Do Bell and PBR together point toward nonlocal reality?

[Ilja]

Umm, Quantum Mechanics?

How does QM derive causality?

Perhaps you know of *something* where indeterminism (raw chance) does not play a part. Anything actually. How about human behavior? Ever seen the slightest indication that A causes B there?

?? Suggests that you seem to think that indeterminism somehow is in contradiction with causality.

Structure of the universe, what caused the sun to be where it is and the Earth to be where it is. Anything...?
And if you even bother to mumble something about initial conditions, you will really bring a smile to my face. In fact you already have...

As I said, it seems that your notion of causality is very different from my ideas about causality.

 

[stevendaryl]

How does QM derive causality?

I can let Dr. Chinese answer for himself, but I thought the point of quantum mechanics is that causality isn't fundamental. There is no causality at the level of microscopic physical laws, so the appearance of causality at the macroscopic is some kind of emergent phenomenon.

 

[Ilja]

This is one position. But I doubt it is well justified, because it depends on the interpretation.

Essentially, independent of the physical theory, it is always possible to use a more solipsistic, positivistic interpretation which remains silent about causality at all. In QM such a positivistic interpretation - the minimal interpretation - is quite popular, that's all.

In the Copenhagen interpretation, there are at least some elements of causality, or at least I think so: The measurement is the cause of the collapse of the wave function. The dBB interpretation is a classical causal interpretation.

The key point for me is that a positivistic interpretation cannot derive any causality at all. It can compute, and derive from more fundamental assumptions, probabilities and correlations. That's all. Observation can give only correlation, and theories which allow to compute only observables, that means, probabilities and correlations, are in a similar situation, they can give only correlations.

You need a theoretical hypothesis to go beyond correlations. Causality is something about the underlying reality.

 

[stevendaryl]

The key point for me is that a positivistic interpretation cannot derive any causality at all. It can compute, and derive from more fundamental assumptions, probabilities and correlations. That's all. Observation can give only correlation, and theories which allow to compute only observables, that means, probabilities and correlations, are in a similar situation, they can give only correlations.

That's certainly right. You can't derive causality from mere correlation. However, the phenomena that gave rise to our notions of causality can be understood without actually using causality. In this case, causality would be an effective theory, rather than fundamental, in the same sort of way that thermodynamics is an effective theory, while the more fundamental theory is the physics of many interacting particles.

I don't think it's accurate to describe non-causal theories as "solipsistic". I would almost go so far as to reverse that. It's human nature to prefer causal theories, but there is no reason for the world to try to work in a way that is intuitively understandable to humans.

 

[stevendaryl]

You need a theoretical hypothesis to go beyond correlations. Causality is something about the underlying reality.

I'm not convinced that there is a non-fuzzy notion of causality that goes beyond correlations. People typically are satisfied with a theory that predicts future states of the world in terms of past states, usually described with differential equations. But a differential equation is simply stating a correlation between future states and past states. It doesn't actually say that the past causes the future. What additional thing do you need to get causality?

I'm not sure.

 

[Ilja]

What you need is a theory. A theoretical hypothesis.

A deterministic equation can be considered, of course, as a particular example of a causal theory. You have the equation of the theory, and the initial state, the result follows with certainty. But, of course, the causal theory is a little bit more: It also presupposes a direction of time (causal influence is from past to future).

But there may be, of course, also causal theories which are not deterministic. Something like the initial conditions A cause B, but we do not observe B but instead B' which with some probability 5% differs from B. Or A and B and C together causes D, but unfortunately we cannot prepare A and B and C with certainty, and A and B, together with some null assumption about C, gives D with probability 95% or so.

That causality goes beyond correlation is obvious. Correlation gives us p((A and B) or (not A and not B)) = 1.
Causality gives us A causes B, or B causes A, or C causes A and C causes B, already three different theories, in fact an infinity because for different C we have different causal explanations.

 

[halfrealist]

What is the status of measurement problem in the light of PBR theorem?

 

[eloheim]

Does considering a specific scenario, like the one presented below, help any in sorting out the differing notions of causality (and implications thereof) discussed in this thread?

