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

[PeterDonis]

Bell non-locality doesn't mean that you can't calculate the future state using only local information.

What do you mean by "the future state"?

Suppose we have a system consisting of two particles which are entangled. Then neither particle has a definite state by itself; only the two-particle system does. If the particles are separated, there simply is no local state, so it can't be possible to calculate any future state using only local information. You can only calculate the future state of the two-particle system, which is inherently nonlocal. And making measurements on the particles will produce correlations that violate the Bell inequalities.

 

[PeterDonis]

We have a (at the practical level) consistent local theory of the electron field and the electromagnetic field. It is called QED.

This theory is "local" in the sense that operators at spacelike separated events commute. But I don't think that's the meaning of "local" that @akvadrako and @Heikki Tuuri are (implicitly) using.

 

[A. Neumaier]

This theory is "local" in the sense that operators at spacelike separated events commute. But I don't think that's the meaning of "local" that @akvadrako and @Heikki Tuuri are (implicitly) using.

I agree.

To calculate a property at a single spacetime position $x$ one needs the complete state information from a nonempty intersection of its past cone with a Cauchy surface. But in relativity theory, this is the only proper meaning of ''local''. More is not available and not needed.

 

[Heikki Tuuri]

We have a (at the practical level) consistent local theory of the electron field and the electromagnetic field. It is called QED. The electron is only an approximate, asymptotic concept in this theory.

QED is a perturbation method which can be used to calculate collisions of particles. It applies to very limited phenomena.

Classically, I imagine electrons as fishing floats on the waves of water. The correct future theory must handle the complicated interaction between the water and floats. The future theory is "local", though. We do not have any spooky action at a distance when we fish.

 

[PeterDonis]

To calculate a property at a single spacetime position $x$

But many things we are interested in when studying multi-particle quantum systems are not properties at a single spacetime position $x$.

We do not have any spooky action at a distance when we fish.

We do if the Bell inequalities are violated.

 

[A. Neumaier]

But many things we are interested in when studying multi-particle quantum systems are not properties at a single spacetime position $x$.

For predicting in quantum field theory properties of a whole region X in spacetime (whether distances, areas, volumes, or coincidence counts) one needs the complete state information from a nonempty intersection of the union of the past cones of X with a Cauchy surface. This extended locality is most likely a consequence of the local commutation relations, though I have not seen a proof. But it is what one expects from hyperbolicity and Lorentz covariance.

This is consistent with violations of Bell inequalities since the proofs of Bell inequalities (and its variations) make stronger locality assumptions. They ignore the nonlocal character of the property of being coincident.

 

[akvadrako]

What do you mean by "the future state"?

Suppose we have a system consisting of two particles which are entangled. Then neither particle has a definite state by itself; only the two-particle system does. If the particles are separated, there simply is no local state, so it can't be possible to calculate any future state using only local information. You can only calculate the future state of the two-particle system, which is inherently nonlocal. And making measurements on the particles will produce correlations that violate the Bell inequalities.

I mean state in a physical sense, not any specific representation, meaning all the information contained within the past light cone of some system. The best proof of the locality in general is this paper from David Deutsch, Vindication of Quantum Locality, a followup from a series of papers from 1999. But even more clearly, there are plenty of demonstrations of how Bell inequality violations and other quantum features can be reproduced with only casually local operations, meaning only systems (qubits) that interact affect each other. I have not found a paper showing an example of a quantum feature that can't be reproduced this way.

@DarMM has some good posts where he lays out all the ways that Bell non-locality doesn't imply dynamic non-locality. The way I think about it is Bell non-locality means that the state can't be factored into regions within a single spacetime. But it's easy enough to violate Bell inequalities with multiple outcomes which create new (local) worlds that later combine into the right ratios – I assume you have seen this.

 

[PeterDonis]

I mean state in a physical sense, not any specific representation, meaning all the information contained within the past light cone of some system.

