How can one event affect another instantly over a distance

[εllipse]

How can one event affect another instantly over a distance if there is no absolute concept of simultaneity? In which reference frame does the cause have a "simultaneous" effect?

 

[Timbuqtu]

This is a pretty tough issue. Firstly let me state that when, in quantum mechanics, two measurements on the same wavefunction done at separated locations can not really be seen as one measurement affecting the other, but we can say they are correlated to each other. Such correlation doesn't prescibe a chronical ordering like in the case of a causal interaction between both experiments, in which the 'cause' must ly within the past light-cone of the affected measurement according to special relativity.

Now, this of course isn't the whole story, because we know that on conducting a measurement on the wavefunction, it will collapse/be projected to an eigenstate, which also affects the wavefunction localized at the location, where the other measurement is to take place. So wavefunctions themselves do not obey the causal relations as demanded by special relativity. We can get away with this by stating that the wavefunction is not a direct observable. It is, by examining both measurements, impossible to tell which one affected the other, or which one took place first.

But ultimately it is true that quantum mechanics is flawed and that we need another theory which does obey the rules of special relativity, for instance quantum field theory.

 

[ttn]

But ultimately it is true that quantum mechanics is flawed and that we need another theory which does obey the rules of special relativity, for instance quantum field theory.

But the "flaw" (non-locality) is present in quantum field theory as well. Indeed no known quantum theory that respects (what Bell dubbed) "serious Lorentz invariance" is known. Quantum non-locality isn't just some dismissable problem that afflicts non-relativistic quantum theories; it's inherent in quantum theory (and, as the combination of EPR and Bell's Theorem demonstrates) inherent in nature as well.

So it seems that the most likely solution is to accept that quantum non-locality is real -- and to accept that it conflicts with what we thought relativity required -- and hence to back away from the traditional interpretation of relativity theory. This doesn't mean that all the standard relativistic formalism has to be dumped, but one apparently has to regard Lorentz invariance as some kind of emergent property -- emergent, that is, from an underlying reality that is fundamentally not relativistic.

The obvious first cut at a way to do this is simply to return to something like the Lorentz ether theory -- a theory which actually predicts all the same formalism (Lorentz transformations, etc.) as standard relativity but does so on the assumption that there exists a preferred (ether) reference frame. What good does this do? It gives a definite *meaning* to the (near?)-simultaneous action-at-a-distance that is involved in quantum non-locality.

Check out Bell's paper "How to Teach Special Relativity" for a nice, readable intro to some of these ideas. (It's reproduced in "Speakable and Unspeakable in Quantum Mechanics".) Also, for anyone who wants to understand quantum non-localilty and its relation to relativity, there is a spectacularly clear treatment of all of this in Tim Maudlin's book: "Quantum Non-Locality and Relativity." There are a lot of *bad* (muddled, unclear, wrong) books on this topic too, so if you really want to understand things you *have* to read Maudlin's book.

 

[selfAdjoint]

The obvious first cut at a way to do this is simply to return to something like the Lorentz ether theory -- a theory which actually predicts all the same formalism (Lorentz transformations, etc.) as standard relativity but does so on the assumption that there exists a preferred (ether) reference frame. What good does this do? It gives a definite *meaning* to the (near?)-simultaneous action-at-a-distance that is involved in quantum non-locality.

I don't think you can support an ether on the base of quantum nonlocality. Remember that QED, for example, is "manifestly covariant", i.e it does obey everything that relativity requires, and it also exhibits, as you say, quantum nonlocality. So either QED is inconsistent (which has NOT been shown!) or quantum nonlocality does not violate relativity requirements. What relativity requires is that CAUSE not be transferred FTL, and there is no transfer of cause in quantum nonlocality, just an after the fact correlation that shows up in the shared future light cone of the two particles.

The view that this constitutes non locality in the relativistic sense is based on an unexamined tendency to view QM is a classical theory, to treat it as if it were in fact one of the hidden variable theories that the Bell inequalities ruled out.

 

[Sherlock]

How can one event affect another instantly over a distance if there is no absolute concept of simultaneity? In which reference frame does the cause have a "simultaneous" effect?

Nonlocality doesn't mean that an event at A causes an
event at B, where A and B are spatially, maybe even spacelike,
separated.

Nonlocal observational contexts are global contexts involving
the correlation of two or more detection events. But, the
detection events aren't correlated to each other, they're
correlated to changes in a global, independent variable.

For example, a common Bell test setup involves entangled
photons, where you have an emitter, linear polarizers at each
of two arms of the setup, and a photon detector behind each
polarizer. Like this:

detector A <--- polarizer <-- emitter --> polarizer --> detector B

The determining variable in this setup is the value of
Theta, which is the angular difference between the
settings of the two polarizers.

The probabilistic state of the entire system changes
instantaneously (or simultaneously) with changes in
Theta, and Theta changes instantaneously (simultaneously)
as the setting of either polarizer is changed.

If Theta is disregarded and we simply change
the polarizer setting at A, then no corresponding change in
the photon flux (rate of detection per unit of time) at B
is seen. In fact, nothing done at A is seen to have any
effect on the detection rate at B, or vice versa.

It's only when the combined results, (A,B), are correlated
wrt Theta that predictable changes in the rate of
*coincidental* detection are seen.

Results at A and B are paired or correlated initially via
a coincidence interval defined by a common clock, and then
those pairs are correlated to the specific Theta for that
interval.

As should be evident, all of this transpires in real time
in accordance with the constraints of special relativity.

The problem is this: wrt the underlying reality of the
polarizer-incident (emitted) optical disturbances that might
be associated with paired photon detections, what are the
necessary and sufficient preconditions at the submicroscopic
level to produce predictable coincidence rates due to changes
in Theta?

Setups are prepared with the idea in mind that the disturbances
incident on the polarizers must have a common cause (such as
coming from the same oscillator) in order to get Bell inequality
violating results.

Violations of Bell inequalities tell us that this common
origin, and a relationship between the two disturbances
imparted therefrom, can't be the *cause* of the predictable
changes in coincidence rates -- and it isn't.

The changes in coincidence rate are caused by changes in
Theta.

It follows that the relationship (defined by, eg., conservation
of angular momentum) between disturbances having
a common origin is not varying from pair to pair, even though
the specific motional properties (eg., angle of polarization, etc.)
are varying randomly from pair to pair.

It's this underlying relationship, imparted via common origin,
that is the 'entanglement' of the polarizer-incident optical
disturbances at the submicroscopic level.
By itself, ala Bell, it can't account for the observed variable
coincidence rates. Nor can the apparent random variablitity of
specific motional properties from pair to pair.

