Is QM Inherently Non-local in EPR and Bell Discussions?

[vanesch]

I will come back to this tomorrow.

Maybe we should then start another thread, not hijacking this one ? This thread is about the non-locality or not of quantum theory, under the working hypothesis that QM predictions are correct, and it is NOT about whether or not this working hypothesis is acceptable.

 

[Careful]

Maybe we should then start another thread, not hijacking this one ? This thread is about the non-locality or not of quantum theory, under the working hypothesis that QM predictions are correct, and it is NOT about whether or not this working hypothesis is acceptable.

Ok, you start a new one although - as I mentioned before - the answer to the literal message of this thread is rather obvious (it might be pleasant to chat about it however and I am aware that recently some controversy about this has been on the Arxiv, entirely unnecessary and even misguided from time to time). People talk too much about the interpretation of QM and are afraid to really modify it, that's one good reason why progress (especially in quantum gravity) is slow...(not substantial) So, I will check this site later on.

 

[vanesch]

Ok, you start a new one although - as I mentioned before - the answer to the literal message of this thread is rather obvious

I don't think that the answer is obvious. QM presents us with a riddle: Bell locality is violated, but signal locality isn't.
If neither were violated, I think nobody would even think of saying that locality is violated by QM. If both were violated, again, it would be obvious that QM violates locality. But we're in between.

And then it depends on how you look at the internal workings of the theory to decide whether the mathematical operations you execute (and which you "believe" to be associated to an ontology or not) are respecting locality or not. So it depends on what exactly you understand by locality, and what exactly you assign a reality to in the mathematical framework of QM. This involves of course the interpretation you attach to it.

Concerning the predictions:
So if you say: a theory is local if it respects Bell locality, then, no, QM is not local (that's ttn's point of view).
If you say: a theory is local if it respects signal locality, then yes, QM is local (can't build a FTL phone that way).
Concerning the mathematical formalism and its relation to an ontology:
If you 1) assign a reality to the wavefunction and 2) consider the projection postulate as describing something that physically happens, then the inner workings of QM are bluntly non-local.
Denying 1) is the epistemological viewpoint of QM (just a technique for calculating outcomes of experiments) and you're back to the "predictions" side.
Denying 2) (like does MWI) allows you to consider the mathematical machinery of QM as respecting locality.
See, plenty of stuff to argue endlessly over, and spend time on PF :-)

 

[Careful]

I don't understand what you're saying here.

Look, it is very simple: locality in the operational sense means that a measurement at A cannot have measurable influence outside the lightcone of A. The example I gave you violates this. However, it is of crucial importance here that the measurement at B is non-local: such as the projection operator on a localized state or a Wilson loop, but not the integral of a local operator valued density. Such non-local operators are used all the time in QFT, so one cannot claim they are not physical. Therefore, if one assumes the validity of perfect von Neumann measurements and the existence of non-local observables, then one has to conclude that QFT is not local operationally. One could argue that such measurements are impossible, but then one has to develop an accurate measurement theory which respects locality. Such task has not been accomplished yet: therefore my statement is fair.

 

[Careful]

I don't think that the answer is obvious. QM presents us with a riddle: Bell locality is violated, but signal locality isn't.
If neither were violated, I think nobody would even think of saying that locality is violated by QM. If both were violated, again, it would be obvious that QM violates locality. But we're in between.
And then it depends on how you look at the internal workings of the theory to decide whether the mathematical operations you execute (and which you "believe" to be associated to an ontology or not) are respecting locality or not. So it depends on what exactly you understand by locality, and what exactly you assign a reality to in the mathematical framework of QM. This involves of course the interpretation you attach to it.
Concerning the predictions:
So if you say: a theory is local if it respects Bell locality, then, no, QM is not local (that's ttn's point of view).
If you say: a theory is local if it respects signal locality, then yes, QM is local (can't build a FTL phone that way).
Concerning the mathematical formalism and its relation to an ontology:
If you 1) assign a reality to the wavefunction and 2) consider the projection postulate as describing something that physically happens, then the inner workings of QM are bluntly non-local.
Denying 1) is the epistemological viewpoint of QM (just a technique for calculating outcomes of experiments) and you're back to the "predictions" side.
Denying 2) (like does MWI) allows you to consider the mathematical machinery of QM as respecting locality.
See, plenty of stuff to argue endlessly over, and spend time on PF :-)

I agree with you here except that you cannot send signals faster than light in QM. This is a much more subtle issue than just postulating commutation relations (see my previous post) at spacelike separated events. So, you should not talk but develop a theory of non-perfect Von Neumann measurements which respects locality in the operational sense.

