A Quantum nonlocality and "spooky action at a distance"

[Morbert]

From propositional logic and the belief that statements are either true, false or some third undetermined value, I simply mean that reality is the statements (of all possible statements) that are true.
For me that is independent of being observed, measured or anything. They're true or they are not true. If that cannot work in our model of nature, quantum physics has left the foundation of logic and is therefore not anymore an exact science.

This idea (which sounds a bit like Wittgenstein's declaration "The world is all that is the case") is intuitive enough in a classical setting, but issues arise in a quantum setting.

Given some classical system, we can construct some maximally fine-grained structure of propositions about the system, and assign probabilities to the propositions based on what we know about the system.

Given some quantum system, we can construct multiple maximally fine-grained structures of propositions, each internally consistent, but mutually incompatible with one another. If reality is accounted for by some set of propositions about it, then it raises the question: from which of these internally consistent, mutually incompatible, unprivileged structures do we construct our set of propositions?

 

[Structure seeker]

Can you give an example, @Morbert ?

 

[gentzen]

I realize that is off topic but what is his approach? What are the hidden variables?

He uses the names q-expectation and q-correlation for the formal expectations and correlations of the mathematical model, in order to have a clear separation between statements about the mathematical model, and statements about the physical world. For QM, he considers q-expectations as functions of time t, for QFT he considers q-expectation as functions of spacetime (t,x,y,z) and q-correlations as functions of multiple spacetime points (t1, x1, y1, z1), (t2, x2, y2, z2), ... Then he takes for example those q-expectations for which the low frequency components (spatial or temporal, or both, as is most reasonable for the given model) should basically be measurable (in practice), and declares their high frequency components (i.e. those beyond the reach of actually conceivable measurement devices) as hidden variables. And similar for q-correlations where some low order correlation for close spacetime points should basically be measurable, declares their far distant, or higher order correlations, or high frequency parts (i.e. those beyond the reach of actually conceivable measurement devices) as hidden variables.

More abstractly, his HV hidden in plain sight are those "variables" which are obviously part of the mathematical model, and which "the mathematical model itself cannot simply exclude from being measurable", but which are impossible to measure in the physical world for all practical purposes.

 

[vanhees71]

This idea (which sounds a bit like Wittgenstein's declaration "The world is all that is the case") is intuitive enough in a classical setting, but issues arise in a quantum setting.

Given some classical system, we can construct some maximally fine-grained structure of propositions about the system, and assign probabilities to the propositions based on what we know about the system.

Given some quantum system, we can construct multiple maximally fine-grained structures of propositions, each internally consistent, but mutually incompatible with one another. If reality is accounted for by some set of propositions about it, then it raises the question: from which of these internally consistent, mutually incompatible, unprivileged structures do we construct our set of propositions?

I'd say that a system is completely determined if it is prepared in a pure state $\hat{\rho}=|\psi \rangle \langle \psi|$ with $\langle \psi|\psi \rangle=1$. This can be achieved, e.g., by a von Neumann filter measurement of a complete set of compatible observables. Then $|\psi \rangle$ is defined up to a phase (i.e., the state is uniquely defined) as the common eigenvector of the corresponding self-adjoint operators representing these observables.

This is also "complete information" in the sense of the von-Neumann entropy
$$S=-\text{Tr} (\hat{\rho} \ln \hat{\rho}).$$
Which is $S=0$ for a pure state.

 

[Morbert]

Can you give an example, @Morbert ?

Consider a photon. We can construct fine-grained propositions about the linear polarization of the photon, and build a boolean algebra from these propositions. We can also construct fine-grained propositions about the circular polarization of the photon, and build a boolean algebra from these propositions. But we cannot combine these propositions into a single boolean algebra.

One tactic for dealing with this multiplicity of algebras is to abandon realism: We no longer seek accounts for isolated microscopic systems, and we only concern ourselves with classical data produced by measurements on microscopic system. With this approach, the experimenter can simply select whichever algebra is most suitable for their experiment.

 

[PeterDonis]

From propositional logic and the belief that statements are either true, false or some third undetermined value

Propositional logic has no third value. Statements are either true or false. We might not know which value a particular statement has, but that doesn't mean it has some third value; it just means our knowledge of the truth values of statements is a separate thing from the truth values themselves.

Whether such propositional logic is applicable to QM is a different question. There is a whole literature on quantum logic which suggests that it is not.

Again, you should not be making this up on your own. You should be looking at the literature. Personal speculations are off limits here.

 

[PeterDonis]

For me "reality" are the objective observations we make in Nature.

Is this how "realism" is defined in the QM literature?

 

[gentzen]

From propositional logic and the belief that statements are either true, false or some third undetermined value

Propositional logic has no third value. Statements are either true or false.