To account for (ie., to produce) predictable variable coincidence
rates, you need a global, instrumental or observational variable,
like Theta, the angular difference between the analyzing
polarizers.

 

[DrChinese]

To account for (ie., to produce) predictable variable coincidence rates, you need a global, instrumental or observational variable,
like Theta, the angular difference between the analyzing
polarizers.

Nonlocality is a very difficult issue. Almost every angle of the discussion involves definitions, and few people will precisely agree about those definitions. So that is often the source of disagreements...

You definitely do not "need" to hypothesize a global (nonlocal) variable called "theta" to explain the observed results. You need the Heisenberg Uncertainty Principle, which still applies in cases of entanglement. You cannot extract more information about the particles than the HUP allows.

Note that theta only explains about the polarization of entangled photons, and does not explain why the other photon attributes are also entangled. I.e. position, momentum, etc.

The real question is: how do you explain the physicality of the results? I don't think non-local hidden variables is the answer. In fact, I am not sure there is an answer.

 

[ttn]

I don't think you can support an ether on the base of quantum nonlocality. Remember that QED, for example, is "manifestly covariant", i.e it does obey everything that relativity requires, and it also exhibits, as you say, quantum nonlocality. So either QED is inconsistent (which has NOT been shown!) or quantum nonlocality does not violate relativity requirements. What relativity requires is that CAUSE not be transferred FTL, and there is no transfer of cause in quantum nonlocality, just an after the fact correlation that shows up in the shared future light cone of the two particles.

The objectionable non-locality is not in Schroedinger's equation (or its analog in the context of a relativistic quantum field theory like QED). So it is irrelevant that those equations are "manifestly covariant". The nonlocality in the orthodox theories is in the collapse postulate. This is something that doesn't get any explicit attention in QED/QFT textbooks because the assumption is, by the time you're learning QED, you already know enough QM to know that to calculate probabilities for things you only need to calculate the appropriate matrix elements. So the texts simply teach you how to calculate matrix elements for certain scattering processes and things like that.

But the collapse postulate is still lurking as an inelimanble (if unmentioned) part of the theory, at least as long as you want to claim that QED is consistent with the fact that when you go into the lab and actually *do* one of the scattering experiments mentioned above, you get some definite outcome (e.g., a certain electron is detected to have scattered into a certain angle... as opposed to: the electron scatters into all angles simultaneously with the whole array of detectors all flashing "bing!" but in parallel universes).

So... it's just what I said originally: orthodox quantum theory is non-local. It violates Bell's Locality condition ("Bell Locality"). And any attempt to blame this *apparent* non-locality on the non-completeness of the quantum mechanical description (i.e., any attempt to explain the correlations by reference to some local common cause that was un-accounted-for in the wave function) must fail. That's Bell's Theorem. Hence Bell Locality is false. Nature violates Bell Locality.

And so to whatever extent Bell Locality accurately captures relativity's prohibition on superluminal causation (and Bell and I and many others think it captures it just perfectly), relativity is wrong. And as Bell pointed out, the cheapest way of dealing with this conflict is to combine something like Bohmian Mechanics and Lorentz ether theory.

The view that this constitutes non locality in the relativistic sense is based on an unexamined tendency to view QM is a classical theory, to treat it as if it were in fact one of the hidden variable theories that the Bell inequalities ruled out.

Hogwash. The view that violation of Bell Locality constitutes a problem for relativity is based on an analysis of relativity -- it's based on taking relativity *seriously* and not just spewing bromides about how relativity prohibits superluminal communication. It's true that relativity prohibits *at least* superluminal communication, but if that's *all* it prohibits, then all sorts of blatantly non-local theories (like orthodox QM and Bohmian Mechanics) which involve blatant non-local action-at-a-distance are rendered consistent with relativity. Bell was smart enough to figure out a way to define a stronger condition, a condition not just prohibiting some vaguely defined act that humans sometimes take ("communication"), but really identifying the guts of relativistic causality. To suggest that Bell's analysis was based on an "unexamined tendency to view QM is a classical theory" is preposterous and insulting to a great genius.

Finally: your last sentence implies that Bell's Theorem rules out hidden variable theories, i.e., proves that QM is complete. That's wrong. Bohmian Mechanics is a counter example to that claim.

 

[DrChinese]

But the collapse postulate is still lurking as an inelimanble (if unmentioned) part of the theory, at least as long as you want to claim that QED is consistent with the fact that when you go into the lab and actually *do* one of the scattering experiments mentioned above, you get some definite outcome (e.g., a certain electron is detected to have scattered into a certain angle... as opposed to: the electron scatters into all angles simultaneously with the whole array of detectors all flashing "bing!" but in parallel universes).

So... it's just what I said originally: orthodox quantum theory is non-local. It violates Bell's Locality condition ("Bell Locality"). And any attempt to blame this *apparent* non-locality on the non-completeness of the quantum mechanical description (i.e., any attempt to explain the correlations by reference to some local common cause that was un-accounted-for in the wave function) must fail. That's Bell's Theorem. Hence Bell Locality is false. Nature violates Bell Locality.

And so to whatever extent Bell Locality accurately captures relativity's prohibition on superluminal causation (and Bell and I and many others think it captures it just perfectly), relativity is wrong.

Well said!

Just as a reminder, Special Relativity is intended to apply within certain constraints. Within a particular reference frame, c is the speed of photons and other force carriers, and less than c is the speed of particles with mass. So just in case someone is bothered by the statement above that "relativity is wrong":

1. We don't know if there are rolled up dimensions or other somethings (causal wormholes?) that would allow causes to propagate in apparent violation of Bell Locality.

2. There are already known cases in which objects are receding from Earth at speeds in excess of 3c. This does not necessarily violate GR though.

 

[Sherlock]

Nonlocality is a very difficult issue. Almost every angle of the discussion involves definitions, and few people will precisely agree about those definitions. So that is often the source of disagreements...

For sure. I was just offering my perspective on a small slice
of the bigger pie ... so to speak. :-) Last night I did a search
at arxiv.org on "entangled" and "entanglement" in quant-ph and
got about 300 results. Tonight I'll try "nonlocality", etc.

The number of variations on the basic theme, and the associated
terminology seems to be expanding at a pretty fast rate.

You definitely do not "need" to hypothesize a global (nonlocal) variable called "theta" to explain the observed results. You need the Heisenberg Uncertainty Principle, which still applies in cases of entanglement. You cannot extract more information about the particles than the HUP allows.
Note that theta only explains about the polarization of entangled photons, and does not explain why the other photon attributes are also entangled. I.e. position, momentum, etc.

