# Is QM Inherently Non-local?

1. Oct 23, 2005

### DrChinese

This thread is following up on some comments being made in another thread by ttn and others, including myself. The basic questions are:

i) Is QM inherently non-local?
ii) If yes, when did this result become clear?

These questions are offshoots of discussions of EPR and Bell. For most readers, posts to this thread will probably end up seeming to be a debate over fine points that may not matter. Or maybe they do matter...

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ttn has argued that QM is inherently non-local, and feels that result was known shortly after EPR. ttn is also, to some degree at least, a member of the Bohmian mechanics (BM) school although I do not purport to convey ttn's position.

On the other hand, I have a more orthodox position on QM that is frequently associated with the Copenhagen interpretation (QM-CI). As such, I do not tend to go much further than the formalism. Of couse, I like to speculate as much as anyone.

Regarding i) above:

I do not believe QM is non-local, assuming certain definitions of locality. As has been pointed out previously:

"According to quantum theory, action at a space-like separated
region does not change the probability of an outcome of a local
measurement." (The fact that anything "non-local" has occurred is never evident until such time as the space-like separated measurement results are brought together.)

I would not characterize the above defintion of locality as universally accepted, although it is certainly popular enough. In fact, the very conclusions you arrive at are usually dependent on your definition of locality.

On the other hand: if you want to explain the "perfect" correlations when you perform Bell tests at 0 degrees between the Alice and Bob polarizers, non-local effects seem to be a pretty good explanation too.

Regarding ii) above:

ttn has argued that the non-locality of QM was evident after EPR, in fact was a conclusion of EPR. I argue that it absolutely was not a conclusion of EPR. It is *possible* that some might deduce that from some readings of EPR. But it was never stated as such in the paper itself.

ttn has also offered up a quote from Einstein's later writing in support of this position. However, I would like to point out the following. Einstein assumed locality was a fact. Since he assumed the predictions of QM were otherwise correct, he felt QM was incomplete and local reality would win in the end. Such a viewpoint would REQUIRE Einstein to believe that an test of the EPR paradox would show that the predictions of QM were wrong. I.e. there would certainly be no perfect correlations!

But guess what!! That would mean that if the Aspect tests were performed without ever knowing about the Bell inequality, and instead simply as a resolution of the EPR paradox... that local reality would have been refuted. If that is true: WHAT DO YOU NEED BELL FOR?

The fact is, Einstein would have been shocked at such results. But others would still have argued that local reality was not excluded. It took Bell to rule out ALL local realistic theories. But the caveat to that is that Bell still does not prove that QM is non-local. You must look elsewhere to draw this conclusion.

Last edited: Oct 23, 2005
2. Oct 23, 2005

### ttn

Too vague. The probability of an outcome of a nearby measurement can be different, depending on whether we conditionalize on space-like separated information (e.g., the setting or outcome of a distant measurement). That already implies a kind of non-locality if the probabilities in question are all conditionalized on a complete specification of the particle states (in the past light cone(s) of the measurement events in question). According to QM, knowing the complete state of the world in the past light cone of a given measurement isn't enough to predict the probability of a given outcome -- conditionalizing also on space-like separated information changes the probabilities. In other words, the probabilites really *depend* on things that are going on at spacelike separation.

The only way to deny that this is a real nonlocal action at a distance is to deny the completeness doctrine. If we had conditionalized on only partial information about the states, then the fact that the probabilities change when we also conditionalize on space like separated information, wouldn't be a big deal.

Don't mistake that for the argument, though! Nobody thinks that non-locality is proved, just because non-locality is *a* way of accounting for the observed correlations. The whole point is: it's the *only* way. But you have to really understand Bell to see that.

I never said non-locality was a conclusion of EPR. The assumed that locality was true, and proved that, for QM, locality entails in-completeness... and hence concluded that the theory wasn't complete. But this is logically equivalent to the proposition that, if you assume completeness, the theory is non-local.

But even that is an overly cumbersome way to say it. It's better to just define what you mean by locality and then look at the theory and see how it works. And it's trivial to see that if you are talking about Bell Locality, orthodox QM violates it.

Huh? It's a trivial matter to explain the perfect correlations in a local way, if you just add the assumption that there are hv's which determine the outcome. You just say: half the pairs come out with the left particle "up" and the right particle "down", with the other half vice versa. Then you always get perfect anti-correlation, and there's nothing non-local going on. There's no need to disagree with this particular prediction of QM. The perfect anti-correlation can be explained easily with a local hvt.