 

[vanesch]

I agree with you here except that you cannot send signals faster than light in QM. This is a much more subtle issue than just postulating commutation relations (see my previous post) at spacelike separated events.

I have seen what you allude to, but I can't make much sense of it. I would think that what is sufficient is that the Green's functions (the propagators) vanish outside of the lightcone ? (and this is related to the commutation relations vanishing at spacelike separated events) How are you going to modify the field in a spacelike way if the Green's function is 0 ?

 

[Careful]

I have seen what you allude to, but I can't make much sense of it. I would think that what is sufficient is that the Green's functions (the propagators) vanish outside of the lightcone ? (and this is related to the commutation relations vanishing at spacelike separated events) How are you going to modify the field in a spacelike way if the Green's function is 0 ?

It is very simple: quantum field theory has NO measurement theory. There is NO principle of reduction of the state functional (that is why the vanishing of the Green function outside the lightcone is sufficient for your purposes) such as in standard QM (you should read Sorkin's paper). This is clearly unsatisfactory and the only thing QFT is good for is to compute S matrices. Summary: in QFT you are restricting yourself to a unitary evolution. Bringing in any discrete/non-unitary reduction of the state principle allows for the possibility of measurable correlations outside the lightcone at least when you do it in the naive Von Neumann sense. So it seems to me you have two possibilties: either (a) you admit that the idea behind QFT needs improvement in order to incoorporate for a suitable measurement theory or (b) you refuse fundamental investigations in the principles of QFT and accept either (i) superluminal signalling or (ii) the fact that QFT allows for a limited number of questions to be asked.

 

[vanesch]

Summary: in QFT you are restricting yourself to a unitary evolution.

But that is maybe a very very good idea

 

[Careful]

But that is maybe a very very good idea

No, it is not
Let me make the full reasoning: let X be the orginal density matrix
(a) you want f(x) and f(y) to commute when x and y are spatially separated since you want MEASUREMENT of f(x) and f(y) to be independent (otherwise there is no sense in doing this)
(b) Let A be in the past of B and C in the future of B but not in the future of A (A,B and C are domains in spacetime). Suppose a and c correspond to local operators on A and C that is : a = integral(f(x), x in A) and c = integral(f(y), y in C). Then clearly a and c commute and if I do a after c or c after a, it does not matter. However the causal relations impose a temporality on the order in which a,b and c have to be performed : that is c after b after a. Now if b is not a local operator (for example the integral of quasi local observables) then
sum_{i,j,k} P_i Q_j R_k X R_k Q_j P_i is not equal to sum_{i,j} P_i Q_j X Q_j P_i even when both density matrices are restricted to the complement of the lightcone of A (P_i Q_j R_k are the orthogonal projection operators associated to c,b and a respectively). Non local operators are for example integrated hamiltonian densities with respect to some observers.

This is clearly a problem. So I expect a better answer from you. On one hand you claim that f(x) and f(y) have to commute since measurements have to be independent and on the other you claim that you do not want to do state reduction when it becomes troublesome. Even funnier, if you would claim that no measurement can be made in QFT, then it is impossible to even tell something about this issue at all :-) It is clear that any quantum theory MUST have a consistent measurement theory for it to be taken seriously. So either you propose one, or otherwise I see no reason why superluminal signalling is banned.

 

[Tez]

No, I think you have it right.
For me personally, the confusion begins when you talk about an object outside the lightcone. Alice makes a measurement, which causes collapse of the shared wave function. Now you know something about something somewhere else, true, and that is outside the lightcone.
But what has happened that is really so weird? We project the knowledge we have back to the point at which the entangled particle pair was created. This is the same thing that happens when only one particle is involved, nothing strange about that. The particle acts as if it had that orientation from the last point something happened.
Say Alice sees a V orientation with a polarizer at 0 degrees. Naturally, all subsequent measurements will be consistent in EVERY WAY with this knowledge AS IF it was always that way from the creation of the particle. So in that sense there is absolutely nothing happening outside any light cone.
In other words, all quantum measurements find a particle in an eigenstate and its eigenvalue is consistent with the quantum measurement rules. Entangled particles are no different in this respect. So the real question to me is: why does a measurement at time T2 cause the particle to assume a specific value as if it had that value at time T1 (where T1 is before T2) ? Does that make oQM non-local? Or is that a case of backwards causality? I am not sure that anything physical occurs along with the collapse, and I think that is a relevant question too.
Naturally, some of these issues show up in our definition of locality. You can see that there is no information transfer which is FTL, and there is no clear causal effect which is FTL. Yet the Bell Locality condition is violated with a strict application of its definition. So what does that condition actually tell us? Of course, it fits with the Bell Inequality too so that is very important.
Inquiring minds want to know...

