Quantum state: Reality or mere probability?

[atyy]

But coming back to PBR, the two possibilities given in the presentation, are:
1- knowledge of lambda determines p(head) and p(tail) uniquely (ontic)
2- knowledge of lambda not enough to determine p(head) and p(tail) uniquely (epistemic)
appear to be criteria for completeness rather than definitions ontic/epistemic. In the second case, lambda is incomplete as far as the prediction of p(head) and p(tail). In the first p(head)/p(tail) is limited to the coin only, in second p(head)/p(tail) is describing the coin and the tossing mechanism.

Yes, some people don't like this terminology, because one can say that both cases assume reality simply by assuming hidden variables. That's fine, and this is widely acknowledged. But given the underlying ontic framework, this is I think a nice definition that allows one to distinguish subclasses of hidden variable theories. The definition comes from Harrigan and Spekkens http://arxiv.org/abs/0706.2661 (see their fig 2, not fig 1).

Since then, explicit ψ-epistemic constructions for the Born rule have been given.
http://arxiv.org/abs/1201.6554
http://arxiv.org/abs/1303.2834

And there is a no-go theorem against "maximally ψ-epistemic" theories
http://arxiv.org/abs/1207.6906
http://arxiv.org/abs/1208.5132

 

[Jabbu]

The most obvious thing about determinism is that every quantum outcome appears completely random (and has no known cause). So the data is against you.

Random? Would you say flipping a coin or rolling a dice produces random outcome, or that it has no known cause? What experiment and what data are you talking about?

 

[DrChinese]

Random? Would you say flipping a coin or rolling a dice produces random outcome, or that it has no known cause? What experiment and what data are you talking about?

No one has been able to point to a root cause for any quantum outcome. That is a far cry different from a coin flip or a die toss, which cause of outcome could be determined precisely in principle. The key here is that one thing has an explanation, the other doesn't.

Of course, no one is disputing that the cause for an random quantum outcome could be discovered next week. Then you would have some evidence. But currently there is none. Otherwise: If it walks like a duck, and quacks like a duck, it's random.

 

[billschnieder]

Why are we unable to experimentally confirm whether knowledge of lambda determines p(head) and p(tail) uniquely, or not?

Because we can't know that we know everything knowable about lambda. And even if we could, we won't be interested in *probabilities*, everything will be certain. That is why I'm not sure the idea of "real probability distributions" makes sense. There is a modal contradiction in there somewhere.

 

[billschnieder]

Actually, there's an interesting way the Bohmian view explains a traditional short-cut in which the particle is assumed to have a classical trajectory. After a particle has passed through a slit (single or double), its momentum just after it has passed through the slit can be measured by detecting its position at a distant screen, and calculating as if the particle had a classical trajectory.

It has always seemed to me that the fact that the Bohmian trajectories are not straight is evidence they are not real. Otherwise there is a momentum conservation elephant in the room. Photons and electrons spontaneously changing direction? How do the Bohmians address this issue.

 

[atyy]

It has always seemed to me that the fact that the Bohmian trajectories are not straight is evidence they are not real. Otherwise there is a momentum conservation elephant in the room. Photons and electrons spontaneously changing direction? How do the Bohmians address this issue.

Ooops, sorry, I deleted my post before you replied. Anyway, the Bohmian laws are not the same as the classical laws. Bohmian trajectories do not have a classical momentum. Anyway, I wouldn't worry too much about how unnatural it is. The point is it works. No one is saying this particular law is correct - for a given choice of hidden variables, the dynamical law isn't even unique. Furthermore, the choice of hidden variables is also not unique. The point is that it solves the measurement problem, and we can conceive as quantum theory as just an effective theory with a common sense reality, just like all of classical physics.

 

[naima]

As a Bohmian, I agree fully with Fuchs! If degrees of freedom can be emergent, then so can ontology:)

Maybe a more serious question to which I don't know the answer - can we take the Bohmian quantum equilibrium distribution in the sense of subjective probability, say de Finetti? If so, then can we make Bohmian mechanics subjective too?

Actually, Wiseman had some comments on subjective probability in Bohmian mechanics, but I think along somehwat different lines: http://arxiv.org/abs/0706.2522.