And that's a perfectly good concept, but, again, it is a different interpretation of the word "local" (which is why @A. Neumaier used the term "extended locality").

only systems (qubits) that interact affect each other

And this requires a particular interpretation of "affect each other" that is not the only possible one.

IMO the best way to approach this is to use qualifiers, such as:

Bell non-locality doesn't imply dynamic non-locality

This makes it clearer what is being talked about: violations of the Bell inequalities, but no FTL signaling, for example.

 

[akvadrako]

And that's a perfectly good concept, but, again, it is a different interpretation of the word "local" (which is why @A. Neumaier used the term "extended locality").

I was just referring to the meaning of local in the post you replied to – that the "next step" can be computed using only local information – the information contained in that region. Of course the further forward you want to compute, the larger region you'll need to consider.

 

[DarMM]

@DarMM has some good posts where he lays out all the ways that Bell non-locality doesn't imply dynamic non-locality. The way I think about it is Bell non-locality means that the state can't be factored into regions within a single spacetime. But it's easy enough to violate Bell inequalities with multiple outcomes which create new (local) worlds that later combine into the right ratios – I assume you have seen this.

The way I think of it: Many Worlds is alocal (term borrowed from @Demystifier) at the ontological level since the universal wavefunction comes prior to Minkowski spacetime which is sort an emergent macroscopic structure. However it is operationally local.

Regarding the papers dealt with here, it is the statement following 3.2.2 in the 2018 paper that I think most would have an issue with:

Thus if we were to measure $\tilde{\mathcal{O}}$, obtaining $\lambda_l$, we would know that:
$\nu(\mathcal{O}) = \lambda_l$ (3.2.2)
concerning the result of then measuring $\mathcal{O}$. Thus $\nu(\mathcal{O})$ would pre-exist the measurement of $O$

It's a consequence of antirealism in views like Copenhagen that knowing what would happen if $\mathcal{O}$ were measured does not imply that $\mathcal{O}$ in fact has a value pre-existing the measurement. You simply know what that value would be if a $\mathcal{O}$ measurement were carried out. This is even borne out in the mathematics of QM in a standard Copenhagen reading. Only a combined set of measurements $\tilde{\mathcal{O}}$ and $\mathcal{O}$ form a complete context that allows you to use Gelfand's theorem and obtain a single sample space on which to perform reasoning like this implication.

"Unperformed experiments have no results" as Peres said.

Many-Worlds and retrocausal stuff can escape the theorem for separate reasons.

 

[PeterDonis]

the "next step" can be computed using only local information – the information contained in that region

And my point is that if the "region" in question includes spacelike separated measurements of entangled particles, this does not satisfy many people's intuitive notion of "local". It's "local" in the sense that everything can be computed in terms of the past light cone of the region as a whole, but that is not the same as the past light cone of either measurement event taken in isolation.

 

[Auto-Didact]

@DarMM has some good posts where he lays out all the ways that Bell non-locality doesn't imply dynamic non-locality. The way I think about it is Bell non-locality means that the state can't be factored into regions within a single spacetime. But it's easy enough to violate Bell inequalities with multiple outcomes which create new (local) worlds that later combine into the right ratios – I assume you have seen this.

And that's a perfectly good concept, but, again, it is a different interpretation of the word "local" (which is why @A. Neumaier used the term "extended locality").
...
This makes it clearer what is being talked about: violations of the Bell inequalities, but no FTL signaling, for example.

I was just referring to the meaning of local in the post you replied to – that the "next step" can be computed using only local information – the information contained in that region. Of course the further forward you want to compute, the larger region you'll need to consider.

And my point is that if the "region" in question includes spacelike separated measurements of entangled particles, this does not satisfy many people's intuitive notion of "local". It's "local" in the sense that everything can be computed in terms of the past light cone of the region as a whole, but that is not the same as the past light cone of either measurement event taken in isolation.