Quantum correlations with no causal order

Here's a popular article describing the research. I know these things tend to be sloppy but I had the bookmarks together so please don't hate me:

Quantum causal relations: A causes B causes A

 

[stevendaryl]

What you need is a theory. A theoretical hypothesis.

But how does the theory predict that a correlation is actual a causal relationship? I'm not convinced that the word "cause" plays any role in physics that can't be played by "correlation".

 

[stevendaryl]

Does considering a specific scenario, like the one presented below, help any in sorting out the differing notions of causality (and implications thereof) discussed in this thread?

Quantum correlations with no causal order

Here's a popular article describing the research. I know these things tend to be sloppy but I had the bookmarks together so please don't hate me:

Quantum causal relations: A causes B causes A

Thanks for the references.

 

[DrChinese]

I can let Dr. Chinese answer for himself, but I thought the point of quantum mechanics is that causality isn't fundamental. There is no causality at the level of microscopic physical laws, so the appearance of causality at the macroscopic is some kind of emergent phenomenon.

Well said. I do not think any notion of causal influences is really necessary for orthodox QM. Does a unique set of initial (quantum) conditions always produce a unique outcome? No, and certainly not as far as anyone knows.

So I guess that the appearance of causality is much like the appearance of a thermodynamic arrow of time.

 

[bohm2]

What is the status of measurement problem in the light of PBR theorem?

PBR has no effect on the measurement problem but, since you brought it up, others do argue that the issue of causality/probability/randomness/time direction discussed in above threads do depend on how the quantum measurement problem is resolved:

In quantum theory, the statistical move plays no particular role: the results of quantum statistical mechanics arise from the quantum dynamics of individual states and do not depend on any additional probabilistic postulate. As a consequence, debates about the nature of classical statistical-mechanical probability are not of direct relevance to our understanding of the actual world as described by contemporary physics. Probability in contemporary physics arises from the probabilistic nature of quantum theory itself, not from any additional posit.

That `probabilistic nature' depends on how the quantum measurement problem is resolved. According to dynamical-collapse theories, it is a fundamental stochasticity, analogous to pre-quantum stochastic mechanics. According to (deterministic) hidden-variable theories, it is a consequence of a probability distribution over the hidden variables, analogous to pre-quantum statistical mechanics. According to the Everett interpretation, it is something new, not analogous to either; it is controversial whether this means that Everettian probability is more or less well understood than pre-quantum probability.

The direction of time in the probabilistic macrodynamics of quantum theory is also dependent on the resolution of the measurement problem. In dynamical collapse theories, it is a consequence of the fundamental time-asymmetry of the dynamics. In the Everett interpretation, and in hidden-variable theories, it is a consequence of a non-probabilistic constraint on the initial quantum state.

Probability in physics: stochastic, statistical, quantum
http://philsci-archive.pitt.edu/9815/1/wilson.pdf

 

[Ilja]

But how does the theory predict that a correlation is actual a causal relationship? I'm not convinced that the word "cause" plays any role in physics that can't be played by "correlation".

There is a correlation between IQ and race. A lot of people care about explanations for such a correlation. Genes? Environment? Which environmental influence?

Of course, this example may be an unfortunate choice, because the various causal theories used to explain this correlation have a strong ideological background, so one may doubt that they are scientific theories. At least in some completely objective, idealized science, one may argue, these theories should be rejected as unscientific.

But even if these theories may be attractive to people with certain ideological backgrounds, they remain scientific. Because they allow to make predictions. The theory that some C is the cause of the correlation can be tested by considering various constellations where C is absent or present. Ok, this part is reducible to correlations: The theory leads to predictions about other correlations.

But this is not the only way to decide if C is a reasonable cause. There should be, in this case, a reasonable causal explanation, that means, a mechanism which explains why C, say more books at home, can lead to a higher IQ.

And, sorry, this part is much more interesting at least for me. If I find a way to replace a claim about A correlates with B by C correlates with A as well as with B, this does not really sound like a scientific progress. But if we find a causal explanation for something where initially there was only a strange correlation, we have a different situation.