Theta isn't a hypothetical variable. It's the actual joint setting of
the polarizers, and it determines the variable rate of coincidental
detection. I used this type of setup as an example, because
it's the most common Bell test setup, and a bit easier to visualize
than some others you might be thinking of.

The real question is: how do you explain the physicality of the results? I don't think non-local hidden variables is the answer. In fact, I am not sure there is an answer.

Not sure what you mean by the "physicality of the results". But
if you mean what I think you mean, then variations in Theta and
a hidden constant would explain the results in the setup I presented.
Theta is the angular difference between the crossed linear
polarizers. It isn't a hidden variable. Bell's analysis holds.
That is, the variable rotational properties of the optical
disturbances incident on the polarizers can't be used to predict
coincidence rates which vary as Theta varies.

Such rotational properties (local hidden variables) could, however,
if we knew what they were, according to Bell, be used to predict
individual detection sequences at either A or B.

 

[εllipse]

Thanks! All these replies have been very helpful, but as usual with quantum mechanics the range of different ideas can be pretty frightenning and hard to make heads or tails of. So I'm still scratching my head on this one. :grumpy:

Just as a reminder, Special Relativity is intended to apply within certain constraints. Within a particular reference frame, c is the speed of photons and other force carriers, and less than c is the speed of particles with mass. So just in case someone is bothered by the statement above that "relativity is wrong"...

This is what bothers me. If you say that Bell's theorem proves that there is some sort of instantaneous information exchange (of any kind) over vast distances, that would mean that you are talking about some sense of "simultaneity", but of course in special relativity you have to have a reference frame from which to state something is "simultaneous". In another reference frame, such things won't be simultaneous. Is there a specific reference frame from which the exchange can be said to happen simultaneously or is it supposed to apply to all reference frames? If it is the former then there would be reference frames in which causality is violated. If it is the latter then the relativity of simultaneity must be wrong, which is very troubling because Minkowskian spacetime and general relativity are built from a framework in which relativity of simultaneity is true. Perhaps this is the reason string theorists are attempting to find a different approach to gravitation... But if relativity is so obviously wrong why haven't we reverted back to an ether theory as someone suggested? Although it is commonly known that relativity and quantum mechanics don't agree in situations where they are both pushed to their limits (black holes, big bang), this seems to be a bit more of a substantial disagreement. And while black holes and the big bang may point to flaws in general relativity and the need to find a theory of quantum gravity, the disagreement between locality and non-locality seems to show that not even special relativity can be valid, unless of course Bell's theorem is wrong. So it seems to me that before we even try to come up with a theory of quantum gravity, we need to know if special relativity is even correct. And if special relativity is valid, then it seems there must be some vital flaw in quantum theory.

 

[DrChinese]

...But if relativity is so obviously wrong why haven't we reverted back to an ether theory as someone suggested? Although it is commonly known that relativity and quantum mechanics don't agree in situations where they are both pushed to their limits (black holes, big bang), this seems to be a bit more of a substantial disagreement. And while black holes and the big bang may point to flaws in general relativity and the need to find a theory of quantum gravity, the disagreement between locality and non-locality seems to show that not even special relativity can be valid, unless of course Bell's theorem is wrong. So it seems to me that before we even try to come up with a theory of quantum gravity, we need to know if special relativity is even correct. And if special relativity is valid, then it seems there must be some vital flaw in quantum theory.

What I am saying is that there is no problem applying QM where it is supposed to be applied, and there is no problem applying SR where is it supposed to be applied. The apparent conflicts may not be real, they may derive from trying to make one theory fit where it shouldn't.

Keep in mind: Bell's Theorem also assumes "reality" as well as "locality". Locality is not ruled out if you accept that reality is observer dependent. Of course, I have no idea what such "non-reality" actually is... but the point is that there is definitely an escape route out of the conflict.

 

[DrChinese]

Theta isn't a hypothetical variable. It's the actual joint setting of the polarizers, and it determines the variable rate of coincidental
detection. I used this type of setup as an example, because
it's the most common Bell test setup, and a bit easier to visualize
than some others you might be thinking of.

Theta is a number, I agree with that. But it is not a fundamental observable, it is derived from 2 other fundamental observables. Those two observables are redundant, because the HUP limits information about any particle.

In some ways, our disagreement is semantic. Theta acts "as if" it were real. But that is not how QM gets to that point. Once you measure particle A, you learn about B. Using that information about B, you measure B at some other polarizer angle but gain absolutely NO information in that process. The resulting stats are no different than if you measured any single photon's spin at 2 angles - which forms the exact same Theta you describe. So Theta has nothing but a tangential relationship to entanglement - it is not required to be fundamental to it.

So to summarize: HUP applies to single particles and entangled systems. Theta also applies to single particles and entangled systems. But Theta can be derived using the HUP, while the HUP cannot be derived from Theta. So decide for yourself which is more fundamental. Don't forget that the HUP also covers position and momentum, while Theta does not.

 

[ttn]

This is what bothers me. If you say that Bell's theorem proves that there is some sort of instantaneous information exchange (of any kind) over vast distances, that would mean that you are talking about some sense of "simultaneity", but of course in special relativity you have to have a reference frame from which to state something is "simultaneous".

I think you are using "information" here in its most general sense, right? Usually people in this field define "information" more narrowly, though -- as the "knowledge stuff" that humans sometimes transfer to one another by talking, etc. There is a certain precise definition of locality that is based on this idea. It's called "signal locality" or "information locality" and means simply that one cannot send a message or signal faster than light. It's possible to write down a certain mathematical condition equivalent to this, and then to ask whether or not various theories satisfy the condition. Regular quantum theory, for example, passes the test -- it is "signal local". And so does Bohmian Mechanics. It too is "signal local". This just means that, according to these theories, it is impossible in principle to transmit a message to another person faster than light. So in that sense of "locality" both of these theories (and of course many others too) are consistent with relativity.

But Bell and others felt that this condition was too weak. As I said before, there's no question that relativity requires at least signal locality. But the two signal local theories I mentioned (orthodox QM and Bohmian Mechanics) are both non-local in another obvious kind of way. In OQM, the collapse postulate seems to rather blatantly violate some kind of common sense notion of local causality. Likewise, in Bohmian Mechanics, the dynamical laws are blatantly non-local: the trajectory of a given particle can depend on the fields or whatever encountered by another entangled particle, even if the other one is very far away. And yet both these theories are consistent with signal locality! So clearly, by example, it's possible to have a theory that seems to rather blatantly violate the no-faster-than-light-causation requirement of relativity, but which, nevertheless, cannot be harnessed by humans to build faster-than-light telephones. This is what motivated Bell to define another mathematical condition ("Bell Locality") which is supposed to test whether a theory is *really* consistent with relativity or not. Orthodox QM turns out to violate Bell Locality. So does Bohmian Mechanics. And Bell proved an amazing theorem: *any* theory that agrees with the (empirically verified) predictions of quantum theory has to violate Bell Locality.