I certainly agree that Einstein would have been shocked to discover that no local theory can agree with experiment -- i.e., that locality is false.

Re: Bell, terminology is getting the best of you. Bell's Theorem doesn't prove that orthodox QM is non-local. It isn't even about orthodox QM -- it's about hidden variable theories. So you're right that "bell still does not prove that QM is non-local." But nobody said it did. What proves that orthodox QM is nonlocal is just, well, orthodox QM. You just look at how the theory works and ask: does it respect Bell Locality? The answer is no. That is trivial. You don't need a theorem. What you *do* need a theorem for is to decide whether some *other* theory (with hv's) might reproduce the QM predictions while respecting Bell Locality. Bell's theorem proves no such theory exists. And experiment proves that the QM predictions are correct. Conclusion: no local theory can match experiment. Nature violates Bell Locality.

3. Oct 23, 2005

### RandallB

Always a lot of angles to argue local/non-local when you look at EPR-Bell or entanglement. But I believe you can see it in the double slit paradox as well.
This “paradox” is only resolved by the uncertainty of HUP/QM. For those not fully up on the double slit paradox; with only single Photons (or electrons) fired at a double slit a pattern is still accumulated that extends both to the left and right of the slits. For the pattern built out on the sides and the photons coming though the closest slit, there must be some form of signaling or help coming via the far away slit. What ever that help is covers a longer distance & therefore travels faster (i.e. FTL). Without some explanation this remains a paradox – BUT QM explains it Non-Locally with, superposition, guide-wave, even MWI & Strings can explain it, all HUP/QM. It’s the need for a faster than light resolution here that requires one of the “non-local” explanations of QM above. It’s the requirement for “uncertainty” within them that defines QM as a “Non-Local” theory.

I’d credit Niels Bohr as first to see “QM inherently non-local” as part of its definition maybe better than Einstein. He defended QM against EPR hard because he new the QM Theory was dead if LR could be show true. I think Einstein would have been happy to modify it to make more “complete”. But by the Bohr definition (pretty well accepted by most) QM has come to mean “Uncertainty”, without that it would mean something new would be required.

Recognizing Non-Local reality as part of the definition of QM is one thing.
But as to when did that “result become clear” I think we’d have to say that it has been accepted as correct by most but doubted by at least some.

Von Newman had the accepted “proof” that EPR was wrong, but Einstein didn’t give.
But in the 60’s Bell should Von Newman’s math as “absurd” and gave the Bell-Theorem hoping that LR could show as real! He readily admitted disappointment experiments showing otherwise.
But were Einstein here I have little doubt that he would say that; Since Bell was able to show Von Newman as wrong, how sure can we be that someone someday might not show the Bell- Proof to be wrong – can we not have some uncertainty about that?

So as to: “when did this result become clear?” Maybe it isn’t clear yet.

Note: Ref a good book by J.S. Bell, “Speakable Unspeakable QM”, recently reprinted
RB

Last edited: Oct 24, 2005
4. Oct 23, 2005

### DrChinese

The funny thing is, that there are plenty of people who think the debate is resolved. The only problem is that they all see the outcome differently.

5. Oct 23, 2005

### DrChinese

1. Vague is a strange comment. I think it is clear that this is not only a true statement, but meaningful for plenty of people. This particular quote is from Vaidman. I completely disagree that the probability of a detection changes due to an event outside the past light cone of the measurement - I cannot imagine you arguing otherwise.

And I don't also don't agree that an incomplete specification has been demonstrated. The question is: was there a more complete specification at the time the entangled pair was created? No, there is no such specification. After you learn some more, then naturally you have a conditionalized view of things. What is non-local about that? You can learn this same information from either of the entangled particles, not exactly a shocking development.

2. I am trying to make sure I do not mis-characterize your views. I think it is more accurate to say that you believe that EPR proved QM was non-local if it is complete. Is that correct?

If so, I will repeat that EPR's conclusion was that if QM is complete, then there is not simultaneous reality to non-commuting observables. Realistically, I think this particular conclusion was understood prior to EPR (at least to a few) although EPR nicely draws a line in the sand on the matter.

Please don't get me wrong: I am a great supporter of EPR (but it does have some flaws).

