Von Neumann QM Rules Equivalent to Bohm?

[TrickyDicky]

Of course, that's precisely what's meant in Weinbergs book. In nature the discrete symmetries P, T, PT, and CP are all independently verified to be violated by the weak interaction. Due to the CPT theorem, valid for local microcausal QFTs, then also C must be violated. So what's the space-time symmetry of nature is the proper orthochronous Poinare group and not larger subgroups of O(1,3).

But can you clarify why the microcausality condition must be added separately then?
And again, I know the weak interaction violates C, but I was trying to restrict the discussion to QED.

 

[Ilja]

OT: Sorry for the side question, but what exactly is Einstein causality? It seems, from the posts above, that it is something different than the usual relativity theory causality that comes from no faster than light signals.

No, it is that faster than light is forbidden.

I prefer to use "Einstein causality" instead of "locality" because a theory with, say, a maximal speed of 10000000 c would still be a local theory, thus, using "locality" instead of "Einstein causality" is suggesting much more horrible consequences if one rejects it. It is one thing to reject Einstein causality and to go back to classical causality connected with some hidden absolute time, where one can later find a new speed limit, so that everything would look like now only with a greater speed limit, and a completely different thing to "reject locality".

 

[Ilja]

So perhaps can we agree to just refer to that statement as "Einstein Causality + classical probability theory"?

I would not object to this. But, then, add Jaynes' concept that probability theory is only extended logic. ;-)

 

[vanhees71]

I agree that Einstein causality, as defined for the Bell inequalities, does include classical probability.

There is also a second sense of locality that quantum mechanics does fulfill, which is "no faster than light transmission of classical information".

So there are two widely agreed upon definitions of locality, one of which is empty or violated by quantum mechanics, the other which is fulfilled by quantum mechanics.

Is there a third definition of locality that corresponds to "Einstein causality without classical probability?" Maybe, but then why call it Einstein causality, which is the causality of classical relativity? Some candidates are information causality http://arxiv.org/abs/1112.1142 and macroscopic locality http://arxiv.org/abs/1011.0246.

I don't know what you mean by "classical probability". Quantum theory provides probabilities, which obey the usual axioms (Kolmogorov) of probability theory as long as you apply it to experiments that make sense within the quantum-theoretical framework.

The linked-cluster theorem, valid for local microcausal relativistic QFTs, guarantees Einstein causality, i.e., no faster-than-light propagation of information (I also don't understand what you mean by classical information; for me information is what an observer can know about a system given its state; this information can be complete (if the system is known to be prepared in a "pure state", i.e., the statistical operator is a projection operator) or incomplete (then we describe it by a statistical operator which is not a projection operator, i.e., a "mixed state").

In other words, for our example, the locality and microcausality guarantees that when A measures the polarization of her photon, A knows immediately that B must find the opposite polarization, but B can only know it by either measuring it himself or getting the information from A, which needs a signal that travels, according to the relativistic space-time structure, at most at the speed of light. A knows B's photon's polarization from her knowledge about the initial state of the biphotons ("polarization singlet") and her local measurement of her photon's polarization.

 

[martinbn]

I think that at least partially the arguments come form "Einstein causality" =/= "no faster than light signalling" and the fact that some take it with "=" instead of "=/=".

 

[Ilja]

I think that at least partially the arguments come form "Einstein causality" =/= "no faster than light signalling" and the fact that some take it with "=" instead of "=/=".

Of course, one has to distinguish "no faster than light signalling" and "no causal influence faster than light". The first holds in quantum theory, the second is violated, because there is no way to explain the violation of the BI in a causal way without FTL.

So, my #212 was sloppy, my point there was a different one.

I think "Einstein causality" should be clearly associated with "no causal influence FTL". First, for historical reasons, because, given the EPR argument, this was clearly Einstein's understanding of causality.

