Graduate A stronger proof of nonlocality, or what?

[Kolmo]

How does Bohmian mechanics, which is a nonlocal hidden variable theory whose predictions exactly match those of QM

Do you have a reference for where that is proved? I know it is equivalent for position measurements, but I've never seen the fully general proof. I'd just need to see it to make sure I'm answering correctly.

 

[PeterDonis]

Do you have a reference for where that is proved?

The math of Bohmian mechanics is equivalent to that of standard QM; that has been known since the 1950s. Since the math is equivalent, it must make the same predictions.

 

[Demystifier]

Do you have a reference for where that is proved? I know it is equivalent for position measurements, but I've never seen the fully general proof. I'd just need to see it to make sure I'm answering correctly.

The trick is that Bohmian mechanics uses the idea that all measurements can be reduced to position measurements, or more precisely, to positions of macroscopic pointers. See e.g. the paper linked in my signature below.

 

[Kolmo]

The math of Bohmian mechanics is equivalent to that of standard QM; that has been known since the 1950s. Since the math is equivalent, it must make the same predictions.

But where is the proof of this is what I am asking? There used to be arguments in the literature that it didn't give the same results for measurements of quantities outside of the basis chosen by the hidden variables. In standard Bohmian Mechanics that would be the position basis, but there are other "Bohmian" Mechanics if one chooses other quantities. Also that it had issues with multi-time correlations.

The mathematical equations are quite different so I'd like to see a proof of the equivalence, I don't think it's true that "it is known" since it was debated at the time and there is a long argument it is not equivalent in R.F. Streater's book "Lost Causes in and beyond Theoretical Physics". I'm not saying Streater is right, just asking for where it was proven.

 

[Demystifier]

Also that it had issues with multi-time correlations.

Multi-time correlations predicted by Bohmian mechanics are also in agreement with standard QM. See Appendix I of F. Laloe, Do We Really Understand QM?

 

[Demystifier]

But where is the proof of this is what I am asking?

See also
https://www.physicsforums.com/threa...es-from-bohmian-mechanics.977585/post-6235376
and
https://www.physicsforums.com/threa...es-from-bohmian-mechanics.977585/post-6236895

 

[Kolmo]

1) P. Holland, The Quantum Theory of Motion, Chapter 8.

Okay regardless of whether that is a full equivalence proof it does give what I need to answer the question.

This new inequality rules out nonlocal theories where the particles can interact nonlocally but always possesses well defined values for observable quantities such as momentum and spin. In Bohmian Mechanics spin is a contextual result of the interaction of the device with the particle, not a property inherent to the particle.

So we might say the current result proves that particles do not intrinsically possesses most of the properties we measure them to have. Up until now this would have been "interpretational", now it is a proven fact.

 

[Demystifier]

Okay regardless of whether that is a full equivalence proof it does give what I need to answer the question.

This new inequality rules out nonlocal theories where the particles can interact nonlocally but always possesses well defined values for observable quantities such as momentum and spin. In Bohmian Mechanics spin is a contextual result of the interaction of the device with the particle, not a property inherent to the particle.

So we might say the current result proves that particles do not intrinsically possesses most of the properties we measure them to have. Up until now this would have been "interpretational", now it is a proven fact.

I don't think that's correct. In Bohmian mechanics, a particle always has both position and momentum. But momentum is not always distributed according to the Born rule, the Born rule for momentum is contextual. Similarly, in the Holland's book you will find Bohmian models in which a particle always has a well defined spin in all 3 directions, but again those values are not always distributed according to the Born rule.

You might revise your statement by saying that we now have a proof that the Born rule is contextual for most observables, but I think we already knew that from older theorems.

 

[Kolmo]

I don't think that's correct. In Bohmian mechanics, a particle always has both position and momentum

Sorry I meant our observed values are not those of the actual particle, i.e. observed spin and momentum are an emergent property of the particle-device set up, we're not just reading off the actual particle momentum for example.

You might revise your statement by saying that we now have a proof that the Born rule is contextual

It's not quite the same as Kochen-Specker contextuality so I wouldn't use that phrase. Also the paper is just looking at correlation-topes, it's not specific to QM so the Born rule as a QM specific thing is not as such a characterization of it.

 

[Kolmo]

Let me try to say it another way. This basically rules out theories were there is a nonlocal interaction between the particles but the device readouts are either directly reading out the properties of the particles or contextual to the device local to the particle.

In essence even nonlocal interactions between the particles combined with contextual values of the measurement results gives a bound which quantum theory violates. You need the values measured in each location to be contextual to both devices.

This is not the same Kochen Specker contextuality which is local and doesn't directly discuss the Born rule since it's about regions in correlation space in general, not about specific features of quantum mechanics.

 

[Sunil]

I don't think that's correct. In Bohmian mechanics, a particle always has both position and momentum.

No. It has both position and velocity. There is a trajectory $q(t)\in Q$ and so there is also a velocity $v(t)= \dot{q}(t)\in Q$. Momentum is contextual - the result of a momentum measurement depends on the position of the measurement device too, thus, is not a property of the particle. There is, in particular, no trajectory $p(t)$. One should be careful to distinguish momentum p and $mv$.