It is, of course, not an accident that I have chosen an example from everyday life and not from fundamental physics. The point is that the everyday life example makes the difference more clear. Instead, the interpretations of fundamental physics I consider as distorted by the influence of positivism.

 

[stevendaryl]

There is a correlation between IQ and race. A lot of people care about explanations for such a correlation. Genes? Environment? Which environmental influence?

But isn't it true that what we're really worried about is how robust the correlation is? Here's an example that's a little less controversial. Suppose we notice a correlation between the length of a tree's shadow and the position of the sun in the sky: In the morning and evening, the shadow is very long, and the sun is low in the sky. At noon, the shadow is very short, and the sun is high in the sky. So can we control the sun by manipulating the length of the shadow? Of course not, but the failure to be able to do that doesn't actually require causality, but can be seen through correlations alone. If you make the shadow shorter by cutting off the top of the tree, the position of the sun doesn't change. The correlation disappears.

It seems to me that most of the time that we are interested in causality, we can re-express our interests in terms of correlations.

 

[Ilja]

It seems to me that most of the time that we are interested in causality, we can re-express our interests in terms of correlations.

This may be indeed possible, but is it helpful?

There is, so to say, a subtype of correlations we can name "causal correlations". These causal correlations have, first, a particular sequence in time, A->B means t(A)<t(B) in a fundamental notion of time. Second, they have realistic explanations, some mechanism which explains it, which, in terms of correlations, may be described as a sequence of other causal correlations, such that A->C₁->C₂->C₃...->C_n->B. Is that all? No, there is also that the smallest causal connections C_k->C_k+1 in this sequence which we are able to find out have more elementary character, they are usually of an especially simple type, say, some bodies simply moving inertially or so, and usually much more universal.

Note also that this explanatory sequence requires that all of these correlations are of the special causal type, thus, t(C_k)<t(C_k+1). And than there is the additional hypothesis that for every intermediate t t(A)<t<t(B), there has to be yet another C_t between them, A->C_t->B. And that this explanation has to be complete, that means, after controlling for the correlations which are explained by this sequence, there is no remaining correlation between A and B, else the explanation is not complete and one has to look for other causal explanations.

Thus, looking for causal connections means looking for especially simple correlations with some special properties. It is, so to say, a guidance for our research, which of the correlations are really interesting and helpful and which are more of less accidental, like all those correlations studied by astrology.

 

[audioloop]

I can let Dr. Chinese answer for himself, but I thought the point of quantum mechanics is that causality isn't fundamental. There is no causality at the level of microscopic physical laws, so the appearance of causality at the macroscopic is some kind of emergent phenomenon.

or the inverse randomness from determinism.

 

[audioloop]

@audioloop: non-signalling is different, and weaker. Violations of Einstein causality may be hidden, associated with a hidden preferred frame. One choice of a preferred frame allows an explanation with superluminal A->B, another choice with superluminal B->A. There is no explanation without superluminal influence. But you cannot use this for superluminal signalling. Because signalling A->B would be impossible, incompatible with the explanation B->A, and signalling B->A incompatible with the explanation A->B. So there is no superluminal signalling, but nonetheless no Einstein causality.
.

well not to Pawłowski:
he recently gave a quantum key distribution protocols based non-local correlations, which is a strictly weaker assumption than the assumption of no-signalling.

http://arxiv.org/abs/0907.3778
http://pra.aps.org/abstract/PRA/v82/i3/e032313

 

[bohm2]

Not sure if this was posted previously but a recent, neat, non-technical summary of the implications of PBR at physicsworld:

That makes four views in total: that realism is nonsense and the wavefunction is simply a good, workaday description of observations (Bohr); that reality exists and the wavefunction represents incomplete knowledge about it (Einstein); that the wavefunction corresponds to part of reality (Bohm); and that the wavefunction corresponds to all of reality (Everett). So far, so good – except for the second and third options, which appear somewhat similar. What is the difference between Einstein's wavefunction, which represents partial knowledge about reality, and Bohm's wavefunction, which is part (but not all) of reality? Roughly speaking, the latter wavefunction corresponds to something physical, whereas the former wavefunction does not...