Since the issue of what exactly is meant by non-locality seems to continually get brought up again and again in this thread, yet still seemingly continues to be misunderstood, I would like to refer to this thread which gives a specific explicit mathematical model of non-locality and contextuality; the model was naturally constructed fairly recently by combining several branches of advanced pure mathematics in a very particular way.

There is a fairly strong argument to make that such a new first principles approach - based on combining and utilizing previously unused advanced mathematics - is precisely the type of mathematical theory as a new foundation which will be needed to literally go beyond QM, e.g. 1) to construct a relativistic version of Bohmian Mechanics based in novel mathematics, and 2) probably also to construct a proper theory of quantum gravity from first principles.

 

[akvadrako]

And my point is that if the "region" in question includes spacelike separated measurements of entangled particles, this does not satisfy many people's intuitive notion of "local". It's "local" in the sense that everything can be computed in terms of the past light cone of the region as a whole, but that is not the same as the past light cone of either measurement event taken in isolation.

I'm not sure if we disagree about the meaning of local or if MWI is local in that sense. In terms of measurements on separated entangled particles A & B, the regions would be around A and around B, taken in isolation. When a measurement happens on A the region splits into A1 and A2, but nothing happens to B – there is no splitting until something from region A interacts with region B. The behavior can be simulated on computers where region A is on Mars and B on Earth and they evolve independenly until you simulate when something from A interacts with something from B. That seems to me like quite a strong definition of locality.

 

[PeterDonis]

When a measurement happens on A the region splits into A1 and A2, but nothing happens to B – there is no splitting until something from region A interacts with region B.

I understand this is an intuitively plausible description of what is going on. But the problem with it is that the configuration space of the system is not ordinary 3-dimensional space, and the state of the system cannot be expressed as a function (even a complex-valued or vector-valued or other thingie-valued function) on ordinary 3-dimensional space. But your description implicitly assumes that it can.

In configuration space, the splitting occurs as soon as a measurement happens, and it splits the entire state--there is no "delay" while part of the state waits for information from the rest of the state. (More precisely, the two-particle system becomes entangled with the measuring apparatus, so it no longer has a definite state on its own; but if we restrict to looking at the portion of the overall state that is in the two-particle configuration space, it "splits" as soon as the entanglement happens.)

From a QFT viewpoint, there are no "particles" as continuous entities moving through space (or spacetime), and there is no "state" of a multi-particle system at a particular time (since "at a particular time" itself has no invariant meaning in relativity). There are just measurement events and correlations between them. That avoids the difficulty about "splitting" above and whether it is "nonlocal" or not, but it also removes the very basis for adopting the MWI in the first place, since the MWI's account assumes that there is a meaningful "state" of the two-particle system at a given time (or the two-particle system entangled with a measuring apparatus).

 

[edmund cavendish]

Is quantum entanglement spooky action at a distance? There seems to be an increasing amount of evidence to support it. Surely early two slit photon experiments at least prefigure the idea not even of measurement or even non measurement having an effect at a distance?

 

[vanhees71]

QED is a perturbation method which can be used to calculate collisions of particles. It applies to very limited phenomena.

Classically, I imagine electrons as fishing floats on the waves of water. The correct future theory must handle the complicated interaction between the water and floats. The future theory is "local", though. We do not have any spooky action at a distance when we fish.

That's a very limited view rather than a limitation of the theory. There's not only "vacuum QED" to calculate cross sections in two-body collisions as needed in accelerator experiments but you can also use the many-body formalism in thermal equilibrium as well as in general off-equilibrium situations to describe macroscopic electromagnetic phenomena in condensed-matter physics (non-relativistic realm) up to relativistic heavy-ion collisions (relativistic realm), though in the latter case the main theory needed is QCD rather than QED.

 

[vanhees71]

Is quantum entanglement spooky action at a distance? There seems to be an increasing amount of evidence to support it. Surely early two slit photon experiments at least prefigure the idea not even of measurement or even non measurement having an effect at a distance?

