Psi Epistemicism & the Reality of Particles & Atoms

[Nick V]

For those of you who have read the theorem, probably have also read Matt Leifer's review of it. In his review he says that the only way to remain psi epistemic is to be an anti realist(copenhagen), or to abandon the bell frame work. Is it viable to be psi epistemic but still believe that particles and atoms are real?

 

[jedishrfu]

I found this discussion on matters related to PBR:

http://www.preposterousuniverse.com/blog/2013/01/17/the-most-embarrassing-graph-in-modern-physics/

It talks about a poll of physicists and what they believe QM to be.

 

[bohm2]

For those of you who have read the theorem, probably have also read Matt Leifer's review of it. In his review he says that the only way to remain psi epistemic is to be an anti realist(copenhagen), or to abandon the bell frame work. Is it viable to be psi epistemic but still believe that particles and atoms are real?

No, assuming that one accepts the assumptions of the PBR theorem. You either have to:

1. Adopt the neo-Copenhagen point of view and hold the quantum state does not represent knowledge about some underlying reality (i. e. only represents knowledge about consequences of measurements that we might make on system). Alternatively,

2. Adopt one of the ψ-ontic views, where the quantum states represents something "real".

The PBR theorem, however, rules out a realist interpretation of QM that is also ψ-epistemic, which is what you are questioning. But like all no-go theorems, the strength of the PBR theory rests crucially on the reasonableness of the PBR assumptions.

 

[Nick V]

No, assuming that one accepts the assumptions of the PBR theorem. You either have to:

1. Adopt the neo-Copenhagen point of view and hold the quantum state does not represent knowledge about some underlying reality (i. e. only represents knowledge about consequences of measurements that we might make on system). Alternatively,

2. Adopt one of the ψ-ontic views, where the quantum states represents something "real".

The PBR theorem, however, rules out a realist interpretation of QM that is also ψ-epistemic, which is what you are questioning. But like all no-go theorems, the strength of the PBR theory rests crucially on the reasonableness of the PBR assumptions.

But when you say that the wave function represents something real, are you saying that it is actually a real wave, like sound waves or EM waves?

 

[vanhees71]

Hm, I've looked at the PBR paper, and I find it pretty unclear. They should give a concrete example in terms of Stern-Gerlach experiments on many-spin systems. The key seems to be what the authors understand under

This Article presents a no-go theorem: if the quantum state
merely represents information about the real physical state
of a system, then experimental predictions are obtained that
contradict those of quantum theory. The argument depends on few
assumptions. One is that a system has a ‘real physical state’—not
necessarily completely described by quantum theory, but objective
and independent of the observer.

What do they understand under "real physical state" concretely (be it mathematically or already physicswise)?

In my opinion, in quantum theory the vectors in quantumtheoretical Hilbert space represent the state of a system completely (pure states) and at the same time imply only probabilistic knowledge. At the same time they are objective, because they are defined by concrete (equivalence classes of) preparation procedures. Is it as in Bell's assumptions that the "real physical state" obeys deterministic rules, i.e., that the complete specification of the "real physical state" implies the determination of all possibe observable of this system? The very existence of quantum theory (in the minimal statistical interpretation) shows that this is not a necessary assumption on our description of nature since quantum theory is very successful in describing nature (in fact the most successful physical theory ever). I don't understand, why a "realistic theory" should be deterministic.

 

[bohm2]

But when you say that the wave function represents something real, are you saying that it is actually a real wave, like sound waves or EM waves?

It isn't anything like a sound or EM wave because it must be non-local. Examples of well-known ψ-ontic models that are still viable after the PBR theorem include de Broglie-Bohm and spontaneous collapse models.

 

[bohm2]

I don't understand, why a "realistic theory" should be deterministic.

It doesn't have to be deterministic. In fact, in the GRW model which is not ruled out by PBR, the wave function randomly collapses; that is, the evolution of the wave function in GRW follows a stochastic jump process in Hilbert space, instead of Schodinger's equation. So just because a model must be ψ-ontic according to PBR, does not imply that any such model must be deterministic.