This is actually an important distinction between a theory and a model (for propositional logic, and also for predicate logic): For a model, statements are either true or false. For a theory, there can also be statements about which the theory stays silent.

 

[vanhees71]

Is this how "realism" is defined in the QM literature?

I don't know, how "realism" is defined in the QM literature, because it has quite varying meaning.

I think in most contexts it means the assumption that all observables always take determined values, no matter whether they are known due to the information about the system or not. That's the case in classical statistical mechanics, i.e., in a many-body system all (point) particles always have determined positions and momenta, but we cannot know them due to the complexity of the system and thus we describe them by (single-particle or in some cases also two- and few-particle) phase-space distribution functions. Here the probabilistic nature of the description is only due to the lack of information due to the complexity of the situation but not inherent in the underlying classical theory ("point-particle mechanics").

In QT, in the standard minimal statistical interpretation, however observables only take determined values, if the system is prepared in a corresponding state. Even being "completely prepared", i.e., being prepared in a pure state, does not imply that all observables take determined values, and this is a inherent property of Nature and not just due to the lack of our knowledge about the minute microscopic details.

That, however, seems not to be the generally accepted meaning, and it's even not so easy to decide, whether this really is the meaning intended by Bell, when he talks about "realistic, local theories", but I understand it as such, at least in his seminal paper.

 

[PeterDonis]

I don't know, how "realism" is defined in the QM literature, because it has quite varying meaning.

Then we shouldn't be using terms like "reality" in this thread at all, since we don't have a good basis for assigning them a useful meaning.

 

[GarberMoisha]

I will give it a try.
Reality is quantum fields - the rock bottom of fundamental "stuff" that everything is made of.
Quantum fields are mathematical.
It is astonishing we are able to discover the code that everything runs on. This code is the laws of physics, which are mathematical.
Math is the language of reality and its essence. The ground of being.

 

[Structure seeker]

We can construct fine-grained propositions about the linear polarization of the photon, and build a boolean algebra from these propositions. We can also construct fine-grained propositions about the circular polarization of the photon, and build a boolean algebra from these propositions. But we cannot combine these propositions into a single boolean algebra.

Circular and linear polarization are both limiting values of elliptical polarization, according to https://en.m.wikipedia.org/wiki/Elliptical_polarization. Does that resolve the issue?

In general, superposition of states doesn't mean state A and B at the same time. That assumes a classical reality in a quantum setting, which doesn't work. A superposed (non-pure) state is a defined quantum state (including the phases of the summand pure states). The statement that it has exactly this superposed state is true, all other values for the state (including A and B) are false.

 

[vanhees71]

Then we shouldn't be using terms like "reality" in this thread at all, since we don't have a good basis for assigning them a useful meaning.

Exactly! As with "locality/non-locality" one has to clearly state what you mean by the term, because it's no longer well-defined as a common scientific term at all. Perferrably you define it in well defined mathmematics.

 

[PeterDonis]

A superposed (non-pure) state

This is not correct. A pure state can be a superposed state. Superposition is basis dependent. For example, the pure state "spin-z up" of a qubit can also be written as a superposition of "spin-x up" and "spin-x down".

 

[PeterDonis]

I will give it a try.

Please don't. As I have already pointed out in response to others, you should not be making up your own definition of "reality". Either find a paper in the literature that gives a definition generally accepted in the appropriate physics community, and use that, or refrain from using the word at all.

 

[Structure seeker]

For example, the pure state "spin-z up" of a qubit can also be written as a superposition of "spin-x up" and "spin-x down".

True, I assumed orthogonal basis states A and B. Superposition is basis-dependent indeed.

 

[kered rettop]

And violating a Bell inequality means local noncontextual theories are ruled out. There is nothing to debate about this point, it’s been standard science for nearly a half century.

Why would we try to convince people to reject the very thing Einstein called “spooky action at a distance”? He knew full well what that meant, and that if the EPR argument was wrong (as Bell later proved) that would be what we would be left with.

So why wouldn’t we simply point folks to the preferred PF term? Rather than persuading them that nothing is going on, when obviously something is. Either: the quantum context is nonlocal; or there is nonlocal action. That’s Bell, plain and simple. And that what Quantum Nonlocality is.

I provided references saying exactly this. No one can provide a single reference to the contrary. Weihs et al 1998, Violation of Bell’s Inequality Under Strict Einsteinian Locality Conditions… and so on. There’s nothing to interpret on this point.

It seems to me that in reality: for many here, their preferred interpretation actually denies the Bell result, I.e. that they actually believe we live in a local realistic world. It’s that point of view that should be called out clearly - instead of trying to talk posters into denial of the extremely sophisticated experiments being performed that show that Einsteinian locality is not respected. Again, hundreds of papers back up that position. And none say otherwise. If we call ourselves scientists, why back away from published conclusions?