Last year physicists Terry Rudolph and Matthew Pusey at Imperial College London, together with mathematician Jonathan Barrett at Royal Holloway, University of London, took up the challenge. They developed a theorem to determine which realist view, epistemic or ontic, is compatible with the predictions of quantum mechanics...

Pusey, Barrett and Rudolph's theorem, which has come to be known as the PBR theorem, essentially offers an ultimatum. If quantum mechanics is right, then the wavefunction cannot be epistemic – it cannot merely represent an experimentalist's partial knowledge about reality. It must instead be ontic and directly correspond either to part of reality (as Bohm said) or to reality in full (as Everett said).

The life of psi
http://physicsworld.com/cws/article/indepth/2013/may/02/the-life-of-psi

 

[audioloop]

Not sure if this was posted previously but a recent, neat, non-technical summary of the implications of PBR at physicsworld:


The life of psi
http://physicsworld.com/cws/article/indepth/2013/may/02/the-life-of-psi

or exist a Epistemic-Epistemic State.


.

 

[DrChinese]

Not sure if this was posted previously but a recent, neat, non-technical summary of the implications of PBR at physicsworld:


The life of psi
http://physicsworld.com/cws/article/indepth/2013/may/02/the-life-of-psi

Well, this is saying that the Bohmian and MWI interpretations are the big winners. Hmmm.

 

[bohm2]

Well, this is saying that the Bohmian and MWI interpretations are the big winners. Hmmm.

It has no effect on non-realist interpetations e.g. Bohr's. It just rules out certain realist interpretations (e.g. Einstein's). The diagram attached below from the article nicely summarizes the 4 major positions:

 

[Ilja]

It has no effect on non-realist interpetations e.g. Bohr's. It just rules out certain realist interpretations (e.g. Einstein's).

But in fact it is much weaker, because it is possible to preserve a Bayesian interpretation of the wave function if one follows the Bohmian way by introducing the position (configuration) q(t) into reality. In this case, the wave function of a complete system can be interpreted in purely Bayesian terms.

The point is the Bohmian formula for the effective wave function of a subsystem: ψ_{sub}(q)=ψ_{full}(q,q_{env}). So, even if the ψ_{full} is purely Bayesian or nomological, what we consider in PBR is only ψ_{sub}, which depends on q_{env}, which is ontological.

 

[bohm2]

But in fact it is much weaker, because it is possible to preserve a Bayesian interpretation of the wave function if one follows the Bohmian way by introducing the position (configuration) q(t) into reality. In this case, the wave function of a complete system can be interpreted in purely Bayesian terms.

The point is the Bohmian formula for the effective wave function of a subsystem: ψ_{sub}(q)=ψ_{full}(q,q_{env}). So, even if the ψ_{full} is purely Bayesian or nomological, what we consider in PBR is only ψ_{sub}, which depends on q_{env}, which is ontological.

I'm having trouble understanding this part on Bayesian interpretation, so let me summarize how I interpreted the stuff from what I've read. Epistemic interpretations of the quantum state can be divided into 2 types:

1. those that are epistemic with respect to underlying ontic states
2. those that are epistemic with respect to measurement outcomes

The PBR theorem would place serious constraints on 1. but not 2. A quantum Bayesian approach (at least as favored by Caves, Fuchs, etc.) would not be undermined by the PBR theorem, as far as I understand, because Fuchs and that group would deny that quantum states have ontic states. Would you agree with this part?

 

[Ilja]

I would agree that Fuchs and Caves, as far as they are completely anti-realistic, do not have to bother about PBR.

But, wait, I'm not completely sure. Bayesian probability theory is derived. We start with a few common sense principles and obtain all the rules of classical probability theory. Classical probability theory? What does this mean? Probability theory as defined by the Kolmogorov axioms?

If yes: Kolmogorovian probability theory is a probability density defined on a space of elementary events. What are these "elementary states"? Another, mathematical word for the underlying ontic states? Or only for the measurement outcomes? But measurement outcomes are described in classical Kolmogorovian probability theory by stochastic functions, that means, functions on the space of elementary states, not by elementary states.