So (assuming you believe the experiments, and the loopholes are awfully narrow), it's just a fact that Bell Locality is violated in nature. Some people (like me) think this is a problem. Bell certainly thought so:

"For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory..."

Other people disagree that Bell Locality is an appropriate test for relativistic causality. For example, some think that the weaker "signal locality" condition is *all* that relativity requires. So they conclude that there is really no conflict between QM and SR. But then, about 99% of these same people would say that Bohmian Mechanics (and other hidden variable theories) should be rejected because those theories have to be (as proved by Bell's Theorem) non-local. Hopefully you can see now why that's such a preposterous view!

In another reference frame, such things won't be simultaneous. Is there a specific reference frame from which the exchange can be said to happen simultaneously or is it supposed to apply to all reference frames?

An excellent question, one that should be asked about the collapse postulate to any advocate of orthodox QM!

More generally, you're thinking along exactly the right lines here. If you agree that nature's violation of Bell Locality means that there is some kind of instantaneous (or near-instantaneous... much faster than light is all that really matters here) causality-at-a-distance in nature, it just doesn't make sense that nature can be fundamentally relativistic. There would have to be some special frame in which the instantaneous causality *happens* -- some particular frame relative to which "instantaneity" is *defined*. And relativity says there's no such thing.

I think this is all review at this point, but hopefully it clarifies exactly what the problem is and why some people are so resistant to seeing it. Relativity has served physicists well for a hundred years, so you can understand why they're hesitant to admit that, after all, it turns out to be wrong (or at least not as fundamental as everyone thought). This is surely what motivates some of the obfuscation and inconsistency you find everywhere on this issue.

If it is the former then there would be reference frames in which causality is violated. If it is the latter then the relativity of simultaneity must be wrong, which is very troubling because Minkowskian spacetime and general relativity are built from a framework in which relativity of simultaneity is true.

Exactly.

Perhaps this is the reason string theorists are attempting to find a different approach to gravitation...

Actually, the inconsistency between relativity and QM that motivates string theory is a different issue, much more technical. String theory is definitely not motivated by an attempt to reconcile quantum non-locality with relativity. But I agree completely with the sentiment you express below:
it seems premature to be working on some extremely high-level, technical unification of the quantum and relativistic formalisms, if we haven't even figured out how to reconcile them in terms of basic, elementary concepts. Of course, it's possible that fixing the technical details will turn out to lead to some kind of resolution at the level of the fundamentals, too; but to me it seems more like rearranging deck chairs into a very fancy pattern on a titanic that's sinking. Fix the fundamentals first, then worry about the super advanced complicated unifications and such.

But if relativity is so obviously wrong why haven't we reverted back to an ether theory as someone suggested?

It's a bit too simple to say "relativity is wrong." Surely the *equations* of relativity are right, or at least are right in the kinds of situations where we know they're right because we've tested the theory's predictions there. The question is more whether the standard conceptual structure motivating those equations (in particular the so-called "principle of relativity") is true. Part of the problem is that many physicists suffer from a "shut up and calculate" attitude that makes them very resistant to even taking fundamental conceptual or interpretational or foundational issues seriously. Unfortunately, this leaves them susceptible to the kind of obfuscation and muddle-headed thinking I indicated above (e.g., "There's no conflict between QM and SR because you can't use QM to send a signal faster than light; but we shouldn't consider hidden variable alternatives to QM like Bohmian Mechanics, for, as Bell's Theorem proves, those theories are non-local and hence in conflict with SR."). But that's a whole 'nuther can of worms, as they say.

 

[Nicky]

The objectionable non-locality is not in Schroedinger's equation (or its analog in the context of a relativistic quantum field theory like QED). So it is irrelevant that those equations are "manifestly covariant". The nonlocality in the orthodox theories is in the collapse postulate.

I was under the impression that the collapse postulate is only considered an approximation, since it does not define precisely what constitutes "measurement". So if all nonlocality in QM flows from the collapse postulate, then the nonlocality may not be physically real, just an artifact of the approximation.

In the many-worlds approach, for example, there is no need for the notion of nonlocality. I am still trying to understand dynamical collapse theories, so I don't know if they make nonlocality go away as well. Maybe someone who understands them better can answer -- do dynamical collapse theories eliminate the apparent nonlocality of orthodox QM?

 

[Rade]

I enter this discussion because I am confused about statements concerning importance of "locality" to physics and science in general. Perhaps it has to deal with definition. Here is a definition that makes sense to me as a scientist, from this link:http://www.mtnmath.com/whatrh/node76.html

"Locality is the denial of action at a distance.

It requires that all the information useful in predicting what will happen at a given location and time is contained in a sphere of influence. For an event that will occur in one second the sphere has a radius of 300,000 kilometers, the distance light travels in one second.

Locality is the most powerful simplifying assumption in physics. Without it any event no matter how distant can influence any other event. Prediction would be impossible without locality or some other powerful restriction on what events can affect other events. Otherwise one would need to know the state of the universe to predict anything.

Quantum mechanics is a local theory in configuration space but not in physical space."

Now, if the above holds, then clearly QM and Relativity will not find conflict in questions dealing with "configuration space", but they may very well be in conflict within "physical space"--which is also called "real space". If I read the above correctly, QM attributes of an entity must have "non-local" affects only within physical space.

But what is configuration space and how does it differ from "real space" ? One answer is from Nick Herbert, 1985, Quantum Reality, pp. 135, 169-170. According to Herbert, it is only within configuration space that exist the attributes of "position and momentum" of the waveform. Within "real space" (physical space) the major attribute is spin orientation Sx, Sy, Sz in three orthogonal directions.

Next, Herbert makes an important statement (p 169-170) that I quote:

"The reason that quantum waves become phase-entangled and ordinary waves don't is that quantum waves do not make home in ordinary three-dimensional space (e.g. the place of spin orientation--my added) but in a place called configuration space".

Thus, Herbert seems to suggest (correct me if I error) that the QM concept of the waveform only applies to the configuation space aspect of Reality, and DOES NOT EXIST within the physical space of Reality--in short--as known by Einstein, QM is a theory with a limit, and that limit is called physical reality. This outcome obtains because QM holds most dear the concept of "phase entanglement"--which is a process that is limited to configuation space.

