Another theorem ruling out ψ-epistemic models:
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.
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.
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:
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.
Of course not - they are silent about it. But obviously Occam's razor applies and you don't read more into it than intended.
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.
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?
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.
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.
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.
It is often said that a measurement occured if it left a "robust" trace. How do ontic and epistemic theorists describe that?
Are you arguing that the Bayesian approach is not anti-realist, or am I misunderstanding? In case, you are, here's what Leifer wrote:
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 [Broken] "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.)
There are two main approaches to probability - the Baysian one based on Coxes axioms:
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.
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.
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.
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.
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:
That's true - there are variants of Baysian - I was speaking in general.
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".
I believe he was very correct. We can hash that out offline if you care.
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".
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