 

[Nugatory]

But when you say that the wave function represents something real, are you saying that it is actually a real wave, like sound waves or EM waves?

If we compare PBR with Bell's Theorem: It's fair to state the conclusion of Bell's theorem as "No theory that would satisfy EPR can reproduce all the predictions of QM" even though a more precise statement would be "If a theory allows the wave function to be written in a particular form, then that model cannot reproduce all the predictions of QM". This works because the "particular form" will apply to everything that meets our and EPR's informal expectation of a what local hidden variable theory should do.

It's different with PBR, which can be stated as "If there is an underlying ontological reality, then states of that reality must map one-to-one to the wave function, a situation that we define to be ψ-ontic instead of ψ-epistemic"? That's a useful and important statement about the nature of the wave function, but that statement doesn't lead to a similar intuitive clarity about how the world must work.

The price that we pay for the precise PBR definition of "ψ-ontic" is that it allows models that are ψ-ontic but won't satisfy your hunger for a simple answer to the imprecise question "is the wave function real?".

 

[Nick V]

It isn't anything like a sound or EM wave because it must be non-local. Examples of well-known ψ-ontic models that are still viable after the PBR theorem include de Broglie-Bohm and spontaneous collapse models.

I'm asking you, that by saying the wave function is real, or that it is ontic, are you saying that it is a real wave or something else?

 

[Nugatory]

I'm asking you, that by saying the wave function is real, or that it is ontic, are you saying that it is a real wave or something else?

And we are answering that the question is ill-formed, as you are unable to tell us what you mean by "real".

 

[Nick V]

And we are answering that the question is ill-formed, as you are unable to tell us what you mean by "real".

As in real that it is an actual wave in physical space.

 

[Nick V]

like mechanical waves are real. EM waves are real, they both exist in physical space( even though they aren't actual objects)

 

[bohm2]

I'm asking you, that by saying the wave function is real, or that it is ontic, are you saying that it is a real wave or something else?

Something else. It cannot be anything like a classical wave/field in ordinary three-dimensional space.

 

[Nick V]

Something else. It cannot be anything like a classical wave/field in ordinary three-dimensional space.

But isn't that what wave function is supposed to be, a 3 dimensional standing wave?

 

[Nick V]

But isn't that what wave function is supposed to be, a 3 dimensional standing wave?

And when you say it's something else, what do you mean?

 

[Nugatory]

But isn't that what wave function is supposed to be, a 3 dimensional standing wave?

No. It's an element in an infinite-dimensional Hilbert space.

In your first class on QM, which will come after a year and a half of classical mechanics, E&M, and the behavior of classical waves, you will be introduced to the simplest case of quantum mechanics, a single particle in a classical potential. There and only there is it possible to simplify the wave function down to a function that looks like a standing wave in three-dimensional space - but even then the amplitude of the wave will be a complex number.

The more complete treatment of quantum mechanics, which leads into quantum field theory, will come after that.

 

[Nick V]

No. It's an element in an infinite-dimensional Hilbert space.

In your first class on QM, which will come after a year and a half of classical mechanics, E&M, and the behavior of classical waves, you will be introduced to the simplest case of quantum mechanics, a single particle in a classical potential. There and only there is it possible to simplify the wave function down to a function that looks like a standing wave in three-dimensional space - but even then the amplitude of the wave will be a complex number.

So, in psi ontic view that wave function is real, does it exist like a classical wave in physical space , or does it exist as an actual object that is oscillating in physical space?
Or that the wave function is real, but just not a physical object?

 

[Nugatory]

So, in psi ontic view that wave function is real, does it exist like a classical wave in physical space , or does it exist as an actual object that is oscillating in physical space?

Hey, you started this discussion by pointing to the PBR paper... It says what the ψ-ontic view means: roughly that if there is an underlying physical state, positions in that state space can be put in one-to-one correspondence with elements of the set of wave functions.

And no matter what view one takes of the wave function, if you're asking "does it exist like a classical wave in physical space , or does it exist as an actual object that is oscillating in physical space?" the answer is neither. The thing has a complex amplitude, so it can represent neither a classical wave nor the motion of an actual object, and it's defined in an infinite-dimensional Hilbert space instead of three-dimensional physical space.