 

[Dr.Yes]

Associative simultanianeous events

How can one event affect another instantly over a distance if there is no absolute concept of simultaneity? In which reference frame does the cause have a "simultaneous" effect?

Forgive me for even typing near you guys but, I would interject that a "region" or locale does not necessarily mean all in one area. It can also apply to the commonality of events and their common, root causes. Those events of a similar origin will occur, sometimes simultaneously, in a region of homogeneous but random "locations". The "relative" distance between them is not "distance" as we see it but is another type of "region" we call "distance" that is an arbitrary boundary for an infinitely varied number of other "regional events". I don't know if this helps.

 

[Rade]

Locality is not ruled out if you accept that reality is observer dependent. Of course, I have no idea what such "non-reality" actually is... but the point is that there is definitely an escape route out of the conflict.

It seems to me that if we hold as true the statement: Locality exists if <reality is observer dependent>, then by logic we must conclude that non-locality exist if <non-reality is observer independent>.

For example, travel > c (an aspect of non-locality) is possible for entities that are non-reality and which exist independent of observer [e.g., think virtual pions within proton which exist in essence in the zero point vacuum (configuration space) but not in fact (physical space of the valence quarks)]. I think this line of reason helps explain what "non-reality actually is " (or may be) in terms of QM.

 

[Sherlock]

Theta is a number, I agree with that. But it is not a fundamental observable, it is derived from 2 other fundamental observables. Those two observables are redundant, because the HUP limits information about any particle.

Theta is the angular difference between the polarizer settings.
In the joint observational context, it's a single variable correlated
to (A,B).

I'm not familiar with Bell tests that require HUP. That is, I don't
recall HUP being mentioned in the experiments that I have copies
of here (Aspect et al., and a few others). So, I'm not sure
what you're saying.

In some ways, our disagreement is semantic. Theta acts "as if" it were real. But that is not how QM gets to that point. Once you measure particle A, you learn about B. Using that information about B, you measure B at some other polarizer angle but gain absolutely NO information in that process. The resulting stats are no different than if you measured any single photon's spin at 2 angles - which forms the exact same Theta you describe. So Theta has nothing but a tangential relationship to entanglement - it is not required to be fundamental to it.

Theta doesn't "act as if" it were real. It is real. It's an
instrumental setting that defines the observational context.
The context, so defined, is a nonlocal context.

This context isn't looking at individual particles. It's looking
at the combined results, (A,B), and how these results are
related to Theta.

So to summarize: HUP applies to single particles and entangled systems. Theta also applies to single particles and entangled systems. But Theta can be derived using the HUP, while the HUP cannot be derived from Theta. So decide for yourself which is more fundamental. Don't forget that the HUP also covers position and momentum, while Theta does not.

In the observational context that I described (the one that has
been most commonly used in Bell tests), we're not looking at
individual results. QM isn't describing individual results at A or
individual results at B in this context, because (A,B) and Theta
(the angular difference between the polarizers) are one system.

Theta is analyzing (measuring) a common (global) property of the
polarizer-incident optical disturbances that isn't varying, and
isn't present in the individual measurement context.

Bell's analysis showed that formulations based on treating
A and B as separate systems with variations in (A,B) being
determined by a variable global Lambda are inadequate.
This doesn't necessarily mean that a variable global Lambda
isn't present in the joint context -- but it does mean that
even if it is present, it isn't relevant to (A,B). What *is*
determining (A,B) is the variable Theta. This observational
fact allows for some reasonable inferences about some
general characteristics of what the polarizers are jointly
analyzing in the combined context.

Hence, experimental violations of Bell inequalities are taken to be
an indicator of the presence of a global, emission-imparted property
(a hidden constant), ie. the presence of entanglement.

Tests of Bell inequalities are comparing the efficacy of a
separable formulation to a nonseparable formulation.

A and B are not being related to each other, but rather (A,B) is
being related to variations in a global instrumental variable (Theta).
So, Theta must be analyzing some global property of the
incident optical disturbances. It's logical to assume that
this global property is created via common cause or local
interaction and carried by the optical disturbances to the
polarizers. Bell's lhv formulation doesn't contradict this idea.
What Bell's lhv formulation contradicts is the idea that, in
the global context, the global property of the optical disturbances
that is determining variable rates of coincidental detection
is a variable. It isn't. It can't be, because Theta is the variable
that's determining variable rates of coincidental detection.

 

[Sherlock]

This is what bothers me. If you say that Bell's theorem proves that there is some sort of instantaneous information exchange (of any kind) over vast distances, that would mean that you are talking about some sense of "simultaneity", but of course in special relativity you have to have a reference frame from which to state something is "simultaneous".

If you want to model the system-dependent behavior
of two spatially separated objects (that are part of the
same encompassing behavioral system) in terms of the
separated behaviors of the individual objects, then you'll
need some sort of instantaneous signal propagating between
the two in order to get the right joint predictions.

But you don't have to do it that way. :-)

Consider two points on opposite sides of the circumference
of a circle in some coordinate system. Rotate the circle.
Did the points change coordinates in a predictable way
because they're communicating with each other, or because
of the rotation of the circle and their unchanging relationship
wrt each other on the circumference of the circle?

Although this is an oversimplification, the principle here
is the same wrt nonlocality (qm or Bohmian or whatever).
It has to do with system-dependent behavior.

In typical optical Bell tests, paired photons don't need to
be sending any sort of signals back and forth to each
other. They just need to have a more or less unvarying
relationship wrt each other prior to hitting the polarizers.

In Bell's lhv formulation, Lambda (the global property of the
incident optical disturbances) is a hidden variable in the
global context. Bell showed that such a formulation doesn't
adequately describe the global context. Why? Is it because
the global property of the incident optical disturbances
isn't due to a common cause or local interaction? Or, is
it because the relevant global property of the incident
optical disturbances, in the system-dependent view, isn't
varying?

Qm correctly describes the observational context (albeit
somewhat incompletely describing the physical reality, so that
there are still problems with collapse and projection, etc.),
because it treats the emission-produced *relationship* between
the incident optical disturbances as a constant rather than a
variable.

 

[ttn]

Quantum mechanics is a local theory in configuration space but not in physical space."[/I]

Now, if the above holds, then clearly QM and Relativity will not find conflict in questions dealing with "configuration space", but they may very well be in conflict within "physical space"--which is also called "real space". If I read the above correctly, QM attributes of an entity must have "non-local" affects only within physical space.

But what is configuration space and how does it differ from "real space" ?

