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

[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.

 

[Auto-Didact]

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.

The point is though that his entire argument that non-locality doesn't exist is based on assuming the validity of Bohmian mechanics, which is an explicitly non-local theory. Carrying out this argument as a logical derivation therefore leads to a contradiction and so quite ironically actually proves that non-locality does exist.

Moreover, Tipler despite being a serious physicist with a professorship is a known crackpot, with his work on theological physics rivalling only Polkinghorne. This just goes to show that even the best pedigree in physics means almost nothing.

 

[Lord Jestocost]

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

No problem with this statement. More or less what the minimal statistical interpretation - if correctly understood – says: The square amplitude of the wave function is the probability that certain statistical correlations will be found if corresponding measurements are made on entangled quantum systems.

Thinking of the post-measurement situation in a statistical way, however, doesn’t allow to infuse statistical considerations into the thinking of the pre-measurement situation: “The deeper reason for the circumstance that the wave function cannot correspond to any statistical collective lies in the fact that the concept of the wave function belongs to the potentially possible (to experiments not yet performed), while the concept of the statistical collective belongs to the accomplished (to the results of experiments already carried out).”(V. A. Fock)

A collective of identically prepared entangled quantum systems can thus not be understood as a “statistical collective”; that’s what has been unambiguously proven by Bell. The term “ensemble” denotes a “statistical collective“; otherwise, no physicist would use this term as it is connoted to the “Gibbs ensemble” reasoning. Thus, any ensemble interpretation is nonsensical when viewed from the standpoint of Bell’s proof.

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.

Where is the corresponding deterministic physical model which proves this statement?

 

[PeterDonis]

the experimental setup is defined in some reference frame (say, the "lab frame")

If every single piece of experimental apparatus is at rest relative to every other piece, then yes, one can pick out a "lab frame" that is picked out in some meaningful physical way. But if Alice and Bob are on spaceships light-years apart, with curved spacetime in between so there isn't even an invariant notion of them being "at rest" relative to one another, let alone a global reference frame covering both of them with the properties that would be required, QM still predicts the same Bell inequality violating correlations. So I don't think the statement you make here is a valid one to rely on.

 

[PeterDonis]

The preparation of the entangled state is done locally

Not necessarily; in entanglement swapping experiments, qubits can be entangled that have never encountered each other locally.

 

[PeterDonis]

See for example Quantum nonlocality does not exist. The splits happen locally and only spread via interactions.

If the MWI is true and the rest of Tipler's reasoning is valid. I haven't reviewed the paper and Tipler has published some other rather outlandish claims. But in any case, his claim is certainly interpretation dependent since it requires the MWI to be true.

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.

I'll take a look. But once again, showing that MWI -> locality is not the same as showing that QM -> locality. MWI is only one interpretation of QM.

 

[vanhees71]

If every single piece of experimental apparatus is at rest relative to every other piece, then yes, one can pick out a "lab frame" that is picked out in some meaningful physical way. But if Alice and Bob are on spaceships light-years apart, with curved spacetime in between so there isn't even an invariant notion of them being "at rest" relative to one another, let alone a global reference frame covering both of them with the properties that would be required, QM still predicts the same Bell inequality violating correlations. So I don't think the statement you make here is a valid one to rely on.

While QFT in curved spacetime is really difficult to formulate and even more complicated to interpret, that's not the case for special relativistic QFT. You can describd an experiment in any given reference frame. If Alice and Bob are in relative motion to each other, just choose thd restframe of either one. Where should there be a problem with a Poincare-covariant theory? Do you have an example, where problems occur?

 

[Lord Jestocost]

it's just admitting the statistical terms in which the theory is presented,

See comment #107

 

[Tendex]

See comment #107

Do you mean mixed states shouldn't be part of quantum mechanics?

 

[Lord Jestocost]

Yes, that's what I said.

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

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.

 

[Lord Jestocost]

Do you mean mixed states shouldn't be part of quantum mechanics?

What the heck has this question to do with my comment #107?

 

[PeterDonis]

You can describd an experiment in any given reference frame.

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).

 

[ftr]

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

But isn't by your own account that the spin EV is zero, so then how does measurement grantees anti-correlation? Maybe I misunderstood something.

 

[A. Neumaier]

Not necessarily; in entanglement swapping experiments, qubits can be entangled that have never encountered each other locally.

The entanglement swapping is just a second local cause for correlations that needs to be taken into account in the causal analysis.

 

[A. Neumaier]

But isn't by your own account that the spin EV is zero, so then how does measurement grantees anti-correlation? Maybe I misunderstood something.

Spin eigenvalues of a 2 state system cannot be zero. You confuse it with the q-expectation.

 

[PeterDonis]

Spin eigenvalues of a 2 state system cannot be zero.

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).