Second, there is, of course, the possibility to reject Reichenbach's principle of common cause, which is sufficient together with Einstein causality to prove the Bell inequalities. Now, causality without Reichenbach's principle of common cause is not worth to be named causality. In other words, if we reject Reichenbach's principle of common cause, we reject causality.

But "no faster than light signalling" is preserved. Thus, if one names this "Einstein causality", we obtain the paradox that to preserve Einstein causality we have to reject causality.

 

[atyy]

I don't know what you mean by "classical probability". Quantum theory provides probabilities, which obey the usual axioms (Kolmogorov) of probability theory as long as you apply it to experiments that make sense within the quantum-theoretical framework.

The linked-cluster theorem, valid for local microcausal relativistic QFTs, guarantees Einstein causality, i.e., no faster-than-light propagation of information (I also don't understand what you mean by classical information; for me information is what an observer can know about a system given its state; this information can be complete (if the system is known to be prepared in a "pure state", i.e., the statistical operator is a projection operator) or incomplete (then we describe it by a statistical operator which is not a projection operator, i.e., a "mixed state").

In other words, for our example, the locality and microcausality guarantees that when A measures the polarization of her photon, A knows immediately that B must find the opposite polarization, but B can only know it by either measuring it himself or getting the information from A, which needs a signal that travels, according to the relativistic space-time structure, at most at the speed of light. A knows B's photon's polarization from her knowledge about the initial state of the biphotons ("polarization singlet") and her local measurement of her photon's polarization.

Good - why didn't you make this clear earlier - I have stressed repeatedly that in my definition Einstein causality is not "no faster than light transfer of classical information".

I'm pretty sure your definition is not EPR's, but it doesn't matter since that's debatable.

But there is still a problem - how does physical collapse violate your definition of Einstein causality?

 

[TrickyDicky]

So going back to the argument about collapse in QFT, my understanding is that in order to obtain finite results in renormalized perturbative QED calculations one must regularize, i.e. make the representation space provisionally discrete (finite number of degrees of freedom) until the proper limits are taken and continuous free fields are recovered.

 

[vanhees71]

Good - why didn't you make this clear earlier - I have stressed repeatedly that in my definition Einstein causality is not "no faster than light transfer of classical information".

I'm pretty sure your definition is not EPR's, but it doesn't matter since that's debatable.

But there is still a problem - how does physical collapse violate your definition of Einstein causality?

Collapse, in our example, would violate Einstein causality, because it claims that A's measurement is the cause of B's finding, and that's not the case. There is no causal connection between A's and B's measurements if the measurement events (the click of the photon detector after the polarization foil) are space-like separated by definition, because otherwise the relativistic space-time description would be flawed. It may well be that this is the case, and one needs a more refined space-time model, but at least these Bell experiments only provide a case for such a violation of Einstein causality, if you interpret the "collapse" as a cause for B's measurement. As I think, is pretty clear from the meaning of "states" in QT, that's not the case here, because the cause for the correlations is not A's measurement of her photon's polarization but it was inherent for the whole time due to the creation of the photon pair by parametric down conversion. Thus, although the single-photon polarizations are maximally uncertain (in the sense of von Neumann entropy) the 100% correlation between the outcome of A's and B's measurement is there from the very beginning. This is very unintuitive for our everyday-experience trained minds, but it's the only way to make relativistic QT consistent with the underlying space-time structure, which has proven very successful given the fact that a lot of the specific structure of relativistic QFTs follows from Poincare invariance (symmetry under proper orthochronous Poincare transformations), among other things the necessity for massless vector bosons to be described by gauge theories.

 

[zonde]

See this is why I dislike discussions about the foundations of QM, b/c it invariably goes in a circle and we end up redefining words. Post 102's definition of Einstein Causality, or Bell's local causality criteria given in the wiki article is a bit weasly. The problem, as correctly pointed out in 102, is that it presupposes notions of beables and classical probability theory. So I would call it Einstein Causality + classical concepts about what a state really *is* and how it is allowed to combine. Aspects experiment shows that this is wrong, but that just means that you have to give up one, but not necessarily both concepts.