No, quantum entanglement is not "spookky actions at a distance". The usual and successful relativistic QFT are all of the local type, i.e., they obey the microcausality constraint, according to which local operators all commute at space-like separation of their arguments. A local measurement on one of, e.g., two entangled photons at Alice's place cannot in any way causally affect the photon at Bob's far distant place. Still the entanglement describes a strong correlation between the two photons, but it's a correlation imprinted on the photon pair by its preparation and not a causal effect of A's measurement on B's photon (or vice versa).

 

[vanhees71]

I understand this is an intuitively plausible description of what is going on. But the problem with it is that the configuration space of the system is not ordinary 3-dimensional space, and the state of the system cannot be expressed as a function (even a complex-valued or vector-valued or other thingie-valued function) on ordinary 3-dimensional space. But your description implicitly assumes that it can.

This is also no conceptual problem since the experimental setup is defined in some reference frame (say, the "lab frame"), and there you have a well-defined split in "time" and "space". Of course, due to Poincare invariance of relativistic QFT you can formulate everything in a Poincare-invariant way and describe the situation in any reference frame you like.

 

[Lord Jestocost]

...but it's a correlation imprinted on the photon pair by its preparation

Vague terminology! The anti-correlation is prescribed by the preparation process, nothing else.

 

[Lord Jestocost]

Is quantum entanglement spooky action at a distance?

No!

"The correlations between entangled particles in quantum mechanics can be said to “violate causality” in the sense that distant correlations arise with no local cause, i.e., no common cause (hidden variables) and no transfer of energy or information between the separate events. "

https://www.mathpages.com/home/kmath731/kmath731.htm

 

[A. Neumaier]

The correlations between entangled particles in quantum mechanics can be said to “violate causality” in the sense that distant correlations arise with no local cause, i.e., no common cause (hidden variables) and no transfer of energy or information between the separate events. "

The preparation of the entangled state is done locally, hence is a local cause.

Violated is only classical local causality (no common classical cause), since the arguments in the proof of the violated inequalities are based on classical concepts.

 

[vanhees71]

Vague terminology! The anti-correlation is prescribed by the preparation process, nothing else.

Yes, that's what I said.

 

[akvadrako]

In configuration space, the splitting occurs as soon as a measurement happens, and it splits the entire state--there is no "delay" while part of the state waits for information from the rest of the state.

I realize that's one way of describing it where the locality is difficult to see, but it's not the only way. And the existence of one local description is sufficient to qualify an experiment as local. See for example Quantum nonlocality does not exist. The splits happen locally and only spread via interactions. They act like labels which determine the probability of different observers interacting. You can model a measurement like this:

1. Create an entangled pair $A$ / $B$ and send to distance regions with observers $O_A$ / $O_B$.
2. In region $A$ measure and locally split into $O_{A\uparrow} + O_{A\downarrow}$
3. In region $B$ measure and locally split into $O_{B\uparrow} + O_{B\downarrow}$
4. Observers come together in a central region and merge into $O_{A\uparrow} O_{B\uparrow} + O_{A\downarrow} O_{B\downarrow}$.

Everything in the above model is described locally.

since the MWI's account assumes that there is a meaningful "state" of the two-particle system at a given time (or the two-particle system entangled with a measuring apparatus).

Though I only have some understanding of the non-relativistic case, I think it's sufficient to show that it's possible to do things like violate Bell inequalities without non-locality. Yet there doesn't seem to be any reason MWI doesn't also work in the relativistic case. For example, see Observers and Locality in Everett Quantum Field Theory.

 

[Tendex]

Vague terminology! The anti-correlation is prescribed by the preparation process, nothing else.

How calling it prescribed instead of imprinted by preparation makes any difference here beats me.

 

[vanhees71]

The preparation of the entangled state is done locally, hence is a local cause.