 

[Nick V]

Hey, you started this discussion by pointing to the PBR paper... It says what the ψ-ontic view means: roughly that if there is an underlying physical state, positions in that state space can be put in one-to-one correspondence with elements of the set of wave functions.

And no matter what view one takes of the wave function, if you're asking "does it exist like a classical wave in physical space , or does it exist as an actual object that is oscillating in physical space?" the answer is neither. The thing has a complex amplitude, so it can represent neither a classical wave nor the motion of an actual object, and it's defined in an infinite-dimensional Hilbert space instead of three-dimensional physical space.

http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
But the PBR paper says that the wave function must be physically real after all. You said that wave function only exists in Hilbert space which would make it not physically real and this would go against the Ψ ontic view. That's why I was asking about the Ψ ontic view: if the wave function is real, would it be existence in physical space like a wave, or would it exist as a physical object.

 

[atyy]

http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
But the PBR paper says that the wave function must be physically real after all. You said that wave function only exists in Hilbert space which would make it not physically real and this would go against the Ψ ontic view. That's why I was asking about the Ψ ontic view: if the wave function is real, would it be existence in physical space like a wave, or would it exist as a physical object.

The Hilbert space can be considered real in Ψ-ontic models. It would be analogous to extra dimensions in string theory that we cannot directly see.

 

[JPBenowitz]

The wave function is a mathematical "object" in an infinite dimensional Hilbert Space, yet our description of spacetime is a real vector space, specifically minkowski spacetime. The wave function being a physical object is incompatible with a minkowski background since this would require an infinite dimensional embedding in 3+1 dimensions. If the wave function is indeed a physical object then this would necessitate that spacetime has a structure very similar to if not identical to Hilbert Space, a Hilbert Spacetime if you will. Under this assumption spacetime events may interfere with one another where the notion of causality is radically different than that of a minkowski background.

 

[Nick V]

The wave function is a mathematical "object" in an infinite dimensional Hilbert Space, yet our description of spacetime is a real vector space, specifically minkowski spacetime. The wave function being a physical object is incompatible with a minkowski background since this would require an infinite dimensional embedding in 3+1 dimensions. If the wave function is indeed a physical object then this would necessitate that spacetime has a structure very similar to if not identical to Hilbert Space, a Hilbert Spacetime if you will. Under this assumption spacetime events may interfere with one another where the notion of causality is radically different than that of a minkowski background.

So your saying that wave function cannot be a physical object?

 

[atyy]

So your saying that wave function cannot be a physical object?

If by definition you consider Hilbert space unphysical, then the wave function cannot be a physical object. However, one can consider the Hilbert space physical, like a sort of hidden extra dimensions.

 

[Nick V]

If by definition you consider Hilbert space unphysical, then the wave function cannot be a physical object. However, one can consider the Hilbert space physical, like a sort of hidden extra dimensions.

But, they can wave function be a real physical object in Hilbert space? Or did nugatory already say that that cannot be?
(Considering that Hilbert space is physical)

 

[atyy]

But, they can wave function be a real physical object in Hilbert space? Or did nugatory already say that that cannot be?

Yes, it is possible to interpret the wave function as a physical object in Hilbert space.

 

[Nick V]

That is one possible interpretation.

Can one view that the wave function is real in the Hilbert space, but just not a physical object?

 

[atyy]

Can one view that the wave function is real in the Hilbert space, but just not a physical object?

I don't understand the distinction you are making.

 

[Nugatory]

http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
But the PBR paper says that the wave function must be physically real after all.

The paper says no such thing, and we've reached a point in the discussion where pointing to that Nature.com article is no substitute for reading and understanding the paper itself. The paper says that any correspondence between an underlying physical state and the wave functions of pure states must be one-to-one. That's a reasonable basis for claiming that the wave function is ontic, but it doesn't take you to "physically real".

 

[Nick V]

I don't understand the distinction you are making.

For example, an EM wave is real, but it is not a physical object. Can one view the wave function as that in the Hilbert space? Would this still be viable with a Ψ ontic view?