3. There is not a local realistic way to explain the perfect correlations, if you consider the behavior of PDC entangled pairs. You don't need Bell's Theorem to realize that something is terribly wrong with naive LR explanations (the ones you call trivial). Recall the original post in the thread "A Paradox: Do LHV Theories Need the HUP?" to see that this is probably not possible any more to argue. Use 2 orthogonal BBO crystals and you get the "perfect" correlations. Use 1 and you get nothing but randomness, even though the naive LR explanation should still apply.

6. Oct 23, 2005

### DrChinese

I don't think terminology is getting the better of me in the least. From my perspective, your terminology is far off! But it really should be no surprise to either of us.

I think it is necessary to have common meaning for these terms and ideas to discuss them intelligently. Any survey of the literature will show exactly how difficult this is with EPR/Bell subject matter. Most authors struggle to nail down terms like "locality" (your Norsen reference needs 6 pages to make a dent in the subject, for example). And even after such definition, there is simply not full agreement anyway. But if we can come to common meaning, then more productive discussion can follow.

I don't mind shifting to terminology you prefer (when there are differences in expression) if that makes the discussion easier. But please, it is a bit condescending to suppose that you :rofl: are somehow in possession of the only "correct" key to decoding the language - or even the most common usage thereof. That is why I often quote EPR and Bell directly RATHER than use lingo which may create disagreement. So I would encourage you to be lenient in this regard, and simply home in on areas in which our usage obviously diverges.

I am very interested in your ideas, and understanding better some of the concepts that drive your views. In many areas I suspect we are far more in agreement than in disagreement. And I absolutely agree with you that Bell is about classes of Hidden Variable theories, and is not a test of QM itself.

7. Oct 23, 2005

### ttn

According to the mathematical condition called "Bell Locality", we must have
$P(A|\hat{a},\hat{b},B,\lambda) = P(A|\hat{a},\lambda)$
where A is some outcome of Alice's experiment, a-hat is some controllable parameter of Alice's experiment (like the orientation of her SG device), lambda is a complete specification of the state of the system in the past light cone of Alice's measurement, and b-hat and B are variables outside that past light cone. (Obviously in the case at hand we are particularly interested in the setting and outcome of Bob's experiment, both of which are assumed to be spacelike separated from alice's experiment.)

Now suppose this condition is violated. What does that mean? It means that the probability for event A changes depending on whether you do or don't conditionalize on some information that isn't in the past light cone of the event in question. This wouldn't necessarily imply non-locality -- it only does so when we conditionalize on a complete description, lambda. But we're doing that, by assumption. So any violation of Bell Locality means that, in some sense (made precise by the equation above!), the outcome at A (or the probabilities for the various possible outcomes at A) depends on something going on in a spacelike separated region.

Now we simply ask: does orthodox QM respect this mathematical condition? Answer: no, it doesn't. Orthodox QM *violates* Bell Locality.

So, yes, I absolutely do think that the probability of an event changes (according to orthodox QM) due to an event outside the past light cone. That's just what a violation of Bell Locality *means*. Of course, you have to be careful about what you mean by "the probability". If you take out the conditionalization on the complete specification lambda, or if you talk about marginal probabilites, etc., then you can state truthfully that the probability of an event doesn't depend on what's going on outside the past light cone (according to oQM). But if the probabilities we're talking about are the ones appearing in the equation above, then there is no ambiguity and no question about the facts: oQM violates this condition.

BTW, who cares about this condition? Why should we accept this particular definition of locality? Because it's the very one Bell uses in deriving his theorem. So if you want to say his theorem proves that hvt's have to be nonlocal, you must apply the same condition to oQM when you ask: is it local?

Completeness isn't merely a claim about what someone does or can know. In Bohm's theory, for example, you can prepare a particle by putting its wf in a certain state, and it turns out that you can't *independently* control the particle's position. You have to accept a Born-rule P(x) distribution. So you can know the wf but you can't know the particle position (initially). But that doesn't mean the wf alone provides a complete description. Bohm's theory says the position exists, whether we know it or not, so, according to Bohm's theory, a complete specification of the state has to include both the wf and the position.

Yes.

Then I'll have to repeat that you haven't understood their argument (and that maybe it's podolsky's fault for writing a crappy paper). Read Einstein's later comments on this, e.g., in his essays in the Schilpp volume, in the Born-Einstein letters, read Arthur Fine's book, read "Einstein's Boxes", etc.