Say you have a 2-particle system. Each particle is able to move around in the usual 3 dimensions of space, to to specify the precise configuration of the system at some point you'd have to specify x1, y1, z1, and x2, y2, and z2 -- that is, the coordinates for each particle. Configuration space is just an abstract space which (in this example) is 6 dimensional -- the 6 dimensions being x1, y1, z1, x2, y2, and z2. Thus, the configuration of the whole system can be specified by specifying a *point* in the configuration space. This is really just a mathematical device. Sometimes it's convenient to think abstractly of the system configuration as a single "particle" that just moves around (in time) in the configuration space. But there is no more or no less meaning to this than: each indidvidual particle is just moving around in some way in regular 3d physical space.

So the claim that QM is non-local in physical space but local in configuration space is really pretty inane. It is admittedly possible to give a meaning to the latter part of the statement, but it certainly isn't a meaning that reduces in any way the tension between QM and relativity. To be local in configuration space is still to permit instantaneous action at a distance between separated particles in real physical space. So it's just a red herring or diversion tactic.





One answer is from Nick Herbert, 1985, Quantum Reality, pp. 135, 169-170. According to Herbert, it is only within configuration space that exist the attributes of "position and momentum" of the waveform. Within "real space" (physical space) the major attribute is spin orientation Sx, Sy, Sz in three orthogonal directions.

Next, Herbert makes an important statement (p 169-170) that I quote:

"The reason that quantum waves become phase-entangled and ordinary waves don't is that quantum waves do not make home in ordinary three-dimensional space (e.g. the place of spin orientation--my added) but in a place called configuration space".

Thus, Herbert seems to suggest (correct me if I error) that the QM concept of the waveform only applies to the configuation space aspect of Reality, and DOES NOT EXIST within the physical space of Reality--in short--as known by Einstein, QM is a theory with a limit, and that limit is called physical reality. This outcome obtains because QM holds most dear the concept of "phase entanglement"--which is a process that is limited to configuation space.[/QUOTE]

 

[ttn]

I was under the impression that the collapse postulate is only considered an approximation, since it does not define precisely what constitutes "measurement".

Something like that, though I don't think "approximation" is quite the right word. Isn't it more accurate to say that the orthodox formulation of QM (which says that different dynamical laws apply depending on whether or not a measurement is being made) is just *vague* since it doesn't provide any definition of "measurement"?

So if all nonlocality in QM flows from the collapse postulate, then the nonlocality may not be physically real, just an artifact of the approximation.

Remember, QM (or what I always like to call "orthodox QM" to make sure to distinguish it from other alternative interpretations/theories like Bohmian Mechanics, Many Worlds, Spontaneous Collapse, etc.) is just a theory. It's not synonymous with "the truth" or anything like that. The question of whether *nature* violates some kind of locality postulate is a very difficult one, not at all the same question as whether some particular *theory* (like Orthodox QM) violates it. Once you have a clear/mathematical definition of locality in hand (e.g., the "signal locality" or "Bell Locality" concepts I mentioned before) it's relatively easy to just look at how a given theory is supposed to work and say "Aha, this theory violates signal locality" or whatever. You just look at the theory.

Maybe what you meant is that the non-locality that is apparent in orthodox QM is, perhaps, merely apparent -- as in, you could get rid of it be tweaking the theory in some minor way (e.g., by providing a clean definition of "measurement"). But this doesn't appear to work. The EPR argument shows quite clearly what is needed to "tweak" orthodox QM into something that respects Bell Locality. (What you need is a certain kind of deterministic local hidden variables.) But then Bell's theorem shows that this project cannot succeed -- local hidden variable theories can never be made to reproduce the right (empirically tested) predictions. So it does turn out that Bell Locality is violated by nature -- no possible theory of any kind can respect it. (But that's just a map of an argument: you'd have to really understand Bell's theorem and EPR and so forth to really grasp the conclusion with certainty.)

In the many-worlds approach, for example, there is no need for the notion of nonlocality.

Yes, many worlds is hard to pin down in regard to locality. The argument I sketched above is premised on the idea that these correlation experiments actually give rise to definite outcomes on either side -- outcomes which are compared later to compile correlation statistics which can then be tested against the prediction of this or that theory. But MWI denies that experiments have definite outcomes. Some people seem to think it makes sense to accept that rather than accept that inescapable violations of Bell Locality (inescapable if you believe that experiments actually have definite outcomes!). But frankly I think it's crazy. Literally.

I am still trying to understand dynamical collapse theories, so I don't know if they make nonlocality go away as well. Maybe someone who understands them better can answer -- do dynamical collapse theories eliminate the apparent nonlocality of orthodox QM?

No, they don't. The GRW type theories violate Bell Locality, just like orthodox QM and Bohmian Mechanics. (They are, however, consistent with signal locality -- at least most of the theories, and in most of the situations that could be tested any time soon!)

 

[DrChinese]

I'm not familiar with Bell tests that require HUP. That is, I don't recall HUP being mentioned in the experiments that I have copies
of here (Aspect et al., and a few others). So, I'm not sure
what you're saying.

Theta doesn't "act as if" it were real. It is real.

...

Hence, experimental violations of Bell inequalities are taken to be
an indicator of the presence of a global, emission-imparted property
(a hidden constant), ie. the presence of entanglement. ...

First, EPR was all about entanglement and the HUP. EPR assumed that it would eventually be determined that you could violate the HUP using the combined results of experiments on entangled particles.

Second, Bell saw EPR's assuption as flawed, because the simultaneous reality of non-commuting observables was a key element of its conclusions. So, that is the key assumption Bell attacked - that unmeasured spin components exist. They don't, as we now know from experiments. Similarly, photon attributes such as frequency, position, energy, wavelength, etc. are also equally observer dependent.

Third, there is nothing special about Theta. The entangled (PDC-I) photons have identical polarization - if you measure it. They have identical wavelengths - if you measure it. They have opposite momenta, if you instead measure that. Etc. Theta is a number that is derived from one set of these fundamental properties of entangled particle pairs, and is completely dependent on how the observations are performed. If you measure both photons' positions, your Theta disappears entirely.

So to recap: HUP is not usually mentioned explicitly in Bell tests. But it is the limits of the HUP that drive the relations between entangled particle pairs. Whatever you learn about A is what you learn about B; and B thereafter acts accordingly in 100% agreement with the limits of the HUP. No other assumptions are required to describe the further behavior of entangled particles. Wave collapse for one is wave collapse for both.

I agree that for spin component tests, Theta acts as if it were real. And as such, it leads you to believe that it is fundamental and a global variable. But that view requires you to ignore the full range of possible experiments that can be performed on the entangled particles. Recall that the basic delta(p)delta(q)>h of the HUP always applies. Thus there are any number of permutations of experiments that will yield any number of hypothetical alternate Thetas... are these all real too? Or are they just numbers that act as if they are real?