You add wave functions to calculate fringes. Fuchs says that "there is no state function"

 

[billschnieder]

Ooops, sorry, I deleted my post before you replied. Anyway, the Bohmian laws are not the same as the classical laws. Bohmian trajectories do not have a classical momentum. Anyway, I wouldn't worry too much about how unnatural it is. The point is it works. No one is saying this particular law is correct - for a given choice of hidden variables, the dynamical law isn't even unique. Furthermore, the choice of hidden variables is also not unique. The point is that it solves the measurement problem, and we can conceive as quantum theory as just an effective theory with a common sense reality, just like all of classical physics.

Surely we can. But we don't have to introduce weirdness just because we can. Bohmian "trajectories" don't have to be real to be correct. It can be epistemic and still produce the correct results, and still work very well. In which case the "trajectories" are not really trajectories but rather probability distributions for finding particles. In other words, the particles are not *really" traveling along those curvy lines (often called trajectories).

 

[Jabbu]

Because we can't know that we know everything knowable about lambda. And even if we could, we won't be interested in *probabilities*, everything will be certain. That is why I'm not sure the idea of "real probability distributions" makes sense. There is a modal contradiction in there somewhere.

Can you draw a parallel between a coin toss or dice roll probability compared to QM randomness, and point out what does lambda correspond to in each case? Are classical and QM probability really different kinds of "randomness"?

 

[atyy]

Surely we can. But we don't have to introduce weirdness just because we can. Bohmian "trajectories" don't have to be real to be correct. It can be epistemic and still produce the correct results, and still work very well. In which case the "trajectories" are not really trajectories but rather probability distributions for finding particles. In other words, the particles are not *really" traveling along those curvy lines (often called trajectories).

Do you mean "epistemic" in the sense of Harrigan and Spekkens, and the PBR paper?

 

[atyy]

Can you draw a parallel between a coin toss or dice roll probability compared to QM randomness, and point out what does lambda correspond to in each case? Are classical and QM probability really different kinds of "randomness"?

Classical and QM probability are not necessarily different kinds of randomness - the Bohmian construction proves that. In fact, the entire assumption behind the distinction between ψ-ontic and ψ-epistemic theories discussed in this thread assumes that classical and QM probability are not different kinds of randomness.

 

[atyy]

You add wave functions to calculate fringes. Fuchs says that "there is no state function"

I don't think there isn't any sign of that in http://arxiv.org/abs/1301.3274.

 

[DrChinese]

Classical and QM probability are not necessarily different kinds of randomness - the Bohmian construction proves that. In fact, the entire assumption behind the distinction between ψ-ontic and ψ-epistemic theories discussed in this thread assumes that classical and QM probability are not different kinds of randomness.

Just to be clear (since there are readers of all levels in this thread): there is absolutely no evidence that there is a Bohmian cause to any quantum event. This is strictly hypothetical.

I don't have any evidence it isn't correct either. But it is something at this point you believe in out of faith.

 

[bohm2]

Not sure if this was posted previously but Matt Leifer recently published a ~100 page exposition on ψ-ontic theorems like PBR and discusses in detail all the more recent criticisms of the PBR assumptions, etc.:

Is the quantum state real? A review of ψ-ontology theorems
http://mattleifer.info/wordpress/wp-content/uploads/2008/10/quanta-pbr.pdf

 

[bohm2]

Since there was a bit of confusion regarding interpretations ruled out when we were discussing this previously (assuming PBR is accurate), Leifer suggests that it rules out the following 3 models:

1. Einstein's
2. Spekken's
3. Ballentine's

The second type of ψ-epistemic interpretation are those that are realist, in the sense that they do posit some underlying ontology. They just deny that the wavefunction is part of that ontology. Instead, the wavefunction is to be understood as representing our knowledge of the underlying reality, in the same way that a probability distribution on phase space represents our knowledge of the true phase space point occupied by a classical particle. There is evidence that Einstein's view was of this type. Ballentine's statistical interpretation is also compatible with this view in that he leaves open the possibility that hidden variables exist and only insists that, if they do exist, the wavefunction remains statistical (as a frequentist, Ballentine uses the term "statistical" rather than "epistemic"). More recently, Spekkens has been a strong advocate of this point of view.