Maybe I'm taking you too literally, but there is a trivial way to explain the *perfect correlations*. Remember, there are perfect correlations (anti-correlations actually) for the case where Alice and Bob measure along the same axis. Whenever Alice gets "up", Bob gets "down" and vice versa. Here's the trivial model which explains those perfect anti-correlations: each particle in each pair carry an "instruction set" that tells them how to react (up or down) to a measurement along any axis at all, and the two particles' instruction sets are anti-correlated... so if the first particle's instruction set includes "be up if you are measured along the x-direction", the second particle's will include "be down if you are measured along the x-direction"... and so forth for *all* the other directions. Obviously such a model will correctly predict the perfect correlations that are observed when Alice and Bob measure along the same axis.

Can it also predict the empirically observed (and QM-predicted) correlation rates when Alice and Bob *don't* measure along the same axis? No, there are no instruction sets that will allow that. That's bell's theorem.

8. Oct 23, 2005

### DrChinese

But the fact is that this explanation fails with a PDC setup. You get perfect correlations when the input pump passes through 2 orthogonal BBO crystals. The explanation works fine, because the instruction set works for the case where Alice and Bob have the same settings. So why does that explanation fall apart when you remove one of the BBO crystals? You still have a pair of entangled photons, the only difference is that they are not in a superposition! The trivial theory says these should also be perfectly correlated, but they aren't. (The superposition only appears with the 2 crystals, not the 1.) Thus our trivial explanation - which is supposed to be local realistic - now needs to incorporate the HUP and collapse postulate. That means it cannot be realistic because these are QM elements.

This was a point I was making in the other thread - that there are lots of problems with LR theories over and above Bell's Inequality. Of course, that is a lot easier to see post-Bell.

9. Oct 23, 2005

### ttn

When you remove one of the crystals, the state of the photon pair is different, right? Certainly the state-according-to-QM (i.e., the wf) is different. And QM's predictions for outcomes/correlations are hence also different. So why shouldn't somebody's pet LHV theory also be able to attribute a different joint state to the two particles?

Don't get me wrong. There's nothing to be gained by trying to cook up a LHV explanation for all possible experimental permutations. I mean, who cares, since we already know that *no LHV theory can agree with the results of the Bell experiment*? That means LHV theories aren't viable, and whether or not they can explain some other random isolated experiment is, well, irrelevant and uninteresting.

That said, I'd be willing to bet a nickel that a LHV explanation could be found for whatever the correlations are when Alice and Bob measure along the same axis (no matter *what* the initial preparation of the pair is like). But I'm just speculating here.

One other point. If I read you right, you said that any theory which includes HUP and/or wf collapse wouldn't be "realistic" because these (HUP and collapse) are elements of QM. Again, you need to be more careful. Bohm's theory incorporates the HUP (interpreted epistemologically rather than ontologically, of course) and can actually deduce the collapse rule (rather than postulate it as a separate measurement axiom, as in the orthodox theory). But isn't Bohm's theory "realistic"? Maybe I'm just not sure what you mean by "realistic".

10. Oct 23, 2005

### DrChinese

This is a pretty good definition of Bell Locality, but certainly you must be aware it is one of many. In fact, it is not the one used in Bell because outcome independence was not part of it as I hav e always read it (see Bell (1) and (2) and text between which makes this pretty clear).

But I thought these always evaluated to .5 anyway. So the likelihood of Alice seeing + or - doesn't change as b is varied (parameter independence).

So, yeah, I guess I am concluding that I don't see how this condition is violated by QM. And yes, I realize some authors have written it and have seen it repeated before as fact. But nothing changes about Alice's results when something is done at space-like separated region around Bob.

You see, the "non-local" element to QM is really entailed in the collapse of the wave function. I don't understand that mechanism (does anyone?) either, and I am not sure if it is actually non-local at all. Once the collapse occurs, nothing mysterious (or spooky ) really goes on. And collapse is something that occurs on single particles everywhere all the time. So I say the mystery is in the collapse, not in the correlations or the factorization.

You make a measurement on an entangled particle and the superposition collapses. Everything thereafter is fully local and within everyone's light cone! But there is no reality to the unmeasured particle observables. This is consistent between entangled multi-particle scenarios and single particle scenarios in oQM scenarios.

