PBR theorem

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Main Question or Discussion Point

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?
 

Answers and Replies

  • #3
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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.
 
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  • #4
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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.
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?
 
  • #5
vanhees71
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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.
 
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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?
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.
 
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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.
 
  • #8
Nugatory
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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?".
 
  • #9
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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.
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?
 
  • #10
Nugatory
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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 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".
 
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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".
As in real that it is an actual wave in physical space.
 
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like mechanical waves are real. EM waves are real, they both exist in physical space( even though they aren't actual objects)
 
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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 real wave or something else?
Something else. It cannot be anything like a classical wave/field in ordinary three-dimensional space.
 
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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?
 
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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?
 
  • #16
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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.
 
  • #17
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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?
 
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  • #18
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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 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.
 
  • #20
atyy
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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 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.
 
  • #21
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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.
 
  • #22
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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?
 
  • #23
atyy
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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.
 
  • #24
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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)
 
  • #25
atyy
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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.
 

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