 

[Demystifier]

No. It has both position and velocity. There is a trajectory $q(t)\in Q$ and so there is also a velocity $v(t)= \dot{q}(t)\in Q$. Momentum is contextual - the result of a momentum measurement depends on the position of the measurement device too, thus, is not a property of the particle. There is, in particular, no trajectory $p(t)$. One should be careful to distinguish momentum p and $mv$.

In the sense in which momentum is contextual, in that sense the velocity $v\equiv m^{-1}p$ is also contextual. And by the way, even the measured position, that is the position of the macroscopic pointer of the apparatus, may differ from the Bohmian position of the measured microscopic particle; the authors who discovered it called it surreal Bohmian trajectories. So in that sense even position can be considered contextual in Bohmian mechanics.

 

[Sunil]

In the sense in which momentum is contextual, in that sense the velocity $v\equiv m^{-1}p$ is also contextual.

No. Because conceptually there is no such equivalence. Momentum is defined in dependence of the Lagrangian, $p_i = \frac{\delta S}{\delta \dot{q}}$. A Lagrangian depends on the context, it is contextual (in this sense) already in classical physics.
And, again, there is a Bohmian trajectory $q(t)$ and correspondingly $\dot{q}(t)$ but no such trajectory $p(t)$.

And by the way, even the measured position, that is the position of the macroscopic pointer of the apparatus, may differ from the Bohmian position of the measured microscopic particle; the authors who discovered it called it surreal Bohmian trajectories. So in that sense even position can be considered contextual in Bohmian mechanics.

First, the measured position is irrelevant, the trajectory $q(t)$ is the real position.

Then, "surreal Bohmian trajectories" are nothing but a subjective feeling of some people who expect the trajectories to look like classical trajectories. They simply failed to develop the correct Bohmian intuitions. That's also quite irrelevant.

The correct intuitions about Bohmian trajectories are not that strange. First, they look much less strange if considered only as average trajectories. In stable energy eigenstates there is, in the average, no motion. The classical motion is circular. The average velocity is zero, which is natural. That it should be exactly zero looks slightly strange. Then, let's look at superpositional states. There, the trajectory will be as if the position would have been measured. And that will be a quite classical trajectory. Only if in one part you make a measurement of something different from position, then even the far away other particle will do some surrealistic things too. If that measurement will be a measurement in the sense of the results made macroscopic or not does not matter.

 

[Demystifier]

I've just had a discussion with two authors (Wiseman and Cavalcanti) of the paper. They explained me that violation of their "local friendliness" would imply that the purely instrumental interpretation a'la "Quantum theory needs no interpretation" https://pubs.aip.org/physicstoday/article/53/3/70/411209/Quantum-Theory-Needs-No-Interpretation is wrong. In other words, the experiment could in principle rule out the interpretation that most practical physicists, including @vanhees71, seem to take for granted. But pure instrumentalists don't need to bother yet, because actual realization of such experiments, involving fine manipulations of quantum properties of the measuring apparatus, would be terribly difficult.

 

[vanhees71]

Which paper are you talking about? The Physics today article by Fuchs and Peres tells it all: All you need is the minimal interpretation. If you find an experiment which clearly and reproducibly contradicts the (probabilistic) prediction of QT, then QT is wrong and has to be substituted by a better theory, but not before that happens.

Whether or not QT or another "better" theory satisfies the one or other philosophical prejudice about how Nature must be because of some "ism" is not part of science.

 

[Demystifier]

Which paper are you talking about?

The one referred to in the first post of this thread. It discusses a thought experiment of the Wigner-friend type, which manipulates the quantum state of the measuring apparatus and concludes that, if quantum mechanics is applicable to the measuring apparatus as to any other quantum object, then the minimal purely instrumental interpretation of QM is wrong. But the actual experiment has not been performed(*), and probably will not be in a near future, so a pure instrumentalist, like you, does not need to worry.

(*) An experiment has been performed in which a true measuring apparatus is replaced with a single qubit, obviously because a single qubit is much easier to manipulate in a way needed for the experiment.

 

[Demystifier]

Whether or not QT or another "better" theory satisfies the one or other philosophical prejudice about how Nature must be because of some "ism" is not part of science.

How about minimal-ism and instrumental-ism, are they philosophical prejudices too?
Remarkably, the thought experiment is supposed to rule out precisely those ism's.

 

[martinbn]

@Demystifier why are you so sure of the outcome of the future experiment? May be it will not rule out but confirm the instrumentalist point of view?

 

[Demystifier]

@Demystifier why are you so sure of the outcome of the future experiment? May be it will not rule out but confirm the instrumentalist point of view?

Sure, it's also a possibility. In fact, this result would be much more interesting.

 

[Demystifier]

If you find an experiment which clearly and reproducibly contradicts the (probabilistic) prediction of QT, then QT is wrong and has to be substituted by a better theory, but not before that happens.

The experiment by itself would not say what a better theory is, but it would tell us that at least one of the 3 common sense assumptions in post #1 must be wrong.