About 10 years after I graduated, I wasted a long time trying to devise a local realistic model to replicate the EPR correlations! Alas, I had not realised that achieving full correlation when using parallel detectors - and zero correlation when crossed - was not sufficient. And I have seen lecturers at prestigious universities make the same mistake. I blame all those "left and right glove" analogies, which can only replicate locally real theories, thereby creating the impression that there is nothing odd happening!

 

[Morbert]

I don't know, what Bell means by "locality".

From La nouvelle cuisine: A sketch of spacetime regions 1 and 2, with corresponding past light cones.

Bell says a theory is causally local if there is some sufficient specification of events at 3, such that a measurement at 2 can not give us any new information about events at 1.

For me locality is the assumption of QFT that we describe everything with a Hamilton density consisting of field operators at the same space-time point, have the usual local realization of the Poincare group on the field operators, and that self-adjoint operators representing local observables (like the em. energy-momentum tensor, which contains the description of photon detection, using the usual dipole approximation) obey the microcausality constraints.

Bell's motivation:

Ordinary ‘local’ quantum field theory does have a causal structure. As everyone knows [...] Could the no-superluminal-signalling of ‘local’ quantum field theory be regarded as an adequate formulation of the fundamental causal structure of physical theory? I do not think so. For although ‘local commutativity’ has a nice sharp-looking mathematical appearance, the concepts involved in relating it to causal structure are not very satisfactory

There are possible responses to Bell here, but the important point is the site of disagreement is over the adequacy of the microcausality constraint in accounting for the causal structure of a theory, rather than the mere stipulation of a condition itself.

[edit to add] - I also suspect a statistical interpretation would itself be interpreted as a refusal to grapple with the issue Bell raises, rather than a solution to it. If a quantum theory is a theory of ensembles, then it does not address the causal relations between individual events.

 

[vanhees71]

My problem with these statement by Bell is that it is not clear, what he really means. In standard local QFT the Hamiltonian is given by a Hamiltonian density, obeying the microcausality condition with all operators representing local observables (including itself, representing energy density, which also makes it unique for gauge theories, where you have to use the gauge-invariant/covariant Belinfante energy-momentum tensor). This implies that there are no causal influences on any local observables over space-like separated distances. That's a mathematical fact and establishs a causality structure. I don't know, which problem Bell is addressing. From an earlier discussion I think to have understood that Bell rightfully stresses the importance of gauge-in/covariance and then calls observable beables, as if renaming things with funny sounding new word creations would solve any problems.

 

[ESponge2000]

I think there could be non-local “conditional” hidden variables in a quantum system (2 entangled particles are of 1 quantum system)

Assume particle A and particle B are entangled to each other from a common origin:
Governing a particular quantum system in question:
“Conditional hidden variables” ——if/then: among many if/thens:
If particle A is measured using method X and property Y at location 1, And particle B is measured also using method X and property Y at location 2, Then particle A will show + And particle B will show - “ , and where changes in method of measurement at either of the 2 locations can each, until collapse of the wave, single-handedly alter the would-be values, though not the measuring method-driven correlations and their associated probabilities between, for both particles A and B, in a new formula, unique to each quantum system, when method of measurement is no longer X, and where certain methods hold weaker correlation success probabilities vs method X which denotes where opposite correlations are 100% probable

This kind of non-local hidden variable theory could still be possible, or not?


I believe what Bell disproved being true was strictly these 2 cases I’ll denote below:
Governing a particular quantum system in question:

-Disproven by Bell- (2 cases)
Disproven Case 1:
“if particle A is measured at location 1 using property Y, particle A will definitively show “+” and if “particle B is measured at location 2 using Property Y, particle B will definitively show “-“ …
This case not accounting for the method of measurement of particle A at measurement affecting the outcome of both particle A and particle B

Disproven Case 2 - this is the one Einstein I think would have speculated to be true in his lifetime
If particle A is measured using method X and property Y at location 1, there will be a definitive result for particle A resulting from the method X and property Y unique to that quantum system by its design, independent of the conditions affecting Particle B altogether, unique to its design

As these 2 cases if true would have in the Bell experiment shown that the correlations match the independent probability sets rather than the ones Quantum mechanics predicted

(The key here is Bell’s tests must have shown that if a measuring method is changed for measuring particle A, it’s not a change in the correlation to particle B ONLY because the value of A was modified (while B’s would have stayed what it would have been if A did the other method) - if that were true the probabilities in Bell’s tests would still have matched the Einstein hidden variables theory predictions
……
but rather it’s a change in the value at B compared AS WELL to what it “would have been” if predicated on a change in the measuring method ONLY at A!)

 

[Nugatory]

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