Violated is only classical local causality (no common classical cause), since the arguments in the proof of the violated inequalities are based on classical concepts.

Yes indeed, but there's also "entanglement swapping", where you get entanglement between photons that have never locally interacted. Of course, it's no violation of Einstein causality either. It's just using the entanglement of each of two photon pairs locally measuring a pair of photons consisting of one photon from each of the previous pairs. So finally indeed also there the entanglement can be traced back to the local interactions preparing the original 4-photon state. There's no way out of this conclusion as long as you argue within standard QED, which obeys the microcausality constraint by construction.

 

[Lord Jestocost]

The preparation of the entangled state is done locally, hence is a local cause.

Violated is only classical local causality (no common classical cause), since the arguments in the proof of the violated inequalities are based on classical concepts.

A “local cause” for what? That the preparation can be thought to be the “cause” for the outcomes of measurements on entangled systems?

“Cause” is a classical notion and cannot arbitrarily be re-defined; it has an unambiguous meaning:

There exist “causes” that determine measurement outcomes, or probabilities of outcomes, for all possible experiments that could be performed on an individual system, no matter whether any experiment — and which experiment — is actually performed (and so, in this sense, would be “real”).
Caslav Brukner in “Elegance and Enigma: The Quantum Interviews” (ed. by Maximilian Schlosshauer)

The assumption that the preparation might be the “cause” for the outcomes of measurements on entangled systems in the singlet state might indeed account for the perfect anti-correlation at equal angles, but it is provably incompatible with the correlations at unequal angles, so it is ruled out. Measurement outcomes are irreducibly probabilistic, there is no place for "causes".

 

[A. Neumaier]

A “local cause” for what? That the preparation can be thought to be the “cause” for the outcomes of measurements on entangled systems?

The preparation is the local cause for the later statistical correlations of measurements.

“Cause” is a classical notion and cannot arbitrarily be re-defined; it has an unambiguous meaning:

There exist “causes” that determine measurement outcomes, or probabilities of outcomes, for all possible experiments that could be performed on an individual system, no matter whether any experiment — and which experiment — is actually performed (and so, in this sense, would be “real”).
Caslav Brukner in “Elegance and Enigma: The Quantum Interviews” (ed. by Maximilian Schlosshauer)

If cause were a classical notion it wouldn't apply to quantum systems.

But there is no question that the probability of paired outcomes of measurements on pairs of entangled photons is fully determined (and fully controllable, hence causally determined) by the preparation and every anticipated measurement setting. The experiments done confirm this.

Only the individual results aren't fully determined.

 

[Tendex]

A “local cause” for what? That the preparation can be thought to be the “cause” for the outcomes of measurements on entangled systems?

The "cause" in the purely operational and almost trivial sense, if you are at least accepting the concept of ensemble in quantum physics, of putting a certain system in a specific state, doing a generally complex set of operations depending on the specific experiment, many quite contrived, and having as outcome the statistics predicted by quantum mechanics, intead of the classical ones. I can't fathom what's wrong with this.

Measurement outcomes are irreducibly probabilistic, there is no place for "causes".

Exactly, so why frame these discussions in terms of "causes" linking "spookily" certain measurements to certain outcomes with spacelike separation when SR tells us this is not possible?

 

[vanhees71]

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 in contradistinction to the failure of local "realistic" hidden-variable models, but that's an empirical fact. Relativstic QFT is both completely consistent with (special-)relativistic causality and the non-local correlations described by entanglement, as soon as you accept this minimal probabilistic/ensemble interpretation. Also the information-theoretical approach is all too often neglected. So there's no wonder why there are still all these debates even ~30 years after the confirmation of QT against LHV theories.

Of course science (and technology) go on. Today it's not a question anymore that entanglement is a phenomenon in nature but it's just used in upcoming modern technology.