 

[PeterDonis]

An experiment has been performed in which a true measuring apparatus is replaced with a single qubit, obviously because a single qubit is much easier to manipulate in a way needed for the experiment.

And just as obviously, makes the experiment irrelevant to the question such experiments are supposed to address, since you can't make a measuring apparatus out of a single qubit.

 

[Fra]

because actual realization of such experiments, involving fine manipulations of quantum properties of the measuring apparatus, would be terribly difficult.

If the difficulty is due to the requirements of information processing capacity, and at some point it simply exceeds what we have at hand, would we still call it just a difficulty, or would be call it not possible in principle?

/Fredrik

 

[Demystifier]

If the difficulty is due to the requirements of information processing capacity, and at some point it simply exceeds what we have at hand, would we still call it just a difficulty, or would be call it not possible in principle?

To say what is possible or impossible in principle, one must first specify - the principle. The principle is a theoretical concept, not an experimental one. The formulation of a principle may be guided by experiments, but it becomes a principle only when we give it a theoretical formulation, either as an axiom of a given theory, or something derived from more fundamental axioms. But our theories, and hence the principles, change and evolve as our knowledge develops. For example, consider the 2nd law of thermodynamics. According to the thermodynamic theory (as formulated before the Boltzmann's statistical mechanics), it is impossible in principle to violate the 2nd law. But according to statistical mechanics, it's possible in principle, but very difficult in practice.

 

[Fra]

To say what is possible or impossible in principle, one must first specify - the principle. The principle is a theoretical concept, not an experimental one. The formulation of a principle may be guided by experiments, but it becomes a principle only when we give it a theoretical formulation, either as an axiom of a given theory, or something derived from more fundamental axioms. But our theories, and hence the principles, change and evolve as our knowledge develops. For example, consider the 2nd law of thermodynamics. According to the thermodynamic theory (as formulated before the Boltzmann's statistical mechanics), it is impossible in principle to violate the 2nd law. But according to statistical mechanics, it's possible in principle, but very difficult in practice.

Yes, the principle I had in mind was what I take implicit to the whole standard paradigm of QM: That inferences are made from experiments in the form of statistics of preparation procedures and detections. Somehow, I think it seems fair to say that it's how it's done, regardless of "interpretations"? Modulo observer equivalence transformations, all observers must be able to agree on the statistics, which is why some says it's on the "classical side".

For example, an experiment with a measurement device that isn't as reliable as "classical record" isn't just difficult, I think it doesn't qualify as a measurement, and thus invalid to use in the QM paradigm?

I agree this is a big problem. But I don't think the problem can be analyzed within QM itself, as it entertains for good reasons "measurements" that should make sense, but are somehow generalisations of the more constrained "quantum measurements", so we can't handle them as per the QM paradigm.

The question then was, is it possible in principle to infer the mentioned problems of QM itself, using its own "inference system" and experimental protocol (without bending the presumed rules)?

/Fredrik

 

[Demystifier]

But I don't think the problem can be analyzed within QM itself, as it entertains for good reasons "measurements" that should make sense, but are somehow generalisations of the more constrained "quantum measurements", so we can't handle them as per the QM paradigm.

The question then was, is it possible in principle to infer the mentioned problems of QM itself, using its own "inference system" and experimental protocol (without bending the presumed rules)?

Is the first quote your answer to your question in the second quote?

 

[Fra]

Is the first quote your answer to your question in the second quote?

Yes. Its my strong hunch. I havent contempled ny proofs though.

/Fredrik

 

[Fra]

This was highlighted earlier in the thread...

1. When someone observes an event happening, it really happened.

To me this is essentially what it means for an observer to be in the "classical world" - where "real" is define as whatever the consensus is among observers, via equivalence transformations.

Without this, I agree as hinted by others that QM paradigm makes no sense, as QM is built on this solid ground.

If we widen our views however, I would of course expect the QM to break down at some point anyway, so this assumption is pretty much the first I would do away with from an agent-centered stance. After all, as I mentioned before, there is a difference between the principle of "no preferred observer", (which seems easy to accept as anybodys views is as right asn anyones elses) and the much stronger "all observers are equivalent". The former does not exclude disagreements, and there is thus perhaps no solid ground? And therefore QM may have limited validity only to the extent that the classical backround IS stable enough, and the more general framework to describe this in, is still missing. This is what I meant with that, in the paradigm of QM, I think (1) must hold. IF we relax it, we leave the QM paradigm?

/Fredrik

 

[Demystifier]

To me this is essentially what it means for an observer to be in the "classical world" - where "real" is define as whatever the consensus is among observers, via equivalence transformations.

I think that reality has nothing to do with classicality. For instance, dreams and hallucinations, which are not real, are equally classical.

 

[martinbn]

I think that reality has nothing to do with classicality. For instance, dreams and hallucinations, which are not real, are equally classical.

Reality of position is related to classicality. But in a non-classical theory why should position be real? Or more generaly why should there be an observable with a classical analog/limit which is real?

 

[Demystifier]

Reality of position is related to classicality. But in a non-classical theory why should position be real? Or more generaly why should there be an observable with a classical analog/limit which is real?

I believe I answered such questions in my "Bohmian mechanics for instrumentalists".