bell sense, even to define the concept, you need an underlying realist model. If you do have such a model, there will be a violation of special relativity.
In other words, you need counterfactual definiteness to even talk about Bell locality. If you do not have an underlying realist model, there is no violation.
Most people claim that there is no underlying realist model to quantum mechanics. In my opinion, they cannot simultaneously claim that quantum mechanics is nonlocal.
March 5, 2012 at 3:14 pm
Hmmm. I’m not sure I entirely agree. Well, I guess it depends. Can an underlying realist model, in your opinion, be deterministic without appealing to things like Bohmian pilot waves and the such?
Perhaps a better term (phrase) than “violates” would be “is inconsistent with.” Special relativity is a local realist theory in that it is local and it is realist (though I suppose one could come up with some whacky interpretation of SR that is anti-realist).
Here’s the thing: if we assume that physics is self-consistent in that, eventually, we will find a way to blend QM and relativity in a single, cohesive way (I do not believe that QFT has done a good enough job of this and, besides, it only includes SR), then either they both have to be local and realist or they both have to be neither. I’m not sure I see any way around that.
March 7, 2012 at 1:15 am
I should perhaps point out that already your statement “we know that choosing a measurement basis physically alters the state of the particle being measured” presupposes a realist model. The quantum state is the hidden variable.
This is the reason for my gut reaction, and the reason that many quantum information people think quantum mechanics is nonlocal. If the state is a physical thing, it has to be nonlocal.
March 7, 2012 at 4:03 pm
Immanual Kant set the guidelines: Appearance, Reality, Theory (ART). “Appearance” = all experimental results. “Theory” = mathematical structures that “save the appearances”. “Reality” = stories we tell about “what’s really happening” in both A and T.
The bottom line is that A is completely local. No FTL experimental results whatsoever.
T is non-local. Wavefunctions can be collapsed FTL. If wavefunctions are “real” then SR is violated. If wavefunctions are mere conventional computational devices (like ths IDL) then SR poses no problem.
R was shown by Bell to be non-local. But R is not observable–Kant’s hypothetical “thing-in-itself”.
If we are moved to look for stories about “what’s really happening” behind appearances, then these stories (R) will necessarily violate SR.
On the other hand if we forego the search for such stories and stick with the quantum facts (A) then SR and QM can peacefully coexist.
There is not one single quantum fact that conflicts with SR. In this sense quantum mechanics is utterly local.
And quantum mechanics is also “complete” in the sense that it predicts the results of all conceivable experiments. But tells us nothing about “what’s really happening behind the scenes”. What a deliciously unsuperfluous theory! Predicts what you can see; is silent about what you can’t see.
If one is satisfied with this situation, then no paradoxes arise–quantum mechanics is local and complete.
Only those who are motivated to postulateulate unobservable wholly unobservable “models of reality” will have a problem with SR.
If one is willing to leave the question of “how nature really works” as a mystery, then the so-called quantum non-locality problem vanishes.
As a pragmatic tool for predicting phenomena quantum mechanics is local and complete.
March 7, 2012 at 2:35 pm
I guess I would prefer “empiricist” to “realist.” Reality is so utterly subjective anyway (we essentially “create” large parts of it as neuroscience and biology have shown). What I do believe is that if we’re to take macroscopic measurements seriously, then we need to take microscopic ones seriously as well since there is still no definitively identified boundary between the two. So, if macroscopic measurements are real, then so are microscopic ones. The microscopic ones are more random and less predictable, but they’re still very real.
March 7, 2012 at 9:55 pm
I guess I’m not entirely sure that I agree with Kant on that point.
March 5, 2012 at 11:11 am
Nick Herbert has a take along those lines:
Abstract: In a truly non-causal world, Bell’s Theorem cannot be formulated because in such a world elemental events are not stable enough for Bell-type non-locality to even be defined.
http://quantumtantra.com/BellRefutation.html
March 6, 2012 at 1:16 am
There is no violation of SR in experiments that you actually did.
Non-locality only arises when you want to consider the results (for the same single event) of experiments THAT YOU COULD HAVE DONE INSTEAD.
A Model of Reality gives results (either statistical or deterministic) for this same single event for all the settings that you could have made, not just the one set of settings that you actually made.
Bell’s Theorem states that all Models of Reality that reproduce the EPR results must be non-local.
If one is satisfied to accept quantum mechanics as a predictive algorithm and declines the search for an underlying hypothetical Model of Reality, then Bell non-locality vanishes.
The fact that one can seemingly “collapse” some theoretical structure called “wavefunction” at a distance is as little a violation of SR as is the formal discontinuity at the International Date Line a doorway into Time Travel. In both cases, nothing measurable goes
FTL or backwards in time.
March 6, 2012 at 9:24 pm
I’m not sure your analogy with the IDL works. Either way, I think the debate here is actually over the interpretation of special relativity and not quantum mechanics. All one needs in order to violate SR is for two events to exhibit a causal relationship when such a relationship is expressly prohibited. The details of how or why they exhibit that relationship are largely irrelevant, though I say that with the caveat that certain interpretations of QM attempt to explain away the bizarreness through those details. The point is that from the standpoint of SR, quantum correlations are not just inexplicable but at least appear to violate one of its most sacred tenets.
March 7, 2012 at 11:43 am
If Myrvold is right, and there’s no true physical separation between entangled particles no matter how far apart in spaciness (per S. Colbert) they appear to be, the controversy becomes moot.
Could be it’s an issue of our embodied cognition screwing us up. We evolved in a classical phenomenal world where spatial separation is something that has to be dealt with. You need to traverse “space” to get from “Point A” to “Point B”. The phenomenal world of facts like that is what we know, maybe all we’ll ever know. But every now and then there’s a seismic event and a chunk of substructure pokes up above the surface. We’re not sure what the hell it is but clearly it’s there now.
March 7, 2012 at 2:30 pm
I didn’t realize Myrvold had that view. Interesting. That’s something that I had thought of 6 or 7 years ago – maybe spacetime is simply bent around on itself in such a way that the two events aren’t actually spatially separated. However, in the intervening years I have come to view spacetime as an emergent phenomenon and I’m not one can reconcile co-location (in terms of a bent spacetime, anyway) with spacetime being emergent.
Personally, I have no problem with macroscopic violations of SR. I don’t think it does anything to undermine SR. It merely helps define the limit of its applicability much like relativity did to Newtonian mechanics.
July 6, 2012 at 9:43 am
Now this ““the chain of events leading to a common origin is too long for them to be correlated”).” was a interesting point to ponder. How do one define where a ‘chain of happenings’ stops having a importance for what follows, and how would I deffer a ‘correlation’ from a ‘common origin’?
And also, what allows for the ‘chain’ to exist in the first place? The arrows linearity?
Without a arrow, where do I find a ‘correlation’?
July 7, 2012 at 7:41 pm
Hmmm. I don’t think you necessarily need an arrow to have a correlation, but I will say it is something I am in the midst of working on as a research project. Hopefully I’ll have a more definitive answer fairly soon.
July 6, 2012 at 9:48 am
Also “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!”
What about probability here?
Doesn’t that define probable outcomes.
Although theoretically defined it’s still only some outcomes that can take place, right? At least it sets a limit of sorts on what can happen with their measurements? Life is truly abstract
July 7, 2012 at 7:42 pm
Yes, probability does set a bit of a limit, but there are still some issues here. Nevertheless, I think I am slowly coming around to the notion that quantum correlations may not violate SR. I’m not there yet, but I’m getting closer.