Reality of the Quantum State: A Stronger Ψ-ontology Theorem

[bohm2]

Another theorem ruling out ψ-epistemic models:

While it is always possible to contrive ψ-epistemic toy models for PBR-type experiments, any full-blown ontological theory which allows arbitrary composition of (sub)systems is necessarily ψ-ontic. We consider this theorem to provide a more convincing case for the reality of the quantum state on the basis that, in light of Bell's theorem, it is known that any ontological theory that accounts for the predictions of quantum theory will necessarily have non-local correlations at the ontological level (as in Bohmian mechanics, for example). This theorem proves ψ-ontology even allowing for non-local correlations in the global ontic state.

http://arxiv.org/pdf/1412.0669.pdf

 

[bhobba]

Such theorems are interesting.

But to be clear the assumption it makes from the outset is:
'The first assumption is that a system has an underlying physical state, described by λ ∈ Λ, which is referred to as the ontic state of the system. This may or may not coincide with the quantum state. The space Λ of ontic states is analogous to classical phase space.'

This is precisely the assumption the ensemble, ignorance ensemble and most versions of Copenhagen reject. The state resides purely in the head of the theorist just like probabilities, which are not physical either.

Thanks
Bill

 

[bohm2]

But to be clear the assumption it makes from the outset is:
'The first assumption is that a system has an underlying physical state, described by λ ∈ Λ, which is referred to as the ontic state of the system. This may or may not coincide with the quantum state. The space Λ of ontic states is analogous to classical phase space.' This is precisely the assumption the ensemble, ignorance ensemble and most versions of Copenhagen reject. The state resides purely in the head of the theorist just like probabilities, which are not physical either.

Yes. Models where the wavefunction is epistemic, but there is no deeper underlying reality (e. g. Copenhagen) are untouched by this theorem, just as in PBR.

 

[Quantumental]

Such theorems are interesting.

But to be clear the assumption it makes from the outset is:
'The first assumption is that a system has an underlying physical state, described by λ ∈ Λ, which is referred to as the ontic state of the system. This may or may not coincide with the quantum state. The space Λ of ontic states is analogous to classical phase space.'

This is precisely the assumption the ensemble, ignorance ensemble and most versions of Copenhagen reject. The state resides purely in the head of the theorist just like probabilities, which are not physical either.

Sure. but this rejects reality to a large degree by stating "There is no physical fact, the fact still exist in some metaphysical way though"

 

[bohm2]

Sure. but this rejects reality to a large degree by stating "There is no physical fact, the fact still exist in some metaphysical way though"

The interesting part of this theorem is the PBR result still holds even when relaxing the 'no-preparation signalling’ assumption (i.e. theorem proves ψ-ontology even allowing for non-local correlations in the global ontic state). With respect to "non-realist" models, it's been argued that no theorem on the planet could rule out such options. I believe this is what Norsen was trying to point out in this part of his paper:

One cannot, as suggested earlier, derive a Bell-type inequality from the assumption of Locality alone; one needs in addition this particular Realism assumption...I do not know for sure that this isn’t what the users of ‘local realism’ have in mind. There is, in favor of this interpretation, the fact that Metaphysical Realism really is assumed in deriving the Bell inequalities, and so, in principle, one could react to the empirical violation of the inequalities either by rejecting Locality (and maintaining Metaphysical Realism) or by rejecting Metaphysical Realism. But there is a crucial point that speaks against this interpretation. Notice that the last sentence of the previous paragraph did not include the perhaps-expected parenthetical “and maintaining Locality”. This was because the choice between rejecting Locality and rejecting Metaphysical Realism is not a choice in the ordinary sense – in particular, one cannot “save Locality” by rejecting Metaphysical Realism.And this is because the very idea of “Locality” already presupposes Metaphysical Realism, a point that is undeniable once we remember what we are using the term “Locality” to mean: the requirement that all causal influences between spatially separated physical objects propagate sub-luminally.

The point here is this: to reject Metaphysical Realism is precisely to hold that there is no external physical world. And once one rejects the existence of a physical world, there simply is no further issue about whether or not causal influences in it propagate exclusively slower than the speed of light (as required by Locality). Or put it this way: “Locality” is the requirement that relativity’s description of the fundamental structure of space-time is correct. But relativity theory is thoroughly “realist” in the sense of Metaphysical Realism. If there is no physical world external to my consciousness, then, in particular, there is no space-time whose structure might correspond to the relativistic description – and so that description’s status would be the same as, for example, that of claims about the viscosity of phlogiston or theories about the causes of cancer in unicorns: false in the strongest possible sense.

http://arxiv.org/pdf/quant-ph/0607057v2.pdf

 

[atyy]

This is precisely the assumption the ensemble, ignorance ensemble and most versions of Copenhagen reject. The state resides purely in the head of the theorist just like probabilities, which are not physical either.

