Realism from Locality? Bell's Theorem & Nonlocality in QM

[A. Neumaier]

Do you mean a single qubit or a system of two entangled qubits?

For a two-qubit system in the singlet state, the operator $Z_A \otimes I_B + I_A \otimes Z_B$, for example, has eigenvalue zero (i.e., the system is in an eigenstate of that operator with eigenvalue zero).

2 entangled qubits form a 4 state system.

 

[PeterDonis]

2 entangled qubits form a 4 state system.

Ok, so you meant a single qubit. But I think @ftr in the post you were responding to, #117, was talking about a 2-qubit system. Otherwise talking about anti-correlation as he did would make no sense; a single qubit can't be anticorrelated with itself.

 

[A. Neumaier]

Ok, so you meant a single qubit. But I think @ftr in the post you were responding to, #117, was talking about a 2-qubit system. Otherwise talking about anti-correlation as he did would make no sense; a single qubit can't be anticorrelated with itself.

Then I don't know what he means by my ''own account''.

 

[Demystifier]

That's the problem: Still in the 21st century many people, particularly philosophers, cannot accept the probabilistic and epistemic interpretation of the quantum state and then of course have a lot of troubles given the success of Q(F)T

They can accept its truth, but not its completeness. They want to know what happens behind the curtain.

On the other hand, those who are satisfied with the purely epistemic interpretation either
(i) don't care about things behind the curtain, or
(ii) care a little bit but don't think that it is a scientific question, or
(iii) claim that there is nothing behind the curtain at all.
Those in the category (i) have a mind of an engineer, which would be OK if they didn't claim that they are not engineers but scientists. Those in the category (ii) often hold double standards because in other matters (unrelated to quantum foundations) they often think that questions about things behind the curtain are scientific. Those in the category (iii) are simply dogmatic, which contradicts the very essence of scientific way of thinking.

 

[Demystifier]

While QFT in curved spacetime is really difficult to formulate and even more complicated to interpret

What is complicated to interpret about QFT in curved spacetime?

 

[vanhees71]

To say it clearer:
Regarding an entangled system in the singlet state: One might say that the perfect anti-correlations found at equal angles might be prescribed or imprinted by the preparation, but this cannot hold for the statistical correlations found at unequal angles; otherwise on should be able to present a corresponding statistical physical model.

The state (any state, i.e., pure or mixed, all described by statistical operators) describes the statistics about the outcome of measurements of all possible observables. You can freely choose the observables you want to measure, subject to what's possible to measure (i.e., all definable observables of the system).

Of course you can measure the polarization of one photon at an arbitrary angle (relative to some arbitrary direction in space) and that of the other one at another arbitrary angle. If the photons are polarization entangled, then you'll also find the correlations, which are not 100% anymore in general. That's also the way how the violation of Bell's inequality gets confirmed with overwhelming significance.

 

[vanhees71]

Yes, which means none of them are picked out as being preferred, which means you can't rely on "space" and "time" having a unique well-defined meaning. But in the original post I was responding to in this subthread (which was not yours, it was #83 by @akvadrako), the poster was making an argument that implicitly assumed that "space" and "time" do have a unique well-defined meaning (because it implicitly assumed that spacelike separated measurements have a well-defined ordering).

Of course, but that's also the case within classical relativistic physics. There's no problem whatsoever in this. I don't understand what your point is. In the real world experiments are defined by real-world experimental setups, and they are described in some (and thus also in any) frame of reference.

Of course space-like separated events do not have a frame-independent temporal ordering, and that's why within relativistic spacetime such events cannot be causally connected, and that's why one constructs local QFTs, i.e., QFTs which fulfill the microcausality principle. That's why I always insist on the fact that, as long as some experiment like all the beautiful quantum-optics experiments we are discussing here can be described by a local relativistic QFT there cannot be (by construction!) a contradiction to Einstein causality, i.e., if there are space-like separated measurement events (here clicks of a photo detector) they are not causing anything mutually to each other. This is demonstrated in many experiments today, where you can post-select subensembles with given properties by applying these properties in the selection process after the observable considered is measured (see the experiment with four photons by Jennewein et al in one of the other ongoing debates in this forum).