What you say here is one of the most common misunderstandings of what Bell's theorem tells us. It is categorically not the interesting nonlocality of QM.

Ask yourself if that type of nonlocality would enable you to "win" this game:

The game is you and a friend are imprisoned, and told you're going to be separated. Once separated you will each randomly be asked either "what is X?" or "what is Y?" to which you must answer either 1 or -1. If you are both asked the X question then you must give opposite answers, but in all other cases (one of you asked X the other Y, or both asked Y) you must give the same answer. You win the game, you get released.

A minutes thought will let you know that unless you can tell what question the other person is asked there's no way to guarantee you winning the game. Your best bet is simply to agree to always answer the same thing and rely on the 3/4 chance that this'll win you the game.

But wait: if you carried entangled particles you can delay the decision of what to answer to your captors - once asked the question you make a measurement on the particle and output 1 or -1 according to the outcome. This way your probability of being released goes up to 85%. How did the entangled particles do it unless they knew something about what the other particle had been "asked".

In a 3 prisoner version the probability of release can go up to 100%, despite every "logical" strategy allowing for a maximum of 75%.

 

[DrChinese]

But wait: if you carried entangled particles you can delay the decision of what to answer to your captors - once asked the question you make a measurement on the particle and output 1 or -1 according to the outcome. This way your probability of being released goes up to 85%. How did the entangled particles do it unless they knew something about what the other particle had been "asked".

But they don't really! (Obviously, otherwise we could use that for FTL signalling.)

All we know is that our captors communicated in our past light cone and we are using that locally transmitted knowledge to play a logic game. There is no superluminal anything over and above a normal interpretation of a Bell test. After all, our captors can't release us until they compare our answers.

 

[Careful]

But they don't really! (Obviously, otherwise we could use that for FTL signalling.)
All we know is that our captors communicated in our past light cone and we are using that locally transmitted knowledge to play a logic game. There is no superluminal anything over and above a normal interpretation of a Bell test. After all, our captors can't release us until they compare our answers.

Well, enlighten us with a measurement theory which bans superluminal signalling consistently. I did not meet anyone until now who can do this, perhaps a texan chinese can be the first one.

 

[Sherlock]

You can see that there is no information transfer which is FTL, and there is no clear causal effect which is FTL. Yet the Bell Locality condition is violated with a strict application of its definition. So what does that condition actually tell us?

The Bell Locality condition tells us that A and B aren't observationally or statistically independent. This has a local explanation via quantum theory which also tells us that A and B aren't independent. (Paired results are the macroscopic manifestation of quantum-level disturbances that came from the same emitter via the same emission process. They're thus related by the applicable conservation laws, and, when they're entangled, they're entangled due to the ambiguity of certain intermediate states described by the emission process model.)

My current understanding of, and answer to, your original question is that quantum theory is not inherently non-local.

EDIT: I think that maybe the Bell Locality condition is poorly named. Calling it the Bell Independence condition would be less confusing. The assumption that statistical independence of A and B is required in a local universe is, I think, incorrect.

 

[Sherlock]

How did the entangled particles do it unless they knew something about what the other particle had been "asked".

The entangled particles don't need to know anything about what the other particle had been asked. Their motions just need to be related in some way.

Entanglement implies a relationship between the motions of two particles. Exactly how they're related is unknown. But the assumption of some sort of relationship has a purely local basis, and this assumption is conceptually adequate to understand the predictable results.

The fact that a detailed description of the motions (the sub-microscopic evolutions) of the two particles is impossible according to the principles of quantum theory is why the theory can't be made to be explicitly local. But it certainly isn't explicitly non-local either.

 

[Sherlock]

Well, enlighten us with a measurement theory which bans superluminal signalling consistently.

Does Special Relativity qualify?

 

[vanesch]

(b) Let A be in the past of B and C in the future of B but not in the future of A (A,B and C are domains in spacetime).