Giving up beables and classical probability theory won't save you. You can check this by examining this informal proof of Bell inequality:
https://www.physicsforums.com/showthread.php?p=2817138#post2817138
It simply describes hypothetical but rather feasible experimental situation with a bit of "what if" type of reasoning.

 

[atyy]

Collapse, in our example, would violate Einstein causality, because it claims that A's measurement is the cause of B's finding, and that's not the case. There is no causal connection between A's and B's measurements if the measurement events (the click of the photon detector after the polarization foil) are space-like separated by definition, because otherwise the relativistic space-time description would be flawed. It may well be that this is the case, and one needs a more refined space-time model, but at least these Bell experiments only provide a case for such a violation of Einstein causality, if you interpret the "collapse" as a cause for B's measurement. As I think, is pretty clear from the meaning of "states" in QT, that's not the case here, because the cause for the correlations is not A's measurement of her photon's polarization but it was inherent for the whole time due to the creation of the photon pair by parametric down conversion. Thus, although the single-photon polarizations are maximally uncertain (in the sense of von Neumann entropy) the 100% correlation between the outcome of A's and B's measurement is there from the very beginning. This is very unintuitive for our everyday-experience trained minds, but it's the only way to make relativistic QT consistent with the underlying space-time structure, which has proven very successful given the fact that a lot of the specific structure of relativistic QFTs follows from Poincare invariance (symmetry under proper orthochronous Poincare transformations), among other things the necessity for massless vector bosons to be described by gauge theories.

So I think we still disagree. As far as I can tell, whether the collapse is physical or not, all predictions of the theory are the same - the only predictions are the measurement outcomes - those are the "classical outcomes" and the "classical information". If collapse is not physical, and there is no faster than light transmission of classical information, how can a physical collapse result in faster than light transmission of classical information, given that there is no difference in predictions whether collapse is physical or not?

 

[zonde]

There is no causal connection between A's and B's measurements if the measurement events (the click of the photon detector after the polarization foil) are space-like separated by definition, because otherwise the relativistic space-time description would be flawed. It may well be that this is the case, and one needs a more refined space-time model, but at least these Bell experiments only provide a case for such a violation of Einstein causality, if you interpret the "collapse" as a cause for B's measurement. As I think, is pretty clear from the meaning of "states" in QT, that's not the case here, because the cause for the correlations is not A's measurement of her photon's polarization but it was inherent for the whole time due to the creation of the photon pair by parametric down conversion. Thus, although the single-photon polarizations are maximally uncertain (in the sense of von Neumann entropy) the 100% correlation between the outcome of A's and B's measurement is there from the very beginning. This is very unintuitive for our everyday-experience trained minds, but it's the only way to make relativistic QT consistent with the underlying space-time structure, which has proven very successful given the fact that a lot of the specific structure of relativistic QFTs follows from Poincare invariance (symmetry under proper orthochronous Poincare transformations), among other things the necessity for massless vector bosons to be described by gauge theories.

But there is no way this type of reasoning can violate Bell inequality. You understand that, right? Or no?

 

[vanhees71]

So I think we still disagree. As far as I can tell, whether the collapse is physical or not, all predictions of the theory are the same - the only predictions are the measurement outcomes - those are the "classical outcomes" and the "classical information". If collapse is not physical, and there is no faster than light transmission of classical information, how can a physical collapse result in faster than light transmission of classical information, given that there is no difference in predictions whether collapse is physical or not?

Yes, simply leave out the collapse, and take what the formalism predicts, and everything is totally unproblematic. If the collapse is no physical process, then you don't need it!

 

[vanhees71]

But there is no way this type of reasoning can violate Bell inequality. You understand that, right? Or no?