 

[bhobba]

Since there was a bit of confusion regarding interpretations ruled out when we were discussing this previously (assuming PBR is accurate), Leifer suggests that it rules out the following 3 models:

1. Einstein's
2. Spekken's
3. Ballentine's

Well Einstein's ran into problems with Kochen-Specker - you can't have what's observed prior to observing - so its out anyway (decoherence is another way of doing it).

But since Ballentine merely applies a frequentest view to the probabilities to get the view of the state as a CONCEPTUAL ensemble, as I pointed out right from the start, with a quote from the original PBR paper, it doesn't apply to interpretations of the state where its purely an aid to calculation. I would suggest Mati has a misconception about the interpretation - my suspicion being he didn't understand it's purely conceptual.

Added Later:
I did as quick scan of the paper, can't find where he rules it out - the quote you gave doesn't do that.

Thanks
Bill

 

[atyy]

But since Ballentine merely applies a frequentest view to the probabilities to get the view of the state as a CONCEPTUAL ensemble, as I pointed out right from the start, with a quote from the original PBR paper, it doesn't apply to interpretations of the state where its purely an aid to calculation. I would suggest Mati has a misconception about the interpretation - my suspicion being he didnt understand it purely conceptual.

Leifer references the earlier Ballentine interpretation, not the book. I think you said (crediting Fredrik) that the earlier was secretly Bohmian. If so, then Leifer is actually correct.

 

[bhobba]

Leifer references the earlier Ballentine interpretation, not the book.

Indeed that's true.

The 1970 paper, in both my and Frederik's view, is really Bohm, or something similar, in disguise. It's very similar to Einstein's and has exactly the same issue.

But he is careful to avoid that issue in his text.

BTW none of those issues make either interpretation wrong - it simply means they are assuming more than explicitly stated. I suspect Einstein would have secretly liked that because it supported his view QM was incomplete.

In fact my ignorance ensemble runs afoul of a similar issue - an improper mixture becomes a proper one - somehow. It just bypasses Kochen-Sprecker but leaves the fundamental problem floating. The big problem it resolves is exactly what is an observation in purely quantum terms.

Thanks
Bill

 

[atyy]

Can Bohmian Mechanics be made epistemic? In http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/ Leifer says that for "classical epistemic states", it is enough that we assign a probability distribution over phase space, and the system occupies only one phase space point.

Given that Bohmian Mechanics is classical in ontology, and assigns a distribution that is described by the wave function to a point in configuration space (and presumably Bohmian phase space too), can't we use the classical definition of "epistemic" and say the wave function in Bohmian Mechanics is "epistemic"?

 

[bohm2]

Can Bohmian Mechanics be made epistemic? In http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/ Leifer says that for "classical epistemic states", it is enough that we assign a probability distribution over phase space, and the system occupies only one phase space point.

Given that Bohmian Mechanics is classical in ontology, and assigns a distribution that is described by the wave function to a point in configuration space (and presumably Bohmian phase space too), can't we use the classical definition of "epistemic" and say the wave function in Bohmian Mechanics is "epistemic"?

No. I previously had similar sentiments as I considered some Bohmian models (the "minimalist" ones) to be ψ-epistemic but Leifer cleared this up in this 2014 paper linked above and points out why all Bohmian models are ψ-ontic:

Now, in the conventional understanding of de Broglie-Bohm theory, the wavefunction is understood to be part of the ontic state in addition to the particle positions. It is true that the particle positions are in some sense more fundamental than the wavefunction, and they are often called the "primitive ontology" or the "local beables" of the theory. The particle positions are supposed to be the things in the theory that provide a direct picture of what reality looks like to us, e.g. when we observe the pointer of a measurement device pointing to a specific value then it is the positions of the particles that make up the pointer that determine this. Nevertheless, the wavefunction is still needed as part of the ontology because it determines how the particles move via the guidance equation. The response of a measurement device to an interaction with a system it is measuring depends on the wavefunction of the system as well as the particle positions, so the wavefunction is still part of the ontic state, even if it is in some sense less primitive than the particle positions.

I think Demystifier had tried to explain it to me but I didn't get it even though I thought I did. But I don't feel bad because Spekkens also argued similarly as us.

 

[Demystifier]

How is "entangled" state accounted for in cos^2(theta), ...?

How my claims can be interpreted that it is?

 

[Jabbu]

How my claims can be interpreted that it is?

You were talking about entangled states so I thought you could explain it. What does entanglement have to do with quantum states being real or not?