I don't understand this: A and B are time-like connected (A is in the past lightcone of B). C and B are time-like connected (C is in the future lightcone of B). How the hell can A and C then not be time-like connected ??
Imagine a material particle traveling from A to B (is possible: timelike), and have it then travel from B to C (is possible: timelike). So overall, a material particle traveled from A to C, no ?

 

[Careful]

I don't understand this: A and B are time-like connected (A is in the past lightcone of B). C and B are time-like connected (C is in the future lightcone of B). How the hell can A and C then not be time-like connected ??
Imagine a material particle traveling from A to B (is possible: timelike), and have it then travel from B to C (is possible: timelike). So overall, a material particle traveled from A to C, no ?

Look Vanesh, A,B and C are spacetime REGIONS, you cannot speak about measurement theory for points since field operators are distributional, you need to smear it out by test functions (independently of this mathematical worry, locality in QFT must obviously also hold for observables living on such extended regions). I said that : A is in the past of B, this does not imply that B is in the future of A (this is however obviously true for points though). Moreover, sorry that I say this, it is a travesty to think that particles are points in QFT. To make everything crystal clear: I am not saying that it is impossible to construct a measurement theory which is consistent (although I am pretty much convinced it is impossible indeed), but it does not exist yet to my knowledge. Therefore, saying that superluminal signalling is excluded is unfounded.

 

[Careful]

Does Special Relativity qualify?

Sorry, but you should better study QFT first before you make such comments... I am trying to raise a serious issue here: that is the lack of a consistent measurement theory for QFT which is compatible with the demands of special relativity.

 

[DrChinese]

I am trying to raise a serious issue here: that is the lack of a consistent measurement theory for QFT which is compatible with the demands of special relativity.

Wow, you should consider starting a thread on this (as opposed to hijacking an existing one).

 

[Sherlock]

Sorry, but you should better study QFT first before you make such comments... I am trying to raise a serious issue here: that is the lack of a consistent measurement theory for QFT which is compatible with the demands of special relativity.

No offense intended. I saw your smily and thought I'd match it.

So there's no mathematically rigorous and consistent measurement theory for QFT in line with one of its principal components, SR -- and the possibility of superluminality in Nature can't be definitively ruled out. Ok.

Nothing said in this thread is ruling out the *possibility* of superluminality in Nature, afaik. However, the consensus seems to be that the considerations that go into considering whether to refer to QM as inherently non-local do not necessitate the assumption that there *is* superluminality in Nature either.

The problem of developing a consistent measurement theory for QFT which is compatible with the demands of special relativity is a problem for another thread. And I promise that I'll just sit back and watch that one.

As for the topic of this thread, I take it that you would consider quantum theory to be inherently non-local. Maybe one might say that it's kinematically, but not dynamically, non-local. But I think that such statements confuse the issue. The bases of quantum theory are local. It neither predicts ftl phenomena, nor does its formalism imply ftl phenomena.
Its principles do prohibit tracking the continuous evolution of quantum phenomena, thereby prohibiting hidden variable theories of the sort that would allow an explicitly local description of the phenomena responsible for the inequality-violating results of Bell tests.

 

[Careful]

Wow, you should consider starting a thread on this (as opposed to hijacking an existing one).

Sorry this issue is relevant ! You cannot claim that QFT forbids signalling faster than with the speed of light when you do not have an appropriate measurement theory. Instead of being so defensive, look at it as a challenge : you should solve the problem, not me, I am convinced it is a waste of time anyway. If, on the other hand, you might surprise me, then I shall praise you.

 

[Careful]

No offense intended. I saw your smily and thought I'd match it.
So there's no mathematically rigorous and consistent measurement theory for QFT in line with one of its principal components, SR -- and the possibility of superluminality in Nature can't be definitively ruled out. Ok.
Nothing said in this thread is ruling out the *possibility* of superluminality in Nature, afaik. However, the consensus seems to be that the considerations that go into considering whether to refer to QM as inherently non-local do not necessitate the assumption that there *is* superluminality in Nature either.
The problem of developing a consistent measurement theory for QFT which is compatible with the demands of special relativity is a problem for another thread. And I promise that I'll just sit back and watch that one.
As for the topic of this thread, I take it that you would consider quantum theory to be inherently non-local. Maybe one might say that it's kinematically, but not dynamically, non-local. But I think that such statements confuse the issue. The bases of quantum theory are local. It neither predicts ftl phenomena, nor does its formalism imply ftl phenomena.
Its principles do prohibit tracking the continuous evolution of quantum phenomena, thereby prohibiting hidden variable theories of the sort that would allow an explicitly local description of the phenomena responsible for the inequality-violating results of Bell tests.