Something worth to think about. But I tend to think that it shold be at least possible to follow a purely positivistic, anti-realistic direction, without any underlying reality, with measurement results as the only replacement for reality, and probability distributions on them as Bayesian probabilities. For such a Bayesian direction, PBR would be unproblematic.

The other problem is if such a subdivision is that clear. In the Bayesian variant of dBB the effective wave function depends on a purely Bayesian wave function of the universe and the real ontic state of the environment.
The first question - the Bayesian wave function of the universe is expistemic with respect to what? The very question does not make sense, I think.

The second question: The q_env(t) of the environment is an ontic state, but contains also all the macroscopic measurement results of the preparation procedure. And these measurement results are usually sufficient to define ψ_eff completely.

 

[audioloop]

I would agree that Fuchs and Caves, as far as they are completely anti-realistic, do not have to bother about PBR.

But, wait, I'm not completely sure. Bayesian probability theory is derived. We start with a few common sense principles and obtain all the rules of classical probability theory. Classical probability theory? What does this mean? Probability theory as defined by the Kolmogorov axioms?

If yes: Kolmogorovian probability theory is a probability density defined on a space of elementary events. What are these "elementary states"? Another, mathematical word for the underlying ontic states? Or only for the measurement outcomes? But measurement outcomes are described in classical Kolmogorovian probability theory by stochastic functions, that means, functions on the space of elementary states, not by elementary states.

Something worth to think about. But I tend to think that it shold be at least possible to follow a purely positivistic, anti-realistic direction, without any underlying reality, with measurement results as the only replacement for reality, and probability distributions on them as Bayesian probabilities. For such a Bayesian direction, PBR would be unproblematic.

The other problem is if such a subdivision is that clear. In the Bayesian variant of dBB the effective wave function depends on a purely Bayesian wave function of the universe and the real ontic state of the environment.
The first question - the Bayesian wave function of the universe is expistemic with respect to what? The very question does not make sense, I think.

The second question: The q_env(t) of the environment is an ontic state, but contains also all the macroscopic measurement results of the preparation procedure. And these measurement results are usually sufficient to define ψ_eff completely.

measurements from who or what ? no reality; no who - no what...



.

 

[Ilja]

measurements from who or what ? no reality; no who - no what...

Ask this the anti-realist camp. Its not my problem.

 

[mitchell porter]

I missed this earlier...

I don't think that this theory escapes PBR. True, the wave function psi(x,t) is not a part of its formulation. But the theory is formulated in terms of another function p(x,t), which is essentially a logarithm of psi(x,t). Thus, the reality of p is equivalent to the reality of psi.

Or perhaps your point is that psi is not real in Bohmian mechanics? If that is the case, then I have to say that most Bohmians (including myself) disagree.

If you focus on a particular physical system, psi doesn't have to be a "thing", it can just be a function appearing in the equations of motion of the "classical" beables. As I'm sure you know, this is the point of "nomological" Bohmian mechanics: wavefunction as "law" (or as part of a law), rather than as "thing".

Raykin is interesting because he has actually taken a step beyond Bohmian mechanics, by focusing on the trajectories and beginning to rewrite the equations of motion. Okay, he still has log-psi rather than psi, but it's a start.

 

[Demystifier]

If you focus on a particular physical system, psi doesn't have to be a "thing", it can just be a function appearing in the equations of motion of the "classical" beables. As I'm sure you know, this is the point of "nomological" Bohmian mechanics: wavefunction as "law" (or as part of a law), rather than as "thing".

Let me repeat that Bohmian "nomological" also belongs to the PBR "ontological" class.

 

[mitchell porter]

Let me repeat that Bohmian "nomological" also belongs to the PBR "ontological" class.

I'm not entirely sure what you're saying... but let me repeat :-) that neither psi-ontic Bohmian mechanics nor nomological Bohmian mechanics (nor Raykin's theory) falls within the scope of the PBR theorem, because of PBR's assumption of ontic overlap between the epistemic states.

 

[halfrealist]

New arXiv posting on PBR theorem http://arxiv.org/abs/1306.5805.