 

[vanhees71]

They can accept its truth, but not its completeness. They want to know what happens behind the curtain.

On the other hand, those who are satisfied with the purely epistemic interpretation either
(i) don't care about things behind the curtain, or
(ii) care a little bit but don't think that it is a scientific question, or
(iii) claim that there is nothing behind the curtain at all.
Those in the category (i) have a mind of an engineer, which would be OK if they didn't claim that they are not engineers but scientists. Those in the category (ii) often hold double standards because in other matters (unrelated to quantum foundations) they often think that questions about things behind the curtain are scientific. Those in the category (iii) are simply dogmatic, which contradicts the very essence of scientific way of thinking.

Well, I can easily accept the claim that QT or any other physical theory is (or may be as long as no empirical facts hint at it) is incomplete. I only deny the existence of problems which are not there. It's disadvantageous for the progress of science debating about pseudoproblems of little to no relevance. E.g., in connection with the foundations of QT it's quite true that "The Hippies Saved Physics" (referring to Kaiser's book), but they also endangered the entire business by invoking relations to esoterics.

Concerning your items above:

ad (i) There may be something behind the curtain, but from a scientific point of view there's not the slightest hint in connection with the here discussed (pseudo-)issues. If there's any hint, it's the lack of understanding of quantum gravity, but there's no hint within the realm of standard quantum physics, i.e., QM and relativistic QFT. I've no problem being called and engineer though I doubt that engineers would consider me being one ;-)).

ad (ii) and (iii) see (i).

 

[vanhees71]

What is complicated to interpret about QFT in curved spacetime?

E.g., start with the only apparently simple question what a particle might be. In special-relativistic (standard) QFT it's already a non-trivial thing, but you can define it thinking hard about the "asymptotic free states". In a general spacetime this recipe is usually not applicable. It's possible for some particularly simple space times of high symmetry (like (anti-)de Sitter spacetime), but not for the general case (and I'm only talking about QFTs in a given "background spacetime").

 

[Demystifier]

E.g., start with the only apparently simple question what a particle might be.

What about the answer that a particle is a click in a particle detector? This answer is widely (though not universally) accepted in the curved spacetime QFT community, and I would expect that you find such an answer satisfying.

 

[Demystifier]

I only deny the existence of problems which are not there.

Consider, for instance, the question how to make Bohmian mechanics compatible with relativistic QFT. Would you say that this problem exists or would you deny its existence?

 

[Demystifier]

I've no problem being called and engineer

OK, I'll keep it in mind.

 

[vanhees71]

What about the answer that a particle is a click in a particle detector? This answer is widely (though not universally) accepted in the curved spacetime QFT community, and I would expect that you find such an answer satisfying.

Yes, that's in fact a very nice definition. Of course you have to describe it somehow with the formalism. I don't know much about QFT in curved spacetime, but I had the impression that's a pretty tough subject when it comes to the physical interpretation.

 

[Demystifier]

Yes, that's in fact a very nice definition. Of course you have to describe it somehow with the formalism. I don't know much about QFT in curved spacetime, but I had the impression that's a pretty tough subject when it comes to the physical interpretation.

Its pretty tough only if one does not accept that there is nothing more about a particle than a click in a detector. And guess what, many experts in the field do not accept it.

 

[vanhees71]

Hm, do you have some paper about how to define particles as "clicks" in a detector in a curved spacetime?

Maybe, I'm willing to accept your definition so easily, because I'm pretty much a phenomenologist. In my field of research, relativistic heavy-ion collisions, we have no "Standard Model" though the HEP Standard Model is the "fundamental theory" we deal with, but it's more about many-body Standard Model than "vacuum QFT". So we cannot afford to ignore what's measureable and what the really observed phenomena are. In fact one of the most important tasks of us theorists in this field is to help the experimentalist to find the interesting observables to learn about strongly interacting matter!

 

[A. Neumaier]

What about the answer that a particle is a click in a particle detector?

Yes, that's in fact a very nice definition. Of course you have to describe it somehow with the formalism.

Its pretty tough only if one does not accept that there is nothing more about a particle than a click in a detector.

How do you prepare such a particle? How can a click have spin or mass?