HUH ? You are claiming for some time now that you *cannot* signal faster than with the speed of light and now you say that it does not matter or that it violates it kinematically while a measurement process is clearly dynamical. Do you know the mathematical foundations of logic?

 

[DrChinese]

1. Sorry this issue is relevant !

2. you should solve the problem, not me, I am convinced it is a waste of time anyway.

1. By that standard, we don't need threads at all. Everything in this subforum relates to QFT in SOME way.

2. Why would you ask me or any other person to expend effort for something you consider a waste of time?

 

[Sherlock]

HUH ? You are claiming for some time now that you *cannot* signal faster than with the speed of light and now you say that it does not matter or that it violates it kinematically while a measurement process is clearly dynamical. Do you know the mathematical foundations of logic?

The assumption that Nature obeys the principle of locality hasn't been falsified. Has it? Where did I say that it doesn't matter? The point is that, as far as is known, there are no superluminal phenomena in Nature. That doesn't mean that it's impossible for such phenomena to exist, does it? How would we know for sure?

That quantum theory is kinematically, but not dynamically, non-local is from something I read by H.D. Zeh.

 

[Hurkyl]

Careful:

I understand that the axioms of Algebraic Quantum Field Theory are derivable from doing things the ordinary way, and it's manifestly evident that in AQFT, that any space-like separated operators commute.

 

[Careful]

Careful:
I understand that the axioms of Algebraic Quantum Field Theory are derivable from doing things the ordinary way, and it's manifestly evident that in AQFT, that any space-like separated operators commute.

This is obvious and not the issue (I suspect you have to be careful when you take products of field operators and so on). What I say, is that this is not sufficient (while it is clearly sufficient in the case of two measurements). Check out the Sorkin 1994 paper. impossible measurements on quantum fields. THINK about it before you reply; I notice that Vanesh is thinking (or he is just absent for some reason, just noticed he was thinking).

 

[Careful]

1. By that standard, we don't need threads at all. Everything in this subforum relates to QFT in SOME way.
2. Why would you ask me or any other person to expend effort for something you consider a waste of time?

Because YOU think QFT is a worthwile enterprise while I have a dozen of other reasons to dispose of it. Look, I am not saying that on this forum, research problems should be solved, but at least we should make the effort in trying to ask the right questions. If you take the Wightman axioms as true, then you need to develop a consistent measurement theory. Vanesh, a few mails ago, said that QM poses us with a riddle and started to argue why we should talk about the different options. Hereby, he assumed that it is a FACT that the Wightman axioms imply that no signalling faster than with the speed of light is possible (which is the crucial assumption for what follows in the entire conversation) without caring for an accurate measurement theory. Now, I transported the Copenhagen scheme to QFT and showed that this cannot be right. So you need to do better and I do not believe such effort it is meaningful in the end. If you would tell an engeneer for example that correlations beyond the lightcone exist in your theory, but you cannot measure them ,then he would mock you and say that your measurement apparatus sucks.

 

[Careful]

The assumption that Nature obeys the principle of locality hasn't been falsified. Has it? Where did I say that it doesn't matter? The point is that, as far as is known, there are no superluminal phenomena in Nature. That doesn't mean that it's impossible for such phenomena to exist, does it? How would we know for sure?
That quantum theory is kinematically, but not dynamically, non-local is from something I read by H.D. Zeh.

No, this assumption has not been fasfied by EXPERIMENT (although this is a very delicate issue and another piece of conversation). The question is whether your THEORY allows for processes FTL and that is NOT known for the moment. We never know for sure if processes FTL exist or not, but if this would be the case then we can forget about relativity and go back to eather theories. I must confess I BELIEVE that this cannot be, since it would be impossible for the justice departement to convict anyone of murder (he could argue that the person in question were killed in a tachyon crime commited by a third person in the future of the event itself). You can find this example in John Bell's book: no, the causality axiom is certainly more holy than anything else (this is certainly also the consensus although I do not like to use such arguments). You should not repeat what doctors write in books and realize that in research, there are many conflicting ideas written by equally qualified doctors. THINK for yourself, that is what Sherlock did, he was not a doctor but much sharper than dr. Watson however.