Do those interpretations really reject the existence of a physical state? The quantum state (density operator) is not necessarily physical in those interpretations, but that is different from saying that a physical state that is not the quantum state doesn't exist. In classical probability, there are interpretations in which probability is not necessarily real, but as I understand them they don't reject the existence of a physical state of the system - in fact they usually assume that systems in reality have physical states.

 

[bhobba]

Do those interpretations really reject the existence of a physical state?

Of course not - they are silent about it. But obviously Occam's razor applies and you don't read more into it than intended.

Thanks
Bill

 

[bhobba]

"There is no physical fact, the fact still exist in some metaphysical way though

Run that by me again. If its physically real it exists out there independent of us like an electric field. Probabilities are not like that (although I guess some interpretations have it as real - but I haven't come across any) nor are some interpretations of the state.

Remember, most physicists and applied mathematicians are pretty literal in how they look at things - they are not into philosophical subtlety.

Thanks
Bill

 

[atyy]

Of course not - they are silent about it. But obviously Occam's razor applies and you don't read more into it than intended.

Probabilities are not like that (although I guess some interpretations have it as real - but I haven't come across any) nor are some interpretations of the state.

I'm not sure I understand what you are saying by bringing up the analogy that probabilities are not physical, because I believe all major interpretations of probability (including subjective Bayesians) assume the existence of a physical state. By saying that the ignorance ensemble interpretation does not assume a "physical state", do you just mean that the wave function is not necessarily real and may be a subjective belief, like probability in the subjective Bayesian sense, ie. do you understand the "state" in "physical state" to refer to the density operator?

 

[bhobba]

I'm not sure I understand what you are saying by bringing up the analogy that probabilities are not physical, because I believe all major interpretations of probability (including subjective Bayesians) assume the existence of a physical state.

Scratching head. Look at Baysian for example. Its a confidence level that resides in the head of the theorist - that's as far from physical as you can get.

An electric field resides out there - it had better or our conservation laws go out the window - probabilities and the state in many interpretations do not.

Thanks
Bill

 

[atyy]

Scratching head. Look at Baysian for example. Its a confidence level that resides in the head of the theorist - that's as far from physical as you can get.

Yes, in the subjective Bayesian example probability is not physical. However, the belief is about something "out there" in reality, which is physical, otherwise it's hard to make sense of Bayesian updating with data, and theorems that guarantee that subjective Bayesianism will arrive at the truth given sufficient data as long as the initial prior is non-zero over the true hypothesis. This is why subjective Bayesians believe in physical states. Here the physical state is not the Bayesian prior, nor the quantum state. I think you think that the assumption of a "physical state" is the assumption that the quantum state is physical, but I don't think that is what the authors mean.

 

[bohm2]

Yes, in the subjective Bayesian example probability is not physical. However, the belief is about something "out there" in reality, which is physical, otherwise it's hard to make sense of Bayesian updating with data...

We discussed this previously. 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

This theorem just as PBR would place serious constraints on 1 but not 2 A purely instrumentalist approach (e.g Bohrian) would be untouched by this theorem. A quantum Bayesian approach (e.g. Caves, Fuchs, etc.) would also not seem to be undermined by this theorem, because Fuchs and that group would deny that quantum states have ontic states. And the assumption made by this paper is same as in PBR. I previously had e-mailed the lead author of the PBR paper and he explained this assumption:

The idea is that the physical properties are "real" in the sense that they are not merely calculation devices in our heads, and can therefore be the cause of measurement outcomes...The result doesn't really depend on your exact philosophical standpoint on the nature of physical reality - we simply show that if a "reality" of some sort exists and satisfies our assumptions then the quantum state is "real" in whatever sense of the word "reality" the assumptions hold.

With respect to Bayesianism, Ilja clarified (for me) this point:

But I tend to think that it should 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.

