PBR & Relativity: Wave Function Uniqueness?

[atyy]

In relativity, the wave function in different frames is not unitarily related, because the wave function collapses at different times. For example, in a Bell experiment, in a frame in which Alice and Bob measure simultaneously, there is no collapse. But in a frame in which Alice measures before Bob, Alice collapses the wave function. Here it seems that there are multiple wave functions for the same situation, but PBR says that the true state (including hidden variables) implies a unique wave function. Does PBR apply, because the true state is different in each frame (a state requires a choice of simultaneity), or does PBR not apply?

 

[Morbert]

but PBR says that the true state (including hidden variables) implies a unique wave function

I think this is probably too strong a statement. Instead I think the PBR theorem only implies the wavefunction cannot simply represent knowledge of an underlying physical state. We do not have to commit to a real wavefunction if we do not attempt to model an underlying physical state. We can for example interpret the wavefunction as representing knowledge of experimental outcomes.

 

[Demystifier]

The PBR theorem considers a single measurement by a single observer. It does not consider two or more measurements at different times, so the collapse does not play any role in the theorem. Hence the PBR theorem as such cannot say anything about multiple wave functions associated with different observers. But it would be interesting to study generalizations.

 

[atyy]

I think this is probably too strong a statement. Instead I think the PBR theorem only implies the wavefunction cannot simply represent knowledge of an underlying physical state. We do not have to commit to a real wavefunction if we do not attempt to model an underlying physical state. We can for example interpret the wavefunction as representing knowledge of experimental outcomes.

Yes, I mean assuming hidden variables.

 

[Demystifier]

Yes, I mean assuming hidden variables.

If there are hidden variables a'la Bohmian particle positions, then there is no wave function collapse of the full wave function of the universe. What collapses are the conditional wave functions (*). Even with an absolute Newtonian time, different observers naturally define different conditional wave functions. That's because they condition on different available knowledge they have access to. So yes, there are multiple conditional wave functions, but they are fully compatible with the fact that there is only one wave function of the universe.

(*) For the notion of conditional wave function see e.g. pages 23-24 in my lecture
http://thphys.irb.hr/wiki/main/images/e/e6/QFound4.pdf

 

[atyy]

If there are hidden variables a'la Bohmian particle positions, then there is no wave function collapse of the full wave function of the universe. What collapses are the conditional wave functions (*). Even with an absolute Newtonian time, different observers naturally define different conditional wave functions. That's because they condition on different available knowledge they have access to. So yes, there are multiple conditional wave functions, but they are fully compatible with the fact that there is only one wave function of the universe.

(*) For the notion of conditional wave function see e.g. pages 23-24 in my lecture
http://thphys.irb.hr/wiki/main/images/e/e6/QFound4.pdf

Yes, but the full Bohmian wave function is not the quantum state. The quantum state is the collapsed wave function, and PBR applies to the quantum state.

 

[Demystifier]

Yes, but the full Bohmian wave function is not the quantum state. The quantum state is the collapsed wave function, and PBR applies to the quantum state.

Fine. Then I propose the following conjecture (as a generalization of the PBR theorem to multiple observers):
When there are multiple ontic observers $o_1,o_2,...$, then wave function $\psi_{o_k}$ (associated with any observer $o_k$) is ontic and uniquely defined by $o_k$ and other ontic stuff.

 

[atyy]

Fine. Then I propose the following conjecture (as a generalization of the PBR theorem to multiple observers):
When there are multiple ontic observers $o_1,o_2,...$, then wave function $\psi_{o_k}$ (associated with any observer $o_k$) is ontic and uniquely defined by $o_k$ and other ontic stuff.

Hmmm, so the wave function is still epistemic in some sense? I guess the Bohmian conditional wave function is epistemic?

 

[Demystifier]

Hmmm, so the wave function is still epistemic in some sense? I guess the Bohmian conditional wave function is epistemic?

Yes, the conditional wave function can be considered "epistemic" in the sense that it depends on knowledge of the observer. But if knowldge itself is represented by something ontic (e.g. the ontic state of the brain), then the conditional wave function is naturally viewed as ontic.

 

[Sunil]

Does PBR apply, because the true state is different in each frame (a state requires a choice of simultaneity), or does PBR not apply?

PBR presupposes realism. It is essentially a theorem which tells that if there is some reality, then the wave function should be part of it.

But if you presuppose realism, you have to reject Einstein causality anyway (except you go completely insane accept great conspiracy of superdeterminism) and to go back to a preferred frame. So, PBR is irrelevant for interpretations which want fundamental relativistic symmetry instead of a preferred frame.

Anyway, PBR is a misguided impossibility theorem proving the impossibility of things already known to exist. The counterexample is Caticha's entropic dynamics:

Caticha, A. (2011). Entropic Dynamics, Time and Quantum Theory, J. Phys. A 44 , 225303, arxiv:1005.2357

The error in the theorem is a misguided definition of psi-ontology: There should be no overlap for different wave functions. But in an objective epistemic interpretation, where the state is defined by objective information about the preparation procedure and its result, this objective incomplete information is part of reality (not of the system, but so what) too.