 

[vanesch]

Look Vanesh, A,B and C are spacetime REGIONS,

Ah, so, if you allow me, we can in fact do things with A and C events (or small regions) and B an extended region somewhere in between, such that a part of B is in the future lightcone of A and a disjoint part of B is in the past lightcone of C.
Defining some observable a,b and c on each of these regions, we can then state:
[a,c] = 0
[a,b] is not 0
[b,c] is not 0
This case is in fact handled in "Modern Quantum Mechanics" by JJ Sakurai (p 33): the correlation between a and c is dependent on whether the b measurement is performed or not.
But, but: here our situation is subtly different:
the correlation of a and c IS NOT AVAILABLE to C because C is outside of the future lightcone of A. So what is only available to C is the REDUCED density matrix of the state, tracing out A and B (B also, because the result of B, being a region, is only available to an event which has the ENTIRE B in its past lightcone, let us call this event B', and B' must necessarily be outside the past lightcone of C). This is one of the reasons why it is in fact not necessary to consider extended regions, because their result of measurement can only become available at an event that has the ENTIRE region in its past lightcone (so only at that point one can say one has "performed the measurement" - if one insists on using the von Neumann picture ; me being an MWI-er, I insist on keeping everything unitary!).
Let us apply von Neumann's measurement scheme:
So you seem to claim that performing the measurement at a, or not, when the B measurement is performed, changes the outcomes of C ?
Let us take an initial state |psi> which is u|a+> + v|a->, |a+> and |a-> being the two eigenstates of A (and also of C, since they commute).
Now, if we perform the measurement at A, we have, with probability u^2, |a+> and with probability v^2, |a->
Now, if we perform the B measurement in the first case, we get, with probability
u^2 |(b+|a+)|^2 + v^2 |(b+|a-)|^2 the state |b+>
with probability u^2 |(b-|a+)|^2 + v^2 |(b-|a-)|^2 the state |b->
When C now performs its measurement (which is the same as A), we obtain:
with probability P_c(a+) =
(u^2 |(b+|a+)|^2 + v^2 |(b+|a-)|^2) |(a+|b+)|^2
+
(u^2 |(b-|a+)|^2 + v^2 |(b-|a-)|^2 ) |(a+|b-)|^2
the state |a+> (that will do, a- will be complementary).
On the other hand, if A does NOT perform his measurement, we have, for the B measurement:
|u(b+|a+) + v(b+|a-)|^2 probability to have b+ and
|u(b-|a+) + v(b-|a-)|^2 probability to have b-.
After C performs then his measurement, we have the probability at C to measure a+:
|u(b+|a+) + v(b+|a-)|^2 |(a+|b+)|^2 + |u(b-|a+) + v(b-|a-)|^2 |(a+|b-)|^2
The difference between both approaches (with A measurement and without A measurement) is then (we take u and v real):
Diff = u v ( (b+|a+) (a-|b+) + (a+|b+) (b+|a-) ) |(a+|b+)|^2
+ u v ( (b-|a+) (a-|b-) + (a+|b-)(b-|a-)) |(a+|b-)|^2
Writing this with U the unitary transformation matrix between the a set and the b set, we rewrite this as:
Diff = u v (U11 U11* U11 U21* + U12* U22 U12 U12* + CC)
If a is not to signal to c, this difference should vanish. Now, let us take that the basis transformation between the a set and the b set is unitary and unimodular (choice of overall phase):
U11 = x
U22 = x*
U12 = y
U21 = - y*
Now, after working this out I obtain:
Diff = u v (-x* x + y* y) (x y + x* y*)
which is, to my great surprise, not zero. I suspect I made an error somewhere...

 

[vanesch]

Now, after working this out I obtain:
Diff = u v (-x* x + y* y) (x y + x* y*)
which is, to my great surprise, not zero. I suspect I made an error somewhere...

I checked my calculation and I don't seem to find an error.
If this is true, this is amazing:
We have an initial state |psi> to which a can, or can not, apply a measurement (decision of a).
b applies always his/her measurement.
c applies the measurement (which is the same, or compatible, with the one done by a) and looks at the probability to get a certain result.
This probability (of c) seems to depend on whether a decided to measure or not (and NOT on the outcome of a), although a and c are spacelike connected points, which would mean that there is a FTL phone from a to c (a can decide, or not, to measure A, and c sees his probabilities change).
I admit being puzzled. There must be some quirk I didn't get.
I suppose that the trick is the spread of the B measurement, which can only be completed at an event which has the entire B section in its past lightcone (probably von Neumann's projection should only apply at that moment - at least, only at that moment I could entangle, in an MWI view, a local observer with the system according to the B measurement), and that this B measurement then doesn't occur BEFORE C.
But I admit, again, to be puzzled !
cheers,
Patrick.