 

[atyy]

We discussed this previously. 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

This theorem just as PBR would place serious constraints on 1 but not 2 A purely instrumentalist approach (e.g Bohrian) would be untouched by this theorem. A quantum Bayesian approach (e.g. Caves, Fuchs, etc.) would also not seem to be undermined by this theorem, because Fuchs and that group would deny that quantum states have ontic states. And the assumption made by this paper is same as in PBR. I previously had e-mailed the lead author of the PBR paper and he explained this assumption:

With respect to Bayesianism, Ilja clarified (for me) this point:

Of course (actually I prefer what you wrote in post #3, this is not so accurate), but this is not accurately conveyed by bhobba's statement "This is precisely the assumption the ensemble, ignorance ensemble and most versions of Copenhagen reject. The state resides purely in the head of the theorist just like probabilities, which are not physical either." In other words, saying the state resides purely in the head of the theories like a probability does not distinguish between the two sorts of epistemic interpretations - unless purely is taken very strictly, but in which case even measurement outcomes need not be real. Of course one can take an anti-realist subjective Bayesian approach, but again, this is not mainstream. The assumption is that quantum states are epistemic and that there are no underlying ontic states - as you stated in post #3 - but that is not what bhobba wrote.

 

[naima]

It is often said that a measurement occurred if it left a "robust" trace. How do ontic and epistemic theorists describe that?

 

[bohm2]

Of course one can take an anti-realist subjective Bayesian approach, but again, this is not mainstream.

Are you arguing that the Bayesian approach is not anti-realist, or am I misunderstanding? In case, you are, here's what Leifer wrote:

If asked what quantum states represent knowledge about, neo-Copenhagenists are likely to answer that they represent knowledge about the outcomes of future measurements, rather than knowledge of some underlying observer-independent reality. Modern neo-Copenhagen views include the Quantum Bayesianism of Caves, Fuchs and Schack, the views of of Bub and Pitowsky, the quantum pragmatism of Healy, the relational quantum mechanics of Rovelli, the empiricist interpretation of W. M. de Muynck, as well as the views of David Mermin, Asher Peres, and Brukner and Zeilinger. Some may quibble about whether all these interpretations resemble Copenhagen enough to be called neo-Copenhagen, but for present purposes all that matters is that these authors do not view the quantum state as an intrinsic property of an individual system and they do not believe that a deeper reality is required to make sense of quantum theory.

http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf

So I take this as implying that Quantum Bayesianism is also unaffected by this theorem, just as in PBR. But Ilja did appear to question this interpretation of Bayesianism in his post. His argument centered around the Bayesian interpretation of probability. But you are right as I missed the part about the ensemble interpretation.

 

[atyy]

Are you arguing that the Bayesian approach is not anti-realist, or am I misunderstanding? In case, you are, here's what Leifer wrote:

http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf

So I take this as implying that Quantum Bayesianism is also unaffected by this theorem, just as in PBR. But Ilja did appear to question this interpretation of Bayesianism in his post. His argument centered around the Bayesian interpretation of probability. But you are right as I missed the part about the ensemble interpretation.

Yes, the most common Bayesian approach is not anti-realist - but it has nothing to do with quantum mechanics - just classical probability. When bhobba says that the state is like probability, it's a representation of belief, I think he is referring to the subjective Bayesian approach. A famous slogan of this approach is that "probability does not exist", which is analogous to "the quantum state is not real". However, this does not mean that a subjective Bayesian does not believe in reality or that physical states do not exist. For example, http://www.stat.cmu.edu/~rsteorts/btheory/goldstein_subjective_2006.pdf "They are analogous to a similar discussion as to whether and when, say, a global climate model is right or wrong. This is the wrong question. We know that the global climate model differs from the actual climate - they are two quite different things." and "When we properly recognise, develop and apply the ideas and methods of subjectivist analysis, then we will finally be able to carry out that synthesis of models, theory, experiments and data analysis which is necessary to make real inferences about the real world." There is also the de Finetti representation theorem, which http://www.cs.berkeley.edu/~jordan/courses/260-spring10/lectures/lecture1.pdf which shows how subjectivist probability can be written in terms of parameter estimation. Another example is http://www.uv.es/bernardo/BayesStat.pdf which says "It follows that, under exchangeability, the sentence “the true value of ω” has a well-defined meaning, if only asymptotically verifiable."