 

[Jimster41]

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 in contradistinction to the failure of local "realistic" hidden-variable models, but that's an empirical fact. Relativstic QFT is both completely consistent with (special-)relativistic causality and the non-local correlations described by entanglement, as soon as you accept this minimal probabilistic/ensemble interpretation.

But what causes the variance - and why that specific structured variance and not another? I don't think it's a shame on philosophy to say it has difficulty accepting - "it's just statistical". Maybe, to many of your points in other threads, the ensemble approach is the best model so far. But do we know for sure that the wave function is the absolute best representation of that ensemble? I mean maybe a multi-fractal network representation or some other iterated non-linear model could provide interesting insight into the in-determinism (over some future causal horizon) that smooth wave-function doesn't - maybe something there can let us get deep multi-body GR nailed down better. I mean isn't that the promise of the Bhomian approach - that if we could tune into how the "Pilot Wave" works we might have you know - more determinism. That sounds so religious... I know. It's totally not. How about "a more detailed map of the Cauchy surface"

I read some sci-fi a long time ago that planted the idea in my head of using "Pilot Wave Interference" or "energy songs" - the "notes" of which are exceedingly specific to manipulate gravitational (space-time) curvature - so boats can fly, etc. I liked that idea a lot.

 

[Lord Jestocost]

...if you are at least accepting the concept of ensemble in quantum physics,...

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

N. David Mermin in “The Ithaca interpretation of quantum mechanics”

“For the notion that probabilistic theories must be about ensembles implicitly assumes that probability is about ignorance. (The "hidden variables" are whatever it is that we are ignorant of.) But in a non-deterministic world probability has nothing to do with incomplete knowledge, and ought not to require an ensemble of systems for its interpretation.”

 

[Tendex]

N. David Mermin in “The Ithaca interpretation of quantum mechanics”

“For the notion that probabilistic theories must be about ensembles implicitly assumes that probability is about ignorance. (The "hidden variables" are whatever it is that we are ignorant of.) But in a non-deterministic world probability has nothing to do with incomplete knowledge, and ought not to require an ensemble of systems for its interpretation.”

Accepting the concept of ensemble is different from commiting to a certain interpretation be it the minimal or any other, it's just admitting the statistical terms in which the theory is presented, so I don't know why you mix those up other than because the word ensemble is mentioned in both.

 

[Auto-Didact]

I realize that's one way of describing it where the locality is difficult to see, but it's not the only way. And the existence of one local description is sufficient to qualify an experiment as local. See for example Quantum nonlocality does not exist.

This article by Tipler is thoroughly confused: he is explicitly invoking Bohmian mechanics in equations 14 - 17 to make his argument. Moreover, Tipler reifies configuration space as a collection of actual worlds which he calls the multiverse instead of viewing configuration space in its traditional role, after which he then even goes on to use a Bayesian scheme to reinterpret Born's rule. This is a nice fiction, but nothing more; this is actually what amateur work in foundations research looks like.

The only good part is that Tipler historically recapitulates the primary status of Bayesian probability theory over frequentist probability theory, by describing that probability theory as invented by Laplace was actually inherently Bayesian until Quetelet introduced a wrong new interpretation. Unfortunately the young Maxwell was influenced by Quetelet, going on to use Quetelet's interpretation in statistical physics, directly causing the standard interpretation of probability to become the dominant frequentist view we have to this very day.

 

[akvadrako]

This article by Tipler is thoroughly confused: he is explicitly invoking Bohmian mechanics in equations 14 - 17 to make his argument.

Thanks for your review. I was trying to select the most focused paper to demonstrate the way local splitting works; next time I'll pick a different one. I was only talking about the initial part though; nothing past equation 11.

 

[edmund cavendish]

Even if entanglement is " done locally" the point I think is that the "effect" of one entangled photon on the other occurs at a speed faster than the speed of light hence must be non local. This also raises issues about collapse or not of the wave function since quantum entanglement allows for non observer driven outcomes. Really enjoying the thread.