Of course, if you adjust the filters at A's and B's place adequately, Bell's inequalities are violated. Also this is caused by the initial preparation of the biphoton and not by either A's or B's measurement. See here

https://en.wikipedia.org/wiki/Bell'...re_violated_by_quantum_mechanical_predictions

Instead of "electron" and "spin" you can read "photon" and "polarization". The math is precisely the same.

 

[zonde]

Of course, if you adjust the filters at A's and B's place adequately, Bell's inequalities are violated. Also this is caused by the initial preparation of the biphoton and not by either A's or B's measurement.

It's clear that QM predictions violate Bell's inequality. And no, you can't violate Bell's inequalities just by the initial preparation of the biphoton.

And again you can't violate Bell's inequality with this type of reasoning:

Thus, although the single-photon polarizations are maximally uncertain (in the sense of von Neumann entropy) the 100% correlation between the outcome of A's and B's measurement is there from the very beginning.

 

[vanhees71]

I don't understand this argument, because what's written in the above quoted Wikipedia article paragraph is calculated by taking the expectation values, defining the correlation measures that violate Bell's inequality, with respect to the singlet state $|\phi \rangle$, which is the one prepared in the very beginning (in our case of photons by parametric down conversion).

 

[zonde]

I don't understand this argument, because what's written in the above quoted Wikipedia article paragraph is calculated by taking the expectation values, defining the correlation measures that violate Bell's inequality, with respect to the singlet state $|\phi \rangle$, which is the one prepared in the very beginning (in our case of photons by parametric down conversion).

Well, take a look at his link that already gave in #220:
https://www.physicsforums.com/showthread.php?p=2817138#post2817138

 

[atyy]

Yes, simply leave out the collapse, and take what the formalism predicts, and everything is totally unproblematic. If the collapse is no physical process, then you don't need it!

Whether or not collapse is a physical process, the quantum formalism does have it.

But you still haven't shown that collapse as a physical process violates your definition of Einstein causality. How does physical collapse lead to faster than light signalling of classical information?

 

[TrickyDicky]

Whether or not collapse is a physical process, the quantum formalism does have it.

True. And therefore the solution must be formal, mathematical. Not metaphisical or interpretational.

 

[vanhees71]

It's purely interpretational. It's even not related to QT but to any probabilistic statement. For me, collapse has a very specific meaning and is part of the interpretation of some branch of the Copenhagen interpretations. It claims that, if I make a precise measurement of an observable on an system, its state instantaneously "collapses" to the corresponding eigenstate of the self-adjoint operator representing the observable. This implies that for a delocalized system something physical instantaneously changes everywhere due to a measurement through a local interaction of the system with the measurement apparatus, which clearly violates Einstein causality. There is no experimental hint whatsoever that this is true, and it is righteously crticized in the famous EPR paper. Now, nowhere in the formalism you need such an interpretation to apply it to real-world observations. I have this argumented repeate often enough in this thread, and can't say anything new about it. I think there's no doubt about the formalism and what's predicted.

 

[TrickyDicky]

It's purely interpretational. It's even not related to QT but to any probabilistic statement. For me, collapse has a very specific meaning and is part of the interpretation of some branch of the Copenhagen interpretations. It claims that, if I make a precise measurement of an observable on an system, its state instantaneously "collapses" to the corresponding eigenstate of the self-adjoint operator representing the observable. This implies that for a delocalized system something physical instantaneously changes everywhere due to a measurement through a local interaction of the system with the measurement apparatus, which clearly violates Einstein causality. There is no experimental hint whatsoever that this is true, and it is righteously crticized in the famous EPR paper. Now, nowhere in the formalism you need such an interpretation to apply it to real-world observations. I have this argumented repeate often enough in this thread, and can't say anything new about it. I think there's no doubt about the formalism and what's predicted.