 

[Demystifier]

You were talking about entangled states so I thought you could explain it. What does entanglement have to do with quantum states being real or not?

It is explained in the paper attached in the first post, so please refer your further questions to the explanation presented in this paper.

 

[stevendaryl]

Well Einstein's ran into problems with Kochen-Specker - you can't have what's observed prior to observing - so its out anyway (decoherence is another way of doing it).

But since Ballentine merely applies a frequentest view to the probabilities to get the view of the state as a CONCEPTUAL ensemble, as I pointed out right from the start, with a quote from the original PBR paper, it doesn't apply to interpretations of the state where its purely an aid to calculation. I would suggest Mati has a misconception about the interpretation - my suspicion being he didn't understand it's purely conceptual.

Added Later:
I did as quick scan of the paper, can't find where he rules it out - the quote you gave doesn't do that.

Thanks
Bill

It seems to me that according to M. S. Leifer's (who is "Mati"?) paper, an ensemble interpretation would count as epistemic.

 

[bhobba]

It seems to me that according to M. S. Leifer's (who is "Mati"?) paper, an ensemble interpretation would count as epistemic.

Its obvious it doesn't.

All he is doing is interpreting the state in a frequentest way as a CONCEPTUALLY large number of similarly prepared systems from which the observation selects an outcome.

Note the key word - CONCEPTUAL - meaning it resides in the head of the theorist.

The problem with Einstein's version and Ballentines 1970 paper is they assumed what was selected was there prior to observation in the same sense as an ensemble in statistical mechanics. His book is more careful about that - the act of observation itself selects the outcome.

Thanks
Bill

 

[stevendaryl]

Its obvious it doesn't.

All he is doing is interpreting the state in a frequentest way as a CONCEPTUALLY large number of similarly prepared systems from which the observation selects an outcome.

Note the key word - CONCEPTUAL - meaning it resides in the head of the theorist.

I'm confused: Who is "he"? Leifer or Ballentine?

If the ensemble is something in the head of the theorist, then that would seem epistemic, to me.

 

[bhobba]

I'm confused: Who is "he"? Leifer or Ballentine?

Sorry - I was being slack - its Matthew Leifer - it's colloquialism out our way that Matthew is shortened to Mati, Matty etc.

If the ensemble is something in the head of the theorist, then that would seem epistemic, to me.

My goof - you are correct - its the other way around - its not ontic - I get confused with these philosophy terms.

But to forestall other questions here is a link to Ballentine's 1970 paper:
http://www.kevinaylward.co.uk/qm/ballentine_ensemble_interpretation_1970.pdf

Now have a look at the bottom of page 361:
'In contrast the Statistical Interpretation considers a particle to always be at some position in space'

That is only possible in some Bohm like theory and is responsible for the remarks of myself and Frederik.

To avoid it you say the act of observation selects a particular position from the ensemble - its not there before observation. He is much more careful about this in his book.

Thanks
Bill

 

[vanhees71]

An "ensemble" is a very real thing. It's just the repetition of an experiment/measurement for many equally an independently prepared setups. This you do from the very beginning of your scientific career in the labs at university and that's what's done in any lab on the world without further thinking of it. Quite often my experimental colleagues say "that's a statistics hungry observable; we definitely need more statistics", which just means they have to collect more data running their accelerator further, trying to increase the luminosity at a given beam energy and what not.

I don't know of any way to verify theoretical predictions (the more those of quantum theory which is probabilistic in the first place) than to interpret probabilities (wherever their estimate comes from) in the frequentist way and use large enough ensembles to check them. I've not yet met any (Q) Baysenist who could tell me what he means with the idea that a probability applies to single events.

Of course, there are examples for very interesting things that meet great difficulties preparing large enough ensembles. One example is the measurement of cosmic neutrinos. E.g., Icecube has collected just some "cosmic neutrinos", and one would like to draw conclusions already on this, but that's a big challenge, indeed. There's no way to gain more insight beyond the standard statistical conclusions (let alone the estimate of systematic errors which must also be performed by the experimentalists).

 

[naima]

I don't think there isn't any sign of that in http://arxiv.org/abs/1301.3274.