 

[atyy]

For example, an EM wave is real, but it is not a physical object. Can one view the wave function as that in the Hilbert space? Would this still be viable with a Ψ ontic view?

I usually consider the EM wave real and a physical object, so I don't understand the distinction.

 

[Nick V]

The paper says no such thing, and we've reached a point in the discussion where pointing to that Nature.com article is no substitute for reading and understanding the paper itself. The paper says that any correspondence between an underlying physical state and the wave functions of pure states must be one-to-one. That's a reasonable basis for claiming that the wave function is ontic, but it doesn't take you to "physically real".

Oh ok.
But, you said that wave function only exists in Hilbert space(I know I might be repeating myself), so is it real and not a physical object in Hilbert space, or is it a real physical object in the Hilbert space?

 

[Nick V]

I usually consider the EM wave real and a physical object, so I don't understand the distinction.

What I mean is that, can one interpret (in Hilbert space) that the wave function is real but is not an actual physical object?

 

[Nick V]

The paper says no such thing, and we've reached a point in the discussion where pointing to that Nature.com article is no substitute for reading and understanding the paper itself. The paper says that any correspondence between an underlying physical state and the wave functions of pure states must be one-to-one. That's a reasonable basis for claiming that the wave function is ontic, but it doesn't take you to "physically real".

And so your saying that the PBR theorem/paper never mentions the wave function as physically real?

 

[Nick V]

The paper says no such thing, and we've reached a point in the discussion where pointing to that Nature.com article is no substitute for reading and understanding the paper itself. The paper says that any correspondence between an underlying physical state and the wave functions of pure states must be one-to-one. That's a reasonable basis for claiming that the wave function is ontic, but it doesn't take you to "physically real".

And isn't a Ψ ontic view of wave function mean that its real? Physically real?

 

[atyy]

What I mean is that, can one interpret (in Hilbert space) that the wave function is real but is not an actual physical object?

Why is the EM wave not a physical object?

 

[Nick V]

Why is the EM wave not a physical object?

I have never really heard that an EM wave or sound wave or any wave is classified as a physical object. But can wave function be real but not a physical object (in Hilbert space)?

 

[atyy]

I have never really heard that an EM wave or sound wave or any wave is classified as a physical object. But can wave function be real but not a physical object (in Hilbert space)?

I don't know. I do think of an EM wave or a sound wave as a physical object, which is what I mean by real.

 

[Nick V]

I don't know. I do think of an EM wave or a sound wave as a physical object, which is what I mean by real.

But I don't think that they are considered physical objects because they are not matter, so they are real but just not physical.

 

[atyy]

But I don't think that they are considered physical objects because they are not matter, so they are real but just not physical.

You mean they are not solid objects, like a table or a cat?

 

[bohm2]

But I don't think that they are considered physical objects because they are not matter, so they are real but just not physical.

I don't understand this part. What is your criteria for considering something as being a "physical" or "material" object? And let's assume you suggest some criteria. Why should one accept it? After all, what is considered "physical" or "material" is based on our best theories/models in physics and this changes as our physics evolves. It's not as if we have some definite and fixed conception of what physical must be, independent of our best theories in physics.

 

[vanhees71]

The paper says no such thing, and we've reached a point in the discussion where pointing to that Nature.com article is no substitute for reading and understanding the paper itself. The paper says that any correspondence between an underlying physical state and the wave functions of pure states must be one-to-one. That's a reasonable basis for claiming that the wave function is ontic, but it doesn't take you to "physically real".

This is not even true for minimally interpreted quantum theory (and that's the only interpretation that does not lead to contradictions with basic principles like causality): A pure state is represented by a ray in Hilbert space.

