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- Thread starter Nick V
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PBR does not rule out the existence of a theory that would satisfy EPR.In summary, the PBR theorem states that the wave function of a quantum system only represents information about the real physical state of the system, and experimental predictions are not always reproduced by quantum theory.f

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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.

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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.

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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?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.

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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.

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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.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?

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It doesn't have to be deterministic. In fact, in the GRW model which is not ruled out by PBR, the wave functionI don't understand, why a "realistic theory" should be deterministic.

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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?".

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I'm asking you, that by saying the wave function is real, or that it is ontic, are you saying that it is a realIt 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.

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And we are answering that the question is ill-formed, as you are unable to tell us what you mean by "real".I'm asking you, that by saying the wave function is real, or that it is ontic, are you saying that it is a realwaveor something else?

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As in real that it is an actual wave in physical space.And we are answering that the question is ill-formed, as you are unable to tell us what you mean by "real".

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Something else. It cannot be anything like a classical wave/field in ordinary three-dimensional space.I'm asking you, that by saying the wave function is real, or that it is ontic, are you saying that it is a realwaveor something else?

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But isn't that what wave function is supposed to be, a 3 dimensional standing wave?Something else. It cannot be anything like a classical wave/field in ordinary three-dimensional space.

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And when you say it's something else, what do you mean?But isn't that what wave function is supposed to be, a 3 dimensional standing wave?

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No. It's an element in an infinite-dimensional Hilbert space.But isn't that what wave function is supposed to be, a 3 dimensional standing wave?

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.

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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?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.

Or that the wave function is real, but just not a physical object?

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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.

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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

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http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

But the PBR paper says that the wave function must bephysicallyreal 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.

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

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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.

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But, they can wave function be a real physicalIf 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.

(Considering that Hilbert space is physical)

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But, they can wave function be a real physicalobjectin 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.

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

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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.

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http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

But the PBR paper says that the wave function must bephysicallyreal 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".

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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 don't understand the distinction you are making.

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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.

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Oh ok.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".

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?

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What I mean is that, can one interpret (in Hilbert space) that the wave function is real but is not an actual physical object?I usually consider the EM wave real and a physical object, so I don't understand the distinction.

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

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

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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?

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