I think that is what he writes:

In this paper, we hope to have given a new and use-
ful way to think of quantum interference: Particularly,
we have shown how to view it as an empirical addition
to Dutch-book coherence, operative when one calculates
probabilities for the outcomes of a factualizable quantum
experiment in terms of one explicitly assumed counter-
factual. We did this and not once did we use the idea of a
probability amplitude

I was very enthusiastic the first time i read this paper. Born's rule was described only with positive real numbers!
Fuchs avoided the complex amplitudes for interferences. he avoided Jones matrices, he also avoided Kraus operators. All those tools which act on amplitude functions.
But alas, he also avoided to calculate interferences. How could he calculate a fringe length?
I googled "qbism interferometry". But i found no caculation.
He starts with a Hilbert space then he says let us ignore its inner product
A part of quantum mecanics remains. Qbists are interested in this subset of QM.
You said that as a Bohmian you agree with Fuchs. Do you also avoid all that "linear stuff"

 

[bhobba]

An "ensemble" is a very real thing. It's just the repetition of an experiment/measurement for many equally an independently prepared setups. This you do from the very beginning of your scientific career in the labs at university and that's what's done in any lab on the world without further thinking of it. Quite often my experimental colleagues say "that's a statistics hungry observable; we definitely need more statistics", which just means they have to collect more data running their accelerator further, trying to increase the luminosity at a given beam energy and what not.

Its the standard way its taught in applied math such as statistical modelling. You think of it as a very large number of repetitions of the same thing.

But in some areas like statistical inference the Bayesian view is more prevalent - however that is NOT the situation in QM.

Sill Copenhagen that views it that way is a popular interpretation.

Thanks
Bill

 

[atyy]

No. I previously had similar sentiments as I considered some Bohmian models (the "minimalist" ones) to be ψ-epistemic but Leifer cleared this up in this 2014 paper linked above and points out why all Bohmian models are ψ-ontic:

I think Demystifier had tried to explain it to me but I didn't get it even though I thought I did. But I don't feel bad because Spekkens also argued similarly as us.

Yes, you are right using the definition of ψ-epistemic in Harrigan and Spekkens and PBR. But I was wondering whether using a different definition one could think that the Bohmian ψ is also epistemic? That's why I asked in post #2 "Can it be said that the Bohmian answer to this question is reality and mere probability?". Or can one have one's cake and eat it? Do these interesting comments from stevendaryl and Demystifier from another thread https://www.physicsforums.com/showthread.php?t=767672 suggest it is possible?

Maybe the answer is that in Bohm, while the wave function is objectively real, its interpretation (when squared) as a probability involves a subjective notion of probability?

Yes.

 

[stevendaryl]

I've not yet met any (Q) Baysenist who could tell me what he means with the idea that a probability applies to single events.

Well, Bayesians are equally mystified by frequentism. I mean, you never have an infinite run of anything, you have a finite run. So what does probably imply for a finite number of trials? Nothing. So ultimately, your decision as to whether a probabilistic theory has been falsified by experiment is subjective.

Everybody makes subjective decisions as to what to believe. Whenever someone does something that has never been done before, whether it's trying a new drug, or performing a new accelerator experiment, or riding in a new space vehicle, people have to make subjective judgments about how safe it is. Maybe you can say: "We've proved using QED [or GR, or whatever] that it's perfectly safe", but you don't know that those theories are correct. So everybody deals with subjective notions of what to have confidence in. It's just that non-Bayesians wouldn't associate such uncertainties with a number, a probability. But if you don't attach probabilities to those uncertainties, then there is no way to consistently reason about them, if you have several sources of uncertainty. Bayesianism is just a way of being systematic and consistent about the uncertainties that everyone deals with in one-of-a-kind events.

 

[atyy]

Well, Bayesians are equally mystified by frequentism. I mean, you never have an infinite run of anything, you have a finite run.

Isn't there a theorem that allows Bayesians to be effectively frequentist? http://en.wikipedia.org/wiki/De_Finetti's_theorem

There's a quantum version: http://arxiv.org/abs/quant-ph/0104088.

 

[Jabbu]

There is also a practical side to things being real or not. So if quantum state of an electron is real, it really means electron itself is not quite real, but rather smeared nowhere and everywhere in the same time, and with no particular position or velocity vector, right? Isn't that actually the opposite of "real"?

How could electrons follow this exact trajectory if their location and momentum vector is not precisely defined at every point in time along that path?

 

[Dale]

Closed pending moderation.