The Bayesian parameter does not have to be a "purely physical parameter" with a true physical value as opposed to a convenient parameterization of one's beliefs. However, if one takes a less purist view, one can show that Bayesian estimation does converge to the true parameter as long as the prior includes the true hypothesis; even on a very pure view the Bayesian theorems show that different Bayesian observers with different priors will converge to the same belief. So even if one did not believe in the existence of an ontic state, one would have to actually forbid the mathematics to prevent the existence of the hidden variable. For example, even if one did not believe that the hidden variables in Bohmian Mechanics were physical, there is nothing to say that Bohmian Mechanics is all unreal and just a parameterization of one's subjective belief, ie. one could take Bohmian Mechanics as a pure unreal interpretation that does not solve a non-existent measurement problem - that is just mathematics. Or at least I think that would be the lesson from the fact that even pure subjective Bayesians believe in the de Finetti representation theorem.

All this classical subjective Bayesianism is different from Quantum Bayesianism in which it is unclear whether any other observer exists for any particular observer. Actually, the other observer may exist at the meta level in Quantum Bayesianism, since Quantum Bayesianism believes in reality, without underlying ontic states. For example http://arxiv.org/abs/1301.3274 rejects hidden variables "Giving up on hidden variables implies in particular that measured values do not pre-exist the act of measurement. A measurement does not merely “read off” the values, but enacts or creates them by the process itself. In a slogan inspired by Asher Peres (Peres, 1978), “unperformed measurements". But it also asserts the existence of a reality: "So, implicit in this whole picture—this whole Paulian Idea—is an “external world . . . made of something,” just as Martin Gardner calls for. It is only that quantum theory is a rather small theory: Its boundaries are set by being a handbook for agents immersed within that “world made of something.”"

Incidentally, regardless of what one thinks of the philosophical details of the Quantum Bayesian programme, one of the solid and beautiful achievements of Caves, Fuchs and Schack is a proof of the quantum de Finetti theorem (first proved by Hudson and Moody), which allows Quantum Bayesians to treat quantum states as true physical states FAPP: http://arxiv.org/abs/quant-ph/0104088. (But at some point I think some of the authors switched from objective Bayesianism to subjective Bayesianism.)

 

[bhobba]

Yes, the most common Bayesian approach is not anti-realist - but it has nothing to do with quantum mechanics - just classical probability. When bhobba says that the state is like probability, it's a representation of belief, I think he is referring to the subjective Bayesian approach.

There are two main approaches to probability - the Baysian one based on Coxes axioms:
http://en.wikipedia.org/wiki/Cox's_theorem

Here probability is simply a degree of belief you have about something that obeys a few reasonable rules. This is similar to Copenhagen.

And the frequentest approach which is based on the law of large numbers from rigorous probability theory and a few common sense correspondence rules such as you can neglect an infinitesimally small probability. This is very similar to the ensemble interpretation.

Most applied mathematicians use the frequentest view because its very pictorial and leads to nice intuition. Those into things like risk and credibility theory used extensively in actuarial work often prefer the Baysian view.

My background is in statistical modelling rather than credibility theory so I am in the frequentest camp.

The real rock bottom however is measure theory and Kolmogorov's axioms - but you must take some kind of stance to apply it - hence the slightly difference stances of the various minimalist interpretations of QM.

Thanks
Bill

 

[billschnieder]

My background is in statistical modelling rather than credibility theory so I am in the frequentest camp.

If you think that's all Bayesian inference is useful for, then you are missing out. I recommend these articles.

Here's how a Bayesian seens it: http://bayes.wustl.edu/etj/articles/cmystery.pdf
Jaynes, E. T., 1989, `Clearing up Mysteries - The Original Goal, ' in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1

In our system, a probability is a theoretical construct, on the epistemological level, which we assign in order to represent a state of knowledge, or that we calculate from other probabilities according to the rules of probability theory. A frequency is a property of the real world, on the
ontological level, that we measure or estimate. So for us, probability theory is not an Oracle telling how the world must be; it is a mathematical tool for organizing, and ensuring the consistency of, our own reasoning. But it is from this organized reasoning that we learn whether our state of
knowledge is adequate to describe the real world. This point comes across much more strongly in our next example, where belief that probabilities
are real physical properties produces a major quandary for quantum theory, in the EPR paradox.
​

http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf
Jaynes, E. T., 1990, `Probability in Quantum Theory,' in Complexity, Entropy, and the Physics of Information, W. H. Zurek (ed.), Addison-Wesley, Redwood City, CA, p. 381;

in our view, the existence of a real world that was not created in our imagination, and which continues to go about its business according to its own laws, independently of what humans think or do, is the primary experimental fact of all , without which there would be no point to physics or any other science. The whole purpose of science is learn what that reality is and what its laws are.​

 

[atyy]

Jaynes was a Bayesian, but he's usually considered an objective Bayesian, whereas de Finetti whom I thought bhobba was thinking of is one of the founders of the beautiful subjective Bayesian school.