 

[εllipse]

Why doesn't Bell's Theorem prove quantum mechanics is incomplete?

It seems to me that Bell's inequality doesn't lead to non-locality for a hidden variable theory. If you're in a distant galaxy and I go half way in between you and some oberserver on Earth and before hand both of you know that I have two blue balls and two red balls and that I will either fire a red ball or a blue ball at you, but we agree that whatever I fire at you I will also fire at Earth, then if you attempt to describe the "state" of the balls before they reach you as a wave of possibilities which collapses when you get your ball, then you have to resort to non-locality to explain why the distant observer will also get the same color ball. But if you just attribute your lack of knowledge to ignorance, then you don't have to explain why both balls are the same color. They'll be the same color because I fired them both from the same location and chose them both to be the same color.. they have hidden variables.. Is such an explanation not possible for Bell's Theorem?

 

[DrChinese]

It seems to me that Bell's inequality doesn't lead to non-locality for a hidden variable theory. If you're in a distant galaxy and I go half way in between you and some oberserver on Earth and before hand both of you know that I have two blue balls and two red balls and that I will either fire a red ball or a blue ball at you, but we agree that whatever I fire at you I will also fire at Earth, then if you attempt to describe the "state" of the balls before they reach you as a wave of possibilities which collapses when you get your ball, then you have to resort to non-locality to explain why the distant observer will also get the same color ball. But if you just attribute your lack of knowledge to ignorance, then you don't have to explain why both balls are the same color. They'll be the same color because I fired them both from the same location and chose them both to be the same color.. they have hidden variables.. Is such an explanation not possible for Bell's Theorem?

No, definitely not! That is what everyone assumed before Bell. Bell's innovation was to show that there are particular angle settings for measurements that don't work out according to this plan. In the situation you describe, the angle settings are no problem to explain. That is the 0 degree case: you measure A and B at the same angle. But don't forget: we need there to be a C, D, etc. because we could have measured at those angles too - IF the results are to be observer independent. These hidden variables are hypothesized to give us the explanation of behavior... so do they?

If you pick some very specific cases - admittedly not just any old cases - the results differ vastly from what would be expected if there are hidden variables. Bell's Theorem leads immediately to "negative probabilities", specifically:

Assume A=0 degrees, B=67.5 degrees, and our hypothetical angle C=45 degrees (which MUST exist in the hidden variable scenario, because the outcome is not to be observer dependent). Then the combined likelihood of the cases: (A+ B+ C-) and (A- B- C+) is -10.36% (that is, less than 0), verified by experiment. This non-physical result demonstrates that C does not exist along with A and B. Follow the link to see the full logic, and I will be glad to answer any questions.

To summarize: the two ball scenario is easy to explain, just as you have. And if you stop there, the world seems simple and there is no problem. But Bell does not let you off so easy! If you can't explain the A=0/B=67.5/C=45 case (there are plenty of others), then you have nothing. QM has a simple explanation: there is NO C, just A and B. Guess what? If there is no C, then there is no problem. If there is no C, then the results are observer dependent. If the results are observer dependent, then there is not simultaneous reality to non-commuting variables. And this explains the EPR paradox perfectly.

 

[εllipse]

Haha, right. I'm sorry. I completely forgot what Bell's theorem was during that post and was thinking along the lines of the EPR paradox. My appologies. How embarrasing.

 

[ttn]

Haha, right. I'm sorry. I completely forgot what Bell's theorem was during that post and was thinking along the lines of the EPR paradox. My appologies. How embarrasing.

That's right -- but your post was actually a pretty good summary (unintentionally) of the EPR argument. According to orthodox QM, the individual balls (particles) don't have definite colors (spin component values) until one of them is measured. But then the measurement of either one causes *both* balls (including the distant one!) to suddenly acquire a definite color. And that violates (at least, Bell) Locality.

But EPR's point was: so much the worse for orthodox QM, specifically, so much the worse for the claim that the individual balls don't have a definite color prior to measurement. Their point was: it makes sense to drop the completeness doctrine (i.e., admit that the balls do have a definite color even before measured) in order to have a local theory.

It is a sad commentary on the state of physics that this simple and obviously valid argument has been so systematically misunderstood and evaded.

Of course, things are different post-Bell. Bell proved that you can't save locality this way. Any hidden variable theory that respects bell locality is unable to reproduce the (empirically verified) predictions of qm. So orthodox QM isn't local, and it turns out to be impossible to construct a local theory by dropping the completeness doctrine. That's precisely the proof that *nature* is nonlocal. If no empirically viable theory is local, then nature isn't local. My point here is simply to stress the important role played by the EPR argument in generating this (correct) conclusion. If you forget about (or evade) EPR (like so many physicists still do), then the whole Bell's Theorem thing looks like an argument against hidden variable theories! In fact, it's nothing of the kind. It's a proof that *even* hidden variable theories have to be non-local, which is just another way of saying: the apparent non-locality of orthodox QM is unavoidable and hence real.

 

[selfAdjoint]

If you forget about (or evade) EPR (like so many physicists still do), then the whole Bell's Theorem thing looks like an argument against hidden variable theories! In fact, it's nothing of the kind. It's a proof that *even* hidden variable theories have to be non-local, which is just another way of saying: the apparent non-locality of orthodox QM is unavoidable and hence real.

But QM isn't nonlocal in the same sense that realist theories are nonlocal. By denying that the "balls" have "color" until they are observed, it avoids having causes travel faster than light. The one ball is observed to be red, and the other to be blue, and there is no definite order that they do that. Different observers will see different orders due to relativity of simultenaity. After the fact, at a place and time with both observations in the past light cone, you can do the Bell inequalities and confirm that they are violated.

The supposed "effect" of one ball color on the other over spacelike separation is precisely the realist position that QM denies.

 

[ttn]

But QM isn't nonlocal in the same sense that realist theories are nonlocal.

You'll have to tell me in precise mathematical terms, then, how you are defining "nonlocal". Because it is an incontestable fact that orthodox QM violates Bell Locality. And this is of course precisely the same kind of locality that Bell proved "realist" (by which I assume you mean hidden variable) theories must violate.

By denying that the "balls" have "color" until they are observed, it avoids having causes travel faster than light.

If the act of measuring ball A causes the distant ball B to suddenly and instantaneously acquire a definite color (where before it had none), that involves causes traveling faster than light.