I still don't understand don't understand what "real" means in this thread, but if anything is "real" concerning quantum states, it's rays in Hilbert space. I would define an object in a physical theory "real" if it can be measured somehow in the real world. In this sense the quantum states are not real, because their physical content is probabilistic and thus can be checked in the lab only by preparing many independent realizations of the corresponding system and measure some observables on them. At the same time the quantum states are objective, because interpreted in this way they are operationally defined by (an equivalence class of) preparation procedures, e.g., how to prepare electrons with a certain momentum within given limits of accuracy (an electron never can have a sharp momentum as in classical physics however, due to the uncertainty relation, but in principle it can be determined with any accuracy you like). The "preparation procedure" is, e.g., an accelerator with all kinds of tricks to get electrons with a "well-defined" momentum. These are for sure real objects in the real worlds, and in this sense the states are "real" in the sense of preparation procedures.

I've the impression PBR's ontology is demanding more than quantum theory in the minimal interpretation, namely that all observables of a quantum object should "in reality" have determined values. That means they take the state description as "real" only if it determines all possible observables, but this contradicts quantum theory, and so far nobody has found an alternative theory which is as successful. Also it seems to me that PBR don't give any description of how the alternatives of an ontic vs. an epistemic interpretation of QT states can be distinguished experimentally in the "real world". That makes their ideas a bit limited in the sense of natural science.

An example of this kind is Bell's work. First of all he gives a clear mathematical description to the "reality" in the sense of EPR and then proves a theorem (the famous "Bell inequality") that can be tested in the "real world" by doing experiments, and this has been done with high accuracy (starting with Aspect's work in the 80ies). The outcome is very clear: If there is a deterministic theory reproducing the quantum probabilities it must be a non-local one, and so far nobody has been able to formulate such a theory. At the same time the predictions of QT have been confirmed.

 

[atyy]

I've the impression PBR's ontology is demanding more than quantum theory in the minimal interpretation, namely that all observables of a quantum object should "in reality" have determined values. That means they take the state description as "real" only if it determines all possible observables, but this contradicts quantum theory, and so far nobody has found an alternative theory which is as successful. Also it seems to me that PBR don't give any description of how the alternatives of an ontic vs. an epistemic interpretation of QT states can be distinguished experimentally in the "real world". That makes their ideas a bit limited in the sense of natural science.

Yes, the real motivation for PBR should be seen as the measurement problem, which requires additional variables to be introduced (unless MWI works). One can roughly think of the PBR hidden variables in the Bohmian sense. Bohmian Mechanics is not a full solution of the measurement problem, but a restatement of quantum mechanics in a form that looks like classical kinetic theory. The uncertainty is traced back to a "quantum equilibrium" distribution of initial positions. However, by analogy to classical kinetic theory, there should be an H-theorem that shows how equilibrium is attained from nonequilibrium. Valentini argued that there is an H-theorem for de Broglie dynamics in the Bohmian framework. Bohmian Mechanics in nonequilibrium should produce deviations from quantum mechanics, and so is in principle testable. Similarly, all other hidden variable theories considered by PBR that do reproduce quantum mechanics should do so only in some regime, and should deviate from quantum mechanics beyond that regime, In that sense, the theories considered by PBR are all testable in principle.

An example of this kind is Bell's work. First of all he gives a clear mathematical description to the "reality" in the sense of EPR and then proves a theorem (the famous "Bell inequality") that can be tested in the "real world" by doing experiments, and this has been done with high accuracy (starting with Aspect's work in the 80ies). The outcome is very clear: If there is a deterministic theory reproducing the quantum probabilities it must be a non-local one, and so far nobody has been able to formulate such a theory. At the same time the predictions of QT have been confirmed.

Indeed. However, the main problem lies in the same place as a lattice formulation of the standard model: chiral fermions interacting with non-abelian gauge fields.

 

[vanhees71]

My problem is PBR then is, why they rule out that quantum theory is valid as it is now (in the minimal interpretation), if you want to call the state ontic? Why can't it be true in an ontic interpretation of the quantum state that only those observables have a sharp value (or determined values at high accuracy if it's not possible for the observable to have a sharp value, which is always the case with observables that have only continuous values as position and momentum) that have them because of the preparation of the system in a state such that this is the case? Then quantum theory simply implies that not all observables can have determined values at once. If nature is like this (and I think a lot of very accurate findings hint that this might be actually the case), it's like this, and then quantum theory in the minimal interpretation is "realistic". So what?