 

[vanhees71]

Well, how do you measure spin and mass in practice? For spin there's the Stern-Gerlach experiment. At the end it's a "click" registering the "particle" at a certain place. From the position of the click you infer the value of the spin component (or more precisely the magnetic moment) you measure.

For mass, e.g., you measure energy and momentum of the particle and then use $E^2-p^2=m^2$. Also this is done by using a detector which clicks at a given position.

 

[A. Neumaier]

Well, how do you measure spin and mass in practice? For spin there's the Stern-Gerlach experiment. At the end it's a "click" registering the "particle" at a certain place. From the position of the click you infer the value of the spin component (or more precisely the magnetic moment) you measure.

For mass, e.g., you measure energy and momentum of the particle and then use $E^2-p^2=m^2$. Also this is done by using a detector which clicks at a given position.

But this does not give the click a mass, but the entity producing the clicks! This proves that a click is quite different from a particle.

 

[Demystifier]

Hm, do you have some paper about how to define particles as "clicks" in a detector in a curved spacetime?

https://arxiv.org/abs/0710.5671

 

[PeterDonis]

Of course space-like separated events do not have a frame-independent temporal ordering, and that's why within relativistic spacetime such events cannot be causally connected

No, that's why measurements at spacelike separated events must commute. But "must commute" is not the same as "cannot be causally connected". It means that if such events are causally connected, you can't specify which one comes first. That violates many people's intuition that causally connected events should have a definite ordering, with the "cause" coming before the "effect", but there is nothing in the physics that requires that to be the case. And if measurements at such events have correlations that violate the Bell inequalities, that certainly suggests that there is some kind of causal connection between them.

This is one of many examples where ordinary language is inadequate to describe what our physical theories and the math involved in them actually say.

 

[A. Neumaier]

if measurements at such events have correlations that violate the Bell inequalities, that certainly suggests that there is some kind of causal connection between them.

It makes it plausible but does not certainly suggest it. It may just mean that quantum causality is different from classical causality.

 

[Auto-Didact]

It makes it plausible but does not certainly suggest it. It may just mean that quantum causality is different from classical causality.

This might be a foreign/native speaker thing, but "certainly suggests" and "makes plausible" are synonymous FAPP.

 

[A. Neumaier]

This might be a foreign/native speaker thing, but "certainly suggests" and "makes plausible" are synonymous FAPP.

I'd say that "suggests" and "makes plausible" are synonymous. But there is nothing certain in a plausibility argument. The appropriate wording in the sentence would have been ''suggests to me'',
since plausibility is in the eye of the beholder.

 

[Lord Jestocost]

...there is nothing more about a particle than a click in a detector.

Reminds me somehow of the thoughts of Aage Bohr, Ben R. Mottelson and Ole Ulfbeck (The Principle Underlying Quantum Mechanics, Foundations of Physics, Vol. 34, 2004)

“A click entirely without a cause, and thus coming by itself, has the novel property of an onset, a beginning from which it develops. The onset, having no precursor, comes as a discontinuity in space and time and is, therefore, unanalyzable.”

 

[Lord Jestocost]

The state (any state, i.e., pure or mixed, all described by statistical operators) describes the statistics about the outcome of measurements of all possible observables.

A pure state allows to predict the “statistics” about the outcome of measurements of observables in question, but the “statistics” itself cannot be predicted by statistical physical models. The motivation behind the desire for an “ensemble interpretation” of quantum probabilities is a yearning for statistical physical models (not always acknowledged), where “classical randomness” is thought to be the cause for the statistics. Bell has shown that this yearning can never be fulfilled. Thus, one should never mix up the "minimal statistical interpretation" with "ensemble interpretations" as this is a fundamental misconception.

...as soon as you accept this minimal probabilistic/ensemble interpretation

Astonishing, that "minimal statistical" reads now "minimal probabilistic".

 

[ftr]

Then I don't know what he means by my ''own account''.

Again, maybe I am misunderstanding something, but I am just thinking about your TI for spin as in this link

https://www.physicsforums.com/threa...tation-of-quantum-physics.967116/post-6152810
So I am just wondering what could have been the "actual" spin of both entangled particles and how is it then that when MEASUREMENT was done then they perfectly anti correlated.