 

[atyy]

Yes, the conditional wave function can be considered "epistemic" in the sense that it depends on knowledge of the observer. But if knowldge itself is represented by something ontic (e.g. the ontic state of the brain), then the conditional wave function is naturally viewed as ontic.

So if consciousness is due to the ontic state of the brain, consciousness causes collapse?

 

[Demystifier]

The error in the theorem is a misguided definition of psi-ontology

A definition may indeed be misguided, but I wouldn't call it an "error in the theorem". In the worst case it can make the theorem irrelevant or uninteresting, but not wrong.

 

[atyy]

PBR presupposes realism. It is essentially a theorem which tells that if there is some reality, then the wave function should be part of it.

But if you presuppose realism, you have to reject Einstein causality anyway (except you go completely insane accept great conspiracy of superdeterminism) and to go back to a preferred frame.

Yes, for the discussion here, let's assume reality and reject Einstein causality (to discuss PBR).

 

[Demystifier]

So if consciousness is due to the ontic state of the brain, consciousness causes collapse?

Yes. But it should be stressed once again that it's collapse of the conditional wave function, while the full wave function remains intact.

 

[Sunil]

Instead I think the PBR theorem only implies the wavefunction cannot simply represent knowledge of an underlying physical state. We do not have to commit to a real wavefunction if we do not attempt to model an underlying physical state. We can for example interpret the wavefunction as representing knowledge of experimental outcomes.

No. PBR seems to imply this but fails. The problem is that knowledge of the preparation procedure is also part of reality. Last but not least, the measurement devices and the record about the preparation procedure are part of reality. Even more, the mind having that incomplete knowledge is also part of reality too. So, if reality is fixed completely, the incomplete information about the system in that mind is fixed too, thus, the corresponding pure state of the quantum system is fixed too. So, it is psi-ontological by definition of psi-ontology.

 

[Sunil]

A definition may indeed be misguided, but I wouldn't call it an "error in the theorem". In the worst case it can make the theorem irrelevant or uninteresting, but not wrong.

Same situation as with von Neumann's impossibility theorem. Also not wrong but misleading, given the counterexample.

Except that Bohmian mechanics came later, while the counterexample for PBR, Caticha's entropic dynamics, came even before the theorem. A side effect of publish or perish science - people simply cannot know all relevant papers even in the domain they are working.

 

[atyy]

Yes. But it should be stressed once again that it's collapse of the conditional wave function, while the full wave function remains intact.

Wonderful, so Bohmian mechanics proves the Copenhagen "knowledge" interpretation, and even von Neumann's interpretation (my personal favourite).

Ok, just to make sure I understand you correctly - in Bohmian mechanics, the conditional wave function is different for different observers because different Copenhagen observers who are part of Bohmian reality are still free to decide when the Copenhagen measurement occurs?

 

[Sunil]

Ok, just to make sure I understand you correctly - in Bohmian mechanics, the conditional wave function is different for different observers because different Copenhagen observers who are part of Bohmian reality are still free to decide when the Copenhagen measurement occurs?

They have different splits between the classical and the quantum part. The classical part is the one where they can see the trajectory, the quantum part is the part where they don't have information about trajectory, but only about the wave function. So Wigner's friend may be yet in the quantum part of Wigner, thus, giving him a cat-like wave function, simply because his real trajectory is not known to Wigner, while the friend himself knows his own trajectory well.

 

[Demystifier]

Wonderful, so Bohmian mechanics proves the Copenhagen "knowledge" interpretation, and even von Neumann's interpretation (my personal favourite).

Ok, just to make sure I understand you correctly - in Bohmian mechanics, the conditional wave function is different for different observers because different Copenhagen observers who are part of Bohmian reality are still free to decide when the Copenhagen measurement occurs?

Yes, except that I would put "free to decide" in quotation marks, because the observers obey the deterministic Bohmian laws too. A freedom to decide is just al illusion emerging from coarse graining.

 

[martinbn]

In relativity, the wave function in different frames is not unitarily related, because the wave function collapses at different times. For example, in a Bell experiment, in a frame in which Alice and Bob measure simultaneously, there is no collapse. But in a frame in which Alice measures before Bob, Alice collapses the wave function. Here it seems that there are multiple wave functions for the same situation, but PBR says that the true state (including hidden variables) implies a unique wave function. Does PBR apply, because the true state is different in each frame (a state requires a choice of simultaneity), or does PBR not apply?

Isn't this just an argument showing that there is no collapse even when one of them mesures first.

 

[atyy]

Yes, except that I would put "free to decide" in quotation marks, because the observers obey the deterministic Bohmian laws too. A freedom to decide is just al illusion emerging from coarse graining.