 

[atyy]

My problem is PBR then is, why they rule out that quantum theory is valid as it is now (in the minimal interpretation), if you want to call the state ontic? Why can't it be true in an ontic interpretation of the quantum state that only those observables have a sharp value (or determined values at high accuracy if it's not possible for the observable to have a sharp value, which is always the case with observables that have only continuous values as position and momentum) that have them because of the preparation of the system in a state such that this is the case? Then quantum theory simply implies that not all observables can have determined values at once. If nature is like this (and I think a lot of very accurate findings hint that this might be actually the case), it's like this, and then quantum theory in the minimal interpretation is "realistic". So what?

That sense of ontic is not ruled out by PBR, they simply don't address it. I don't think PBR is interesting unless one is also asking what potential solutions of the measurement problem can look like.

Actually, the epistemic interpretation of the wave function has problems in the minimal interpretation (Copenhagen!), which is why I usually say "the wave function is not necessarily real, and is a tool to calculate the probabilities of events". Here I do intend to loosely use the "epistemic" view when I say the wave function is a "tool", but by saying that it is not "necessarily real" I don't rule out that it is "ontic". It is hard to transition from this loose use of the term "epistemic" to something sharp. The traditional analogy is that collapse is like throwing a die, and getting a definite result after the die is thrown. In classical probability, the updating after the die is thrown is usually done by Bayes rule, but the analogy is very partial when one really tries to work it out. I think one can see caution in the text by Cohen-Tannoudji, Diu and Laloe, where they don't commit to a purely epistemic view, although they clearly indicate that it helps the intuition to think of collapse in this way.

Two very good attempts that only partially succeed in making the analogy between collapse and Bayesian updating are:
http://arxiv.org/abs/quant-ph/0106166
http://arxiv.org/abs/1107.5849

To get around this, one may say that quantum theory is a generalization of probability theory. But then one may question whether classical probability is really failing, and the hidden variables approaches indicate that one need not generalize classical probability theory, and that quantum mechanics is a special case of classical probability theory.

 

[Nick V]

Why is the EM wave not a physical object?

Here's the bottom line of what I am asking you, In Ψ ontic view ( wave function is real), is like a wave like an EM wave or any other classical wave, or is it an real object that is waving, like a piece of string that is waving?

 

[atyy]

Here's the bottom line of what I am asking you, In Ψ ontic view ( wave function is real), is like a wave like an EM wave or any other classical wave, or is it an real object that is waving, like a piece of string that is waving?

In the Ψ-ontic view, the wave function is a wave like an EM wave. However, the wave function is a wave in Hilbert space, and whereas an EM wave is a wave in spacetime.

 

[Nick V]

In the Ψ-ontic view, the wave function is a wave like an EM wave. However, the wave function is a wave in Hilbert space, and whereas an EM wave is a wave in spacetime.

Ok, so your saying that it's not the like a physical object that's waving like a piece of string that's waving. But, don't Ψ ontic interpretations of QM ( ie. many worlds, de broglie, penrose interpretations) require the wave function to exist in space time? Atleast that's what I read on the Wave Function wikipedia under ontology.

 

[atyy]

Ok, so your saying that it's not the like a physical object that's waving like a piece of string that's waving. But, don't Ψ ontic interpretations of QM ( ie. many worlds, de broglie, penrose interpretations) require the wave function to exist in space time? Atleast that's what I read on the Wave Function wikipedia under ontology.

In both MWI and dBB, the wave function is not a wave in spacetime , it is a wave in Hilbert space.

 

[Nick V]

In both MWI and dBB, the wave function is not a wave in spacetime , it is a wave in Hilbert space.

OK, so the Ψ ontic view of the wave function (MWI, dBB, any other Ψ ontic interpretation), the wave function is real. But the wave function is physically real only in Hilbert space, correct?

 

[atyy]

OK, so the Ψ ontic view of the wave function (MWI, dBB, any other Ψ ontic interpretation), the wave function is real. But the wave function is physically real only in Hilbert space, correct?

The wave function exists only in Hilbert space in all interpretations of QM, so yes, it is real only in Hilbert space in Ψ-ontic proposals such as MWI and dBB.