 

[vanhees71]

No, that's why measurements at spacelike separated events must commute. But "must commute" is not the same as "cannot be causally connected". It means that if such events are causally connected, you can't specify which one comes first. That violates many people's intuition that causally connected events should have a definite ordering, with the "cause" coming before the "effect", but there is nothing in the physics that requires that to be the case. And if measurements at such events have correlations that violate the Bell inequalities, that certainly suggests that there is some kind of causal connection between them.

This is one of many examples where ordinary language is inadequate to describe what our physical theories and the math involved in them actually say.

Hm, in my understanding, causality implies a specific time-ordering. In fact it's the only sense you can give to specific time-ordering, and thus causally connected events cannot be space-like separated. In other words event A can only be the cause of event B if it is time- or light-like separated from B and B is within or on the future light cone of A. It's not clear to me, how you define causality to begin with.

That said, the very point is that due to microcausality there is no cause-effect relation between space-like separated measurement events (like clicks of photo detectors in the here discussed experiments with entangled photons). The correlations are not caused by the measurements but are due to the correlation following from the preparation in an entangled state.

This doesn't necessarily imply that entanglement can only occur when the entangled parts of a system are causally connected, as the example of entanglement swapping show, as in the elsewhere discussed PRL 88, 017903 (2002) by Jennewein et al. In this case the entanglement is due to selection (or even post-selection!) of a subensemble out of an before (in the correct relativistic sense!) created system of two entangled (but not among them entangled) photon pairs. Note however that each of these pairs have been created in an entangled state by causal local interaction (SPDC of a laser photon in a BBO crystal).

 

[vanhees71]

A pure state allows to predict the “statistics” about the outcome of measurements of observables in question, but the “statistics” itself cannot be predicted by statistical physical models. The motivation behind the desire for an “ensemble interpretation” of quantum probabilities is a yearning for statistical physical models (not always acknowledged), where “classical randomness” is thought to be the cause for the statistics. Bell has shown that this yearning can never be fulfilled. Thus, one should never mix up the "minimal statistical interpretation" with "ensemble interpretations" as this is a fundamental misconception.
Astonishing, that "minimal statistical" reads now "minimal probabilistic".

Oh come on, statistical and probablistic is really synonymous if it comes to the application of probability theory to real-world problems, and QT is also a kind of probability theory.

Also the assignment of a mixed state to a situation (formally said a "preparation procedure") leads to the prediction of probabilities. E.g., the equilibrium state of a thermalized gas leads to the prediction of the velocity distribution of particles. BTW the corresponding Maxwell-Boltzmann distribution has been empirically violated by Otto Stern in Frankfurt in the 1920ies for the first time.

I always thought that "minimal statistical" and "ensemble" interpretations are just the name of the same interpretation. If not, what's the difference. Is this again one of these unnecessary confusions due to (unnecessary?) philosophical sophistry?

 

[ftr]

vanhees71, aren't you shooting superposition between the eyes.

 

[vanhees71]

So I am just wondering what could have been the "actual" spin of both entangled particles and how is it then that when MEASUREMENT was done then they perfectly anti correlated.

Good question. According to the usual (minimal) interpretation an "actual spin" (to be more precise an "actual spin component") either has a determined value or not due to the preparation of the corresponding system.

You cannot in all generality say in which state a system might be after a measurement. Maybe it's even destroyed (like photons hitting a photon detector). This depends on the specific measurement apparatus.

For the here obviously discussed example of the Stern-Gerlach experiment. The spin component given by the direction of the magnetic field is prepared in an (almost exact) pure state $|\text{up} \rangle$ or $|\text{down} \rangle$ due to the strict entanglement between position and this spin component after the silver atom has run through the magnet. This is the preparation process: You have a (utmost) completely determined value of the spin component just by looking at particles at the corresponding positions. That's the paradigmatic example for a preparation through (an almost ideal) von Neumann filter procedure (I don't like to call it measurement).

Of course, as soon as you measure the particle's position by letting it hit a photo plate or a CCD cam, it's gone. You cannot easily describe its (spin) state after that, but that's a trivial thought, I'd say.