11. Oct 23, 2005

### DrChinese

Certainly there are ways to incorporate results that mimic the HUP in some LR theories. But Local Realistic theories have problems keeping the application of HUP going fully because because it usually violates either the locality or realistic requirement. Keep in mind that EPR assumed that you could beat the HUP, and essentially so do all LR theories. WF collapse also causes problems in LR theories for similar reasons. I don't consider this to be a problem with BM because it is designed to be more flexible. In other words, it can be realistic (see definition below) because it gets to use its non-local elements to keep the application of the HUP going much further than LR theories can.

Realistic means that particle attributes (observables) have simultaneous definite (real) values independent of their observation - I am trying to be consistent with Einstein's definition of this. So essentially realism means that the HUP is something that arises from our inability to see into the subatomic world, rather than a literal depiction of it. Non-realism, in constrast, drops this requirement just as non-local theories drop the requirement of locality. So the idea of a non-realistic theory does not entail some weird kind of universe, it is simply a universe in which particle attributes are not required to be constrained to definite values when not being observed.

In a world of virtual particles and path integrals, this doesn't seem so weird to me personally. (In fact, I don't think guide waves seem too weird either.) Keep in mind that I think a scientific proof that oQM should evolve to a non-local realistic theory would be great. (Although I wouldn't want Vanesch to feel he isn't loved either.) I just happen to sit on a line in which I am not ready to commit either to non-locality or non-reality. Of course, I have to suffer with the collapse postulate and the baggage it brings so I am not sure if I am in any better position net.

12. Oct 23, 2005

### Hurkyl

Staff Emeritus
May I attempt a restatement?

Suppose we have a state p defined on a space-time region R.

Suppose we have another space-time region S that is causally determined by R. (In the purely geometric sense)

QM is local in the sense that the time-evolution of QM uniquely determines, from p, a state defined on S. (I will call this causal-local, unless someone has a better name for it!)

Furthermore, QM is complete in the sense that any probability only involving observables that are causally determined by R is uniquely determined by p. (I will call this causal-complete)

13. Oct 23, 2005

### DrChinese

Because the explanation they cooked up still applies.

Of course, I agree with your basic assumption that they could continuously modify their theory as new facts present themselves until their theory makes no sense at all. In fact it CAN'T make sense. "CAN'T" in the sense that it is a totally useless ad hoc theory. That is because all LHV theories (post Bell especially!!) are useless ad hoc theories. They purport to do nothing but give the same results as QM anyway. That is their entire purpose, to yield the predictions of QM without adding anything at all. Theories such as SED are an example of something I consider to be totally ad hoc. We already have QM! We don't need another equivalent QM.

I realize that with work in Everett's MWI, Bohm's BM, and Cramer's TI, folks are looking for improvements on QM. But one of the things that slows work in all of these areas is the fact that there is no obvious differences in the physical predictions of these theories. They must first yield oQM as a starting point to be taken seriously, yet this is precisely what makes them weak. Something of a "chicken and egg" problem. You gotta admit that hurts resource allocation in research devoted to them.

I hope I am not stepping on any toes in saying the above... I am sure I am guilty of coming up with ad hoc explanations of my own.