I think I roughly see what you mean especially from @Sunil's Wigner friend in Bohmian mechanics example. But in the relativistic Bell experiment, it seems that there are not different classical-quantum cuts, just a change of frame? If we assume emergent relativity in Bohmian mechanics, what is happening there?

 

[Demystifier]

But in the relativistic Bell experiment, it seems that there are not different classical-quantum cuts, just a change of frame? If we assume emergent relativity in Bohmian mechanics, what is happening there?

That's certainly interpretation dependent. If collapse is observer-independent as in GRW theory, then you are right. But if collapse depends on what information an agent does or does not possesses (as in QBism, for instance), then it cannot be just a change of frame.

In the Bohmian interpretation, the collapse of the conditional wave function depends on the choice of conditioned variables, that is, particle positions treated as known. Since it's natural to identify the conditioned variables with the variables of an agent, such as agent's apparatus variables or agent's brain variables, it follows that in Bohmian interpretation it's not just a change of frame.

But Bohmian mechanics allows you to choose the conditioned variables in many different ways. One interesting choice is to condition on all agents at once, which, I think, is something that does not have an analog in QBism or von Neumann collapse by consciousness. In this way you obtain collapse without being forced to choose either one agent or the other, so it's a kind of collapse that does "not depend" on choice of the agent.

 

[Demystifier]

They have different splits between the classical and the quantum part. The classical part is the one where they can see the trajectory, the quantum part is the part where they don't have information about trajectory, but only about the wave function. So Wigner's friend may be yet in the quantum part of Wigner, thus, giving him a cat-like wave function, simply because his real trajectory is not known to Wigner, while the friend himself knows his own trajectory well.

Well said! I would only add that the friend knows his own trajectory only in a coarse grained sense. He does not know the precise Bohmian trajectories of individual particles, for otherwise he could prove that the Bohmian interpretation is right.

 

[atyy]

In the Bohmian interpretation, the collapse of the conditional wave function depends on the choice of conditioned variables, that is, particle positions treated as known. Since it's natural to identify the conditioned variables with the variables of an agent, such as agent's apparatus variables or agent's brain variables, it follows that in Bohmian interpretation it's not just a change of frame.

What I'm thinking of is that in Copenhagen, the collapse is typically frame dependent. If there is emergent relativitvistic quantum theory in Bohmian mechanics, then wouldn't it be possible to derive the frame-dependent collapse of Copenhagen from Bohmian mechanics?

 

[Demystifier]

What I'm thinking of is that in Copenhagen, the collapse is typically frame dependent. If there is emergent relativitvistic quantum theory in Bohmian mechanics, then wouldn't it be possible to derive the frame-dependent collapse of Copenhagen from Bohmian mechanics?

It depends. How exactly do you formulate frame dependence in Copenhagen? Clearly, you must use relativistic quantum theory. How do you formulate Schrödinger evolution (before collapse) in relativistic theory? Do you use many-time formalism? Or do you use many states, one for each possible choice of the time coordinate?

 

[atyy]

It depends. How exactly do you formulate frame dependence in Copenhagen? Clearly, you must use relativistic quantum theory. How do you formulate Schrödinger evolution (before collapse) in relativistic theory? Do you use many-time formalism? Or do you use many states, one for each possible choice of the time coordinate?

I'm not familiar with the many time formalism, so I guess it is many states. But I haven't heard that term before, so an example of what I'm thinking of is the picture in Fig 1 of https://arxiv.org/abs/0706.1232.

 

[Demystifier]

I'm not familiar with the many time formalism, so I guess it is many states. But I haven't heard that term before, so an example of what I'm thinking of is the picture in Fig 1 of https://arxiv.org/abs/0706.1232.

In the item 1. below the picture it is said that Lorentz covariance is true only at the level of probabilities, not at the level of states. Since Bohmian and Copenhagen interpretations predict the same probabilities (of measurement outcomes), I think it answers your question.

 

[atyy]

In the item 1. below the picture it is said that Lorentz covariance is true only at the level of probabilities, not at the level of states. Since Bohmian and Copenhagen interpretations predict the same probabilities (of measurement outcomes), I think it answers your question.

ie. in Bohmian mechanics, if there is emergent relativity in the true ether frame, then one can use any Copenhagen frame (with different collapse in each frame) to obtain the same answer as the true ether frame?

 

[Demystifier]

ie. in Bohmian mechanics, if there is emergent relativity in the true ether frame, then one can use any Copenhagen frame (with different collapse in each frame) to obtain the same answer as the true ether frame?

If by "answer" you mean probability of the measurement outcome, then yes.

 

[Demystifier]

Isn't this just an argument showing that there is no collapse even when one of them mesures first.

Which interpretation of QM without collapse do you have in mind? If it's statistical ensemble, is it the Ballentine's version or the vanhees's version? Or perhaps you mean many worlds? Or what?

My point is that you cannot just say that there is no collapse without putting it into a consistent framework of thinking.