 

[Tez]

But they don't really! (Obviously, otherwise we could use that for FTL signalling.)
All we know is that our captors communicated in our past light cone and we are using that locally transmitted knowledge to play a logic game. There is no superluminal anything over and above a normal interpretation of a Bell test. After all, our captors can't release us until they compare our answers.

I simply don't understand what you mean. Are you intimating that our captors cannot make a local, independent random choice as to which question to ask, and that therefore the particles can know before they're separated which question/measurement is going to come up? THis is the standard "no free will" loophole to Bell tests. And what is the "normal interpretation of a Bell test"?.

In case it wasn't clear, what I described is not an allegory - the game could be played by real prisoners and captors, and presuming the prisonors can carry concealed entangled particles and stern gerlach appartuses(!) their probability of being released goes up to 85%. And no, it doesn't allow for superluminal communication between the two prisoners, but it certainly would seem to require superluminal communication between the particles in order to achieve.

If you really don't see an issue with this, then perhaps you can outline how your understanding could help one tackle the question of why the probability of being released doesn't go up to 100%?

 

[Careful]

Ah, so, if you allow me, we can in fact do things with A and C events (or small regions) and B an extended region somewhere in between, such that a part of B is in the future lightcone of A and a disjoint part of B is in the past lightcone of C.
Defining some observable a,b and c on each of these regions, we can then state:
[a,c] = 0
[a,b] is not 0
[b,c] is not 0
This case is in fact handled in "Modern Quantum Mechanics" by JJ Sakurai (p 33): the correlation between a and c is dependent on whether the b measurement is performed or not.
But, but: here our situation is subtly different:
the correlation of a and c IS NOT AVAILABLE to C because C is outside of the future lightcone of A. So what is only available to C is the REDUCED density matrix of the state, tracing out A and B (B also, because the result of B, being a region, is only available to an event which has the ENTIRE B in its past lightcone, let us call this event B', and B' must necessarily be outside the past lightcone of C). This is one of the reasons why it is in fact not necessary to consider extended regions, because their result of measurement can only become available at an event that has the ENTIRE region in its past lightcone (so only at that point one can say one has "performed the measurement" - if one insists on using the von Neumann picture ; me being an MWI-er, I insist on keeping everything unitary!).
Let us apply von Neumann's measurement scheme:
So you seem to claim that performing the measurement at a, or not, when the B measurement is performed, changes the outcomes of C ?
Let us take an initial state |psi> which is u|a+> + v|a->, |a+> and |a-> being the two eigenstates of A (and also of C, since they commute).
Now, if we perform the measurement at A, we have, with probability u^2, |a+> and with probability v^2, |a->
Now, if we perform the B measurement in the first case, we get, with probability
u^2 |(b+|a+)|^2 + v^2 |(b+|a-)|^2 the state |b+>
with probability u^2 |(b-|a+)|^2 + v^2 |(b-|a-)|^2 the state |b->
..

You say : B also, because the result of B, being a region, is only available to an event which has the ENTIRE B in its past lightcone, let us call this event B', and B' must necessarily be outside the past lightcone of C.

If you mean by this that B can only effect C if the entire B is in the past of C, then this is utter nonsense. This is not even true classically (sorry but you are cryptic here).

Ah I see that you have posted again.. I was redoing your entire calculation :-) I was pretty confident you did it good since I have redone the sorkin calculations a few years ago and it came out right (moreover you are more ``quantal´´ in the computational sense than I am, I stopped doing this as soon as I realized a few things).

There is nothing mysterious about it however: as I said before the catch is that B is a non local operation in the sense that measurement of A is instantaneously coupled to something which is outside its lightcone (this is what B does). There is nothing wrong with the measurement setup I gave, you might indeed argue that you need to look for a better measurement theory (actually, that is your only way out). Now that you got this insight, you might start wondering WHY I say that it is probably impossible to make a realistic measurement theory which avoids this issue.

Cheers,

Careful

 

[vanesch]

You say : B also, because the result of B, being a region, is only available to an event which has the ENTIRE B in its past lightcone, let us call this event B', and B' must necessarily be outside the past lightcone of C.
If you mean by this that B can only effect C if the entire B is in the past of C, then this is utter nonsense. This is not even true classically (sorry but you are cryptic here).