14. Oct 23, 2005

### ttn

EPR didn't *assume* this -- they *proved* it, based on the assumption of locality. They showed that if you make the locality assumption, the correlations predicted by QM (and long since confirmed by experiment) mean that definite pre-measurement values exist for observables that are governed by a HUP. This is not just some kind of arbitrary assumption. It's actually required by locality.
I don't strongly disagree with anything here, but there are a few dangerous points. In the first sentence you equate attributes with observables. But some of the properties that are observables according to QM are treated very differently according to other theories like Bohmian Mechanics. Another way to say this is that what *attributes* a particle even *possesses* is a very theory-dependent kind of thing. OQM and Bohmian Mechanics (just to use the typical cleanest examples) disagree about what properties these are. So I think it's ultimately not really defensible to describe one of these theories as "realistic" and the other as "non-realistic". Both are realistic, if that means that they both say that particles possess exactly those properties that, according to the theory in question, they actually possess. (Yes, I'm aware that sentence didn't actually say anything. That's my point.) That's really the whole point of the completeness doctrine: there's some real state of the system and it is *completely* characterized by the wave function. That means (in the general case) that the particle doesn't have a particular value for most properties like position, momentum, spin-z component, etc. That's not "non-realistic" or "realistic" -- it's just a particular *theory* about what is real. And in that regard it is no different from Bohm's theory, this being just a *different* theory about what is real, i.e., what properties particles have.
This is why I really don't think the realistic/non-realistic terminology has any place in this debate. "Hidden variables" is a terrible term (for reasons I explained earlier) but at least we can give it an unambiguous meaning: anything that a given theory posits in addition to the wave function is a "hidden variable." So Bohm's theory is a hvt, and oQM isn't. And theories which purport to explain the correlations in EPR/Bell experiments by attributing definite spin components to each particle separately are hvt's. etc.
You make it sound like there is a choice between non-locality or non-reality. But this is not so. You do have a choice between reality or non-reality (whatever that means)... Let's be more careful: you can choose whether or not to accept the completeness doctrine. OQM and Bohm are both able to account for the NRQM results -- the former using the wf alone (but lots of weird extra measurement axioms) and the latter using the wf and definite particle positions (with no extra measurement axioms).
But there is no choice between locality and non-locality. OQM is nonlocal, Bohm is nonlocal, and there is a proof that no local theory can agree with experiment. So there simply is no choice here. You're stuck with nonlocality if you want to agree with experiment. So your only choice is between a nonlocal ugly theory full of "unprofessional vagueness and ambiguity", and a nonlocal "physicist's theory" that makes intuitive sense and treats all of reality from micro- to macro- on an even footing.

15. Oct 23, 2005

### DrChinese

Hurkyl, in your opinion, wouldn't you say that most oQMers follow this program?

16. Oct 23, 2005

### Hurkyl

Staff Emeritus
I can't claim to have a qualified opinion, but I certainly think so.

17. Oct 23, 2005

### ttn

The non-locality of orthodox qm is associated with the collapse postulate, not Sch's equation. So if your restatement here is meant to apply only to the unitary evolution part, it is true but misses the point. And if your restatement is supposed to be general (applying to either/both kinds of evolution that orthodox QM says happen) then it is just false.

18. Oct 23, 2005

### DrChinese

I agree with this.

EPR held out the hope of a more complete specification of the system than the QM wavefunction allows. A more complete specification implies oQM is incomplete. How this is incompleteness is filled in leads to the terms "reality" or "realistic" (corresponding to EPR's "element of reality") or "hidden variables" (implying a deeper underlying mechanism).

But... you could assert the same thing about ANY physical theory, not just QM. I.E. General relativity is incomplete. Nope, it's not incomplete until the better thing actually comes along. THEN it's incomplete. :tongue:

19. Oct 23, 2005

### ttn

I agree with the stuff about LHV theories being useless and ad hoc. But you're being irrationally hard on them if you ridicule them merely for adjusting their initial-state-assignment based on a new experimental setup! I mean, come on, you do this in regular QM, too. The initial quantum state depends on the preparation. And if instead of QM you believe in pumpkin dynamics, then the initial pumpkin state is going to need to depend on the preparation. *That* isn't proof that the pumpkin theory is useless and ad hoc.
This is a dangerous attitude. If you have 7 theories that all give the same empirical predictions, you can't point to one of them and say: the other 6 are useless because we already have this one. The whole problem is: which one do you point to? If they're all equivalent, it's a mistake to pick one based on some random historical or sociological process (like Bohr effectively brainwashed lots of people) and say that that one is special just because it "got in first" or whatever. Judge the theories based on which one is the best theory, not based on which one got in first, which one has the most adherents, which one the textbooks tend to use, etc. That stuff is all non-scientific, sociological.
What we need is a good, consistent, logical theory to explain the experiments. Do you really think orthodox QM does that better than any of the other alternatives? If so, OK. But don't tell me Bohm's theory is out merely because it makes the same predictions as something else. If that's damning for Bohm, it should, by symmetry, be equally damning to the something else, too.

20. Oct 23, 2005

### Hurkyl

Staff Emeritus
Yes, it neglects any comment on wavefunction collapse, but it was meant to. The point of the statement of "causal-locality" is to emphasize the manner in which QM is local. QM does not throw locality to the wind -- the behavior which some call nonlocality only arises when you ask a special kind of question (which itself could be called a nonlocal question).

But in any case, I was just trying to state more rigorously that quote by DrChinese, which you called vague.