Also, Jaynes is wrong when he says "The class of Bell theories does not include all local hidden variable theories; it appears to us that it excludes just the class of theories that Einstein would have liked most." The violation of the Bell inequalities predicted by quantum mechanics is incompatible with all local causal or Einstein causal (to use Ilya's term) theories.

 

[bhobba]

If you think that's all Bayesian inference is useful for, then you are missing out.

Nope. Its simply philosophical waffle. Either view is valid - its just that in credibility theory for example how creditable you find something fits more naturally with a Bayesian view - at least to me and most of the guys I studied this with and the way the lecturer presented it - but we were applied mathematicians - not philosophers. You can also view it as in a large number of similar situations its the percentage of time the statement you are considering will be correct - but it seems less cumbersome in that situation to think of it as a degree of belief you have. Either view is correct - its simply what feels more natural.

In statistical modelling you have something like a queue length and want to figure out how long it will be. This is something very concrete and it's natural to think of it as a conceptual large ensemble of actual queues and what occurs is simply an element of that ensemble. Again it's neither right or wrong - just what seems natural to you and that quite likely was influenced by the textbooks you studied. Its certainly the view of Ross whose textbook is very popular and what I used:
https://www.amazon.com/dp/0123756863/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

Jaynes was a Bayesian, but he's usually considered an objective Bayesian, whereas de Finetti whom I thought bhobba was thinking of is one of the founders of the beautiful subjective Bayesian school.

That's true - there are variants of Baysian - I was speaking in general.

Thanks
Bill

 

[billschnieder]

Jaynes was a Bayesian, but he's usually considered an objective Bayesian, whereas de Finetti whom I thought bhobba was thinking of is one of the founders of the beautiful subjective Bayesian school.

I think Jaynes himself will disagree with "objective" vs "subjective" distinction. For example, he says in the above paper:

Our probabilities and the entropies based on them are indeed "subjective" in the sense that they represent human information; if they did not, they could not serve their purpose. But they are completely "objective" in the sense that they are determined by the information specified,independently of anybody's personality, opinions, or hopes. It is objectivity" in this sense that we need if information is ever to be a sound basis for new theoretical developments in science.​

The main point Jaynes is making, and I agree with him, is that the way you view "Probability" has a profound impact on the way you look at all the paradoxes such as EPR, PBR, and their derivatives. He saw no difficulty with in reconciling Bell and EPR as he explained in those papers, and to understand him, you will have to view his argument from his perspective of what "probability" is. For example, he also explains why he believes both Einstein and Bohr were correct, another argument that is informed by his view of "probability".

Also, Jaynes is wrong when he says "The class of Bell theories does not include all local hidden variable theories; it appears to us that it excludes just the class of theories that Einstein would have liked most." The violation of the Bell inequalities predicted by quantum mechanics is incompatible with all local causal or Einstein causal (to use Ilya's term) theories.

I believe he was very correct. We can hash that out offline if you care.

 

[atyy]

I think Jaynes himself will disagree with "objective" vs "subjective" distinction. For example, he says in the above paper:

Our probabilities and the entropies based on them are indeed "subjective" in the sense that they represent human information; if they did not, they could not serve their purpose. But they are completely "objective" in the sense that they are determined by the information specified,independently of anybody's personality, opinions, or hopes. It is objectivity" in this sense that we need if information is ever to be a sound basis for new theoretical developments in science.​

All Bayesians are "subjective" in the first sense that Jaynes used above, so the distinction between subjective and objective Bayesians lies in whether probabilities must also be "objective" in Jaynes's sense. In other words, subjective Bayesians say that probabilities are not entirely determined by the information specified, independently of anybody's personality, opinions, or hopes. Nonetheless, a subjective Bayesian is a frequentist FAPP as long as his prior is non-zero over the true hypothesis, he considers observations to be exchangeable, and he obtains sufficient data. So subjective and objective Bayesians and frequentists all agree given sufficient data, but in the small data regime they disagree completely. Actually, subjective Bayesians and frequentists agree because all frequentists will admit they are incoherent, and would probably say one can have any opinion in the absence of data, as long as no logical alternative is completely excluded. :) Jaynes would claim that even in the small data one can be "objective".