Well, I'm an MWI-er, so I consider a "measurement" simply as a local entanglement of the observer body with the state, without projecting it. What I meant was that the measurement of B, over the entire region, can only be completed when this entire region is in the past lightcone of the observer who is going to observe this. So the observer doing this "B" measurement can only be completely entangled in this basis when he has the entire B region in the past. That doesn't mean that some unitary evolution cannot be initiated, but as everything here is unitary, I can clearly state that the lightcone will be respected in this way, and that whatever A gets entangled with at A will not influence what so ever at C.

So what I meant was that in the case that you want to apply a projection postulate a la von Neumann, you have in any case a difficult time, because you have to, somehow, take into account the partial unitary evolution during the B region itself, but you cannot have the entire result until all of this evolution was communicated to a (point-like) observer in some way or another, at which moment some magical "collapse" occurs (along a time slice in that pointlike observer's ref frame, I presume). So *IF* you want to do collapse stuff, you should only do it at that event ; but then the measurement at C already took place. It is this magic which makes me prefer the MWI view, BTW.

If I find some time I'll work out the problem from an MWI point of view...

cheers,
Patrick.

 

[Careful]

I simply don't understand what you mean. Are you intimating that our captors cannot make a local, independent random choice as to which question to ask, and that therefore the particles can know before they're separated which question/measurement is going to come up? THis is the standard "no free will" loophole to Bell tests. And what is the "normal interpretation of a Bell test"?.
In case it wasn't clear, what I described is not an allegory - the game could be played by real prisoners and captors, and presuming the prisonors can carry concealed entangled particles and stern gerlach appartuses(!) their probability of being released goes up to 85%. And no, it doesn't allow for superluminal communication between the two prisoners, but it certainly would seem to require superluminal communication between the particles in order to achieve.
If you really don't see an issue with this, then perhaps you can outline how your understanding could help one tackle the question of why the probability of being released doesn't go up to 100%?

Right, you are adressing the good question in my view. What physical mechanism can provide these correlations ?? They are all perverted. Quantum physicists try then to hide behind the no FTL signalling theorem, but as is clear from previous communications, this is by far not good enough! Moreover, QM does not offer any insight into the detailed dynamics of microworld, and this my greatest worry. My healthy peasant brain tells me that excluding faster than light communication is in fact not possible (but that is speculation) in any *natural* quantum theory; it is up to QFT theorists to prove me wrong.

 

[Careful]

Well, I'm an MWI-er, so I consider a "measurement" simply as a local entanglement of the observer body with the state, without projecting it. What I meant was that the measurement of B, over the entire region, can only be completed when this entire region is in the past lightcone of the observer who is going to observe this. So the observer doing this "B" measurement can only be completely entangled in this basis when he has the entire B region in the past. That doesn't mean that some unitary evolution cannot be initiated, but as everything here is unitary, I can clearly state that the lightcone will be respected in this way, and that whatever A gets entangled with at A will not influence what so ever at C.
So what I meant was that in the case that you want to apply a projection postulate a la von Neumann, you have in any case a difficult time, because you have to, somehow, take into account the partial unitary evolution during the B region itself, but you cannot have the entire result until all of this evolution was communicated to a (point-like) observer in some way or another, at which moment some magical "collapse" occurs (along a time slice in that pointlike observer's ref frame, I presume). So *IF* you want to do collapse stuff, you should only do it at that event ; but then the measurement at C already took place. It is this magic which makes me prefer the MWI view, BTW.
If I find some time I'll work out the problem from an MWI point of view...
cheers,
Patrick.

I do not know what MWI is (But I am a classical relativist and there we do not have interpretational clans since everything is crystal clear), but here are some objections to what you say:
(a) make your measurement procedure exact: you will have to apply a non local avaraging procedure as well in time as in space in order to interpret the result of this entanglement in a classical way.
(b) you say that it is only possible for a magical collapse to happen once an observer can have acces to the entire information of B. Now, this collapse is a non local procedure and happens on an entire spacelike hypersurface X containing this point like observer. It is no problem to put C to the future of this X unless X stays in the future lightcone of A which brings along other problems (so your claim is false there). Since this has to hold for any A your collapse has to happen on a null surface (and not even a differentiable one)!
(c) the only reasonable way to save your butt is by coupling realistic detector models to A,B and C and making a measurement theory for those. However, the dynamics to the quantum field under observation is not unitary anymore then (the total dynamics is of course) and the measurement theory itself is an entirely different issue. I presume you are just shifting the problem at this instant.