Fair enough. But I think it is important to make explicit that the source of disagreement here lies in the refusal to make the distinction between Einstein causality and microcausality. The standard QFT textbooks fail to make this distinction so I can understand why for vanhees71 Einstein causality is microcausality and he can never admit its violation. And it is in his logic not to be willing to allow for the distinction between Einstein causality and microcausality, since atyy's notion of Einstein causality which IMO is equivalent to Bell's 1976 notion of "local causality" cannot be violated without breaking Poincare(proper orthochronous) invariance. This vanhees71 (nor most physicists) is not ready to dispose of, so it makes sense he is not willing to even make the distinction. The logic behind this is that there is no solid theory so far that combines loss of Poincare invariance with no ftl signaling.
But quantum experiments are obstinate and show local causality to be violated. Now local causality is a weaker notion than the more usual "local hidden variables" and cannot be separated into a local and a classical deterministic part like the latter giving the chance to save either locality or classical determinism and originating confusion and debate by conflating the word local in the first the second notions derived from the 1976 and the 1964 versions of Bell's theorem as explained in Wiseman's "The two Bell's theorems of John Bell" paper.

 

[atyy]

It's purely interpretational. It's even not related to QT but to any probabilistic statement. For me, collapse has a very specific meaning and is part of the interpretation of some branch of the Copenhagen interpretations. It claims that, if I make a precise measurement of an observable on an system, its state instantaneously "collapses" to the corresponding eigenstate of the self-adjoint operator representing the observable. This implies that for a delocalized system something physical instantaneously changes everywhere due to a measurement through a local interaction of the system with the measurement apparatus, which clearly violates Einstein causality. There is no experimental hint whatsoever that this is true, and it is righteously crticized in the famous EPR paper. Now, nowhere in the formalism you need such an interpretation to apply it to real-world observations. I have this argumented repeate often enough in this thread, and can't say anything new about it. I think there's no doubt about the formalism and what's predicted.

I don't believe you are being consistent in terminology. Your argument is wrong because you are switching back and forth between two different definitions of Einstein causality.

If you define (A) Einstein causality = no faster than light communication, then since physical collapse gives identical predictions to non-physical collapse, physical collapse also does not allow faster than light communication. Physical collapse does not violate this notion of Einstein causality, if it makes the same predictions as non-physical collapse. This notion of Einstein causality is what is used when people talk about spacelike-separated operators commuting.

If you define (B) Einstein causality = classical relativistic causality, then physical collapse clearly violates this. But the Bell theorem shows that any theory reproducing the predictions of quantum mechanics will violate classical relativistic causality, so whether collapse is physical or not is irrelevant, since classical relativistic causality is either empty or gone. Usually when people talk about EPR, this is the definition of Einstein causality they use.

When you say "It's purely interpretational", you are using definition (A), in which there are no differences in predictions. In this definition of Einstein causality, physical collapse does not violate it.

You are using definition (B) when you say "This implies that for a delocalized system something physical instantaneously changes everywhere due to a measurement through a local interaction of the system with the measurement apparatus, which clearly violates Einstein causality. There is no experimental hint whatsoever that this is true, and it is righteously crticized in the famous EPR paper." In this definition of Einstein causality, physical collapse does violate it, but so does non-physical collapse.

 

[zonde]

But quantum experiments are obstinate and show local causality to be violated.

No they don't. Or not yet, if you like it that way.

 

[TrickyDicky]

But can you clarify why the microcausality condition must be added separately then?

Just not to let this hanging here, it must be added obviously because of the Poincare group translations, I must have got fixated on the Lorentz group for some reason.

 

[TrickyDicky]

No they don't. Or not yet, if you like it that way.

Are you referring to the practical issue of loopholes or to something deeper?

 

[zonde]

Are you referring to the practical issue of loopholes or to something deeper?

Probably I am referring to the things that fall under your category of "practical issue of loopholes".
But the word "practical" is a bit confusing. While it is a practical issue to make loophole free experimental setup, loopholes themselves are not practical issues but rather placeholders for different possible fundamental phenomena like systematic effect of feedback or contextuality of measurement.