But it is important that the words in the sentence I wrote aren't the full proof that orthodox QM is nonlocal. That sentence just provides a kind of loose conceptual argument that OQM seems to be nonlocal. The real test -- the precise test that doesn't allow any wiggle room or fuzziness -- is simply to look at how the theory works mathematically and ask: is this consistent with Bell Locality? It isn't.

The one ball is observed to be red, and the other to be blue, and there is no definite order that they do that. Different observers will see different orders due to relativity of simultenaity.

That's the reason the non-locality conflicts with relativity -- it's not any argument that the non-locality isn't really there!

After the fact, at a place and time with both observations in the past light cone, you can do the Bell inequalities and confirm that they are violated.

The Bell Inequalities don't even apply to orthodox QM, because the derivation of the Bell Inequalities presupposes a certain kind of theory (namely a local hidden variable theory) which orthodox QM isn't. So the proof that orthodox QM violates Bell Locality has absolutely -- absolutely! -- nothing to do with Bell's Inequalities. One simply looks at the theory itself and sees whether or not it is consistent with Bell Locality. And it just isn't.

It's really simple. Orthodox QM is not consistent with Bell Locality. Bell wondered if some other theory, a hidden variable theory, might be consistent with Bell Locality. But he proved this isn't possible: all such Bell Local hidden variable theories must obey the Inequality -- i.e., must disagree with experiment. So that's why we know Bell Locality is violated in nature. Orthodox QM violates it, and so does the only kind of theory you might have tried to replace OQM with to save Bell Locality.

The supposed "effect" of one ball color on the other over spacelike separation is precisely the realist position that QM denies.

I don't understand this comment. You'll have to define exactly what you mean by "realism". In my view, this concept doesn't even ever need to be brough up. It's all about Bell Locality.

 

[Hurkyl]

I used http://arxiv.org/abs/quant-ph/0002060 for a reference: QM does satisfy Bell Locality.


It derives as equation (2) the QM prediction:

$$P^{(12)} (\sigma_a = r, \sigma_b = q | \hat{a}, \hat{b}, \Psi_0) = \frac{1}{4} \left[ 1 + r < \sigma_a > + q < \sigma_b > + rq < \sigma_a \sigma_b > \right]$$

where $\hat{a}, \hat{b}$ are the directions along which the spins of particles 1 and 2 are measured, $\sigma_a, \sigma_b$ are the random variables denoting the results of the measurements of particles 1 and 2, and $\Psi_0$ is the wavefunction describing the state. $< \sigma_a >$ means the expected value of this random variable.


Then it states as equation (6) Bell's locality condition:

$$p^{(12)}(\sigma_a = r, \sigma_b = q | \hat{a}, \hat{b}, \lambda) = \frac{1}{4} \left[ 1 + r E^{(1)} (\hat{a}, \lambda) + q E^{(2)} (\hat{b}, \lambda) + r q E^{(12)} (\hat{a}, \hat{b}, \lambda) \right]$$

Where $E^{(1)} (\hat{a}, \lambda)$ is explained to be the expected values of the spin along axis $\hat{a}$ given the hidden variables λ... that is, precisely $< \sigma_a >$. $E^{(12)} (\hat{a}, \hat{b}, \lambda)$ is similarly described to be the expectation value of the product of the spins.

 

[Rade]

Assume A=0 degrees, B=67.5 degrees... QM has a simple explanation: there is NO C, just A and B. Guess what? If there is no C, then there is no problem. If there is no C, then the results are observer dependent. If the results are observer dependent, then there is not simultaneous reality to non-commuting variables. And this explains the EPR paradox perfectly.

But of course in this example you must conclude that reality is observer dependent--because as the basic premise of your argument you assume A = 0, B = 67.5.

I hold that Reality does not allow you to make this assumption, both A and B are what Reality has determined that they are independent of your assumption--they may in fact be A = 0.01 and B = 0.02 or any other infinite set of possibilities as the basic assumption. Unless all statistical a priori possibilities for A & B & C in your example reach a conclusion of "negative probability" any statement that Reality is in fact "observer dependent" is shown to be false--and is why common sense tells us the moon really did exist before humans evolved to observe it--which is really all Einstein was trying to say. In short, Reality (with the big-R) exists independent of humans (it always has) and QM is but one of many theories invented by humans to understand the dynamics of this Reality.

 

[ttn]

I used http://arxiv.org/abs/quant-ph/0002060 for a reference: QM does satisfy Bell Locality.

That conclusion is wrong. The problem is addressed explictly in Maudlin's book ("Quantum Non-Locality and Relativity"). For a shorter and very readable explanation of the point, see

http://arxiv.org/pdf/quant-ph/0408105

 

[Hurkyl]

Ah, the difference (I think) is where the assumption of outcome independence lies: in the reference I used, it was placed in the following text, stating that E(a, b, λ) = E(a, λ) * E(b, λ), but your reference puts the assumption into the equation itself.

 

[Hurkyl]

On the other hand, isn't relativistic QFT locally causal by the definition given by Bell in that paper?

IOW, given a state, isn't its value at a point in space-time completely determined by a slice of the backwards light-cone?

 

[ttn]

On the other hand, isn't relativistic QFT locally causal by the definition given by Bell in that paper?

IOW, given a state, isn't its value at a point in space-time completely determined by a slice of the backwards light-cone?

No, it isn't. That's a common misconception for the reason I mentioned earlier: texts on relativistic QFT (almost) never even mention the issue of measurement and the collapse postulate that is needed (yes, even in QFT) to ensure that measurements actually have definite outcomes.

One sees proofs in some QFT texts that the theory is "locally causal" (or so they say). This is usually a proof that space-like separated operators commute. But what this actually *means* is signal locality. This condition ensures that the theory cannot be used to transmit information faster than light. And in that sense, the theory is consistent with relativity. But in terms of the stronger locality condition (Bell Locality), QFT suffers from the same problem as regular old QM: measurements can have effects on the state attributed to distant locations (effects which change the probabilities for subsequent measurements at those distant locations, but in an unpredictable way that prevents these effects from being used to transmit information).

 

[Hurkyl]

The collapse postulate is an entirely separate issue from the kinematics.


We just have the cool theorem that says that these two algorithms:

(1) Let the system evolve
(2) Do a collapse to see what the two measurements were

and

(1) Let the system evolve
(2) Do a collapse to see what the first measurement is
(3) Let the collapsed system evolve
(4) Do a collapse to see what the second measurement is

are equivalent.


There is no non-locality in the evolution of the system. The non-locality is in the extraction of information, specifically that P(B|A) = P(B) for spatially separated measurements may be false, and the method of wavefunction collapse.