A Realization of a Basic Wigner's Friend Type Experiment

[charters]

Primarily, although if you wish to include QBism that is fine as well.

The problem is F and W don't agree whether F gets entangled with the qubit or causes a collapse. In the former case, the state after F measures the qubit is (4) on pg 7 of Felline. In the latter the state is either (5) or (6). These behave differently "at the second beamsplitter" and affect W's measurement on the +/- or "ok/fail" basis. Observers who share a reality can't disagree about this.

But I stress this is only a provisional problem, not a knockout inconsistency in QT that makes it un-usable. It can be cured in various ways. At least some QBists pay the price of accepting QT as a single user theory, and adopting a general worldview along these lines. Spekkens, Bohmians, TSVF go to hidden variables. MWI and GRW have their obvious answers. But the pied piper has to be paid in some way. The neo-Copenhagen/informational folks seem to deny the existence of price they pay (single user) so I am reluctant to credit them with having a tenable position by imputing one of the acceptable cures.

 

[DarMM]

The problem is F and W don't agree whether F gets entangled with the qubit or causes a collapse. In the former case, the state after F measures the qubit is (4) on pg 7 of Felline. In the latter the state is either (5) or (6). These behave differently "at the second beamsplitter" and affect W's measurement on the +/- or "ok/fail" basis. Observers who share a reality can't disagree about this.

Okay let us stick to Spekkens model for the moment. It can be seen in that model that Wigner uses a state like $|000\rangle + |111\rangle$ but this is not in conflict with the $|00\rangle$ of the friend. I agree with Baumann in the paper you linked with above that the friend would be wrong to conclude that the state of the entire lab is $|000\rangle$.

Now how does the use of $|000\rangle + |111\rangle$ by Wigner and $|00\rangle$ by the friend imply solpsism of some form?

 

[charters]

Now how does the use of |000⟩+|111⟩|000⟩+|111⟩|000\rangle + |111\rangle by Wigner and |00⟩|00⟩|00\rangle by the friend imply solpsism of some form?

It doesn't. The problem is when Wigner measures on the +/- basis. The state after F measures, but before the path recombination is either

W says: |00>+|11> ⊗|ready to measure >

or

F says: |00>⊗|ready to measure >

After (attempted) recombination, these become:

W says: |0+1>⊗|F's brain erased>⊗|+>

or

F says: |00+>+|00->

W says he never gets |->, F says W does. F rejects the premise that (properly) wiping his brain restores the original state of the qubit, W assumes it does. If both these people are correct, they don't share a reality.

 

[DarMM]

Sorry perhaps I'm missing something. Wigner and the Friend have the same number of qubits there. Wigner should have three (system, device, lab) and the friend two (system, device).

 

[charters]

Sorry perhaps I'm missing something. Wigner and the Friend have the same number of qubits there. Wigner should have three (system, device, lab) and the friend two (system, device).

The tension arises when Friend makes a prediction about what Wigner will measure. Are you claiming this is impossible?

 

[DarMM]

The tension arises when Friend makes a prediction about what Wigner will measure. Are you claiming this is impossible?

For the friend to make predictions about what Wigner will measure? No, but what is the tension? He would reason his own experiences permit the use of $|00\rangle$ in future predictions about the system and the device. However he would reason the superposed state is the correct one for Wigner to use rather than $|000\rangle$. Neo-Copenhagenists such as Richard Healey and others agree that the superposed state is correct for measurements on the entire lab that Wigner is capable of. How is this in tension with the $|00\rangle$ for the device and system?

 

[charters]

For the friend to make predictions about what Wigner will measure? No, but what is the tension? He would reason his own experiences permit the use of $|00\rangle$ in future predictions about the system and the device. However he would reason the superposed state is the correct one for Wigner to use rather than $|000\rangle$. Neo-Copenhagenists such as Richard Healey and others agree that the superposed state is correct for measurements on the entire lab that Wigner is capable of. How is this in tension with the $|00\rangle$ for the device and system?

If the device-system is in |00>, it does not behave the same under recombination as |00>+|11>. Friend can't have it both ways. Either he thinks the state collapsed to |00> in which case he predicts no interference effects from the |11> term under recombination, or he thinks the device/system got entangled, in which case he does predict interference effects. Friend can even pass a note to Wigner with this prediction on it as it does not depend on whether Friend saw 0 or 1.

Or, if Friend's state is only valid up to Wigner's choice to do a recombination experiment, at which point Friend has to switch to using Wigner's state (this being one of Baumann & Brukner's ideas to resolve the tension), then Friend is admitting they need MWI or HV type reasoning, at least in some cases/for some predictions. At this point, they might as well just apply this full time, since it will work in all cases.

 

[DarMM]

If the device-system is in |00>, it does not behave the same under recombination as |00>+|11>

You're dropping a system here which is crucial. The friend is using $|00\rangle$ (note two systems) and Wigner is using $|000\rangle + |111\rangle$ (note three systems). The question concerns what is the conflict between the $|00\rangle$ used by the friend and the $|000\rangle + |111\rangle$ used by Wigner.

Wigner does not use $|00\rangle + |11\rangle$

 

[charters]

You're dropping a system here which is crucial. The friend is using $|00\rangle$ (note two systems) and Wigner is using $|000\rangle + |111\rangle$ (note three systems). The question concerns what is the conflict between the $|00\rangle$ used by the friend and the $|000\rangle + |111\rangle$ used by Wigner.

Wigner does not use $|00\rangle + |11\rangle$

This notational difference doesn't matter. The physical experiment is equivalent to Wigner sending Friend's entire lab through an interferometer. The interferometer has 2 exit ports labelled |+> and |->. The question to both parties is simply the statistics for when the lab arrives at each exit. W says it is 100% at |+> when he does a recombination. F says it will be 50/50, if he genuinely believes his measurement collapsed the state. So either someone discovers he is wrong, or they must live in disjoint realities. Friend is wrong = many worlds/hidden variables. Wigner is wrong = GRW. Disjoint realities = Copenhagen/QBism

 

[DarMM]

This notational difference doesn't matter...F says it will be 50/50, if he genuinely believes his measurement collapsed the state

It does, because it is central to how QBism and Neo-Copenhagenism resolve this point. Why would the friend using the $|00\rangle$ state after his measurement believe the outcome of such an interferometry experiment on the entire lab to have 50:50 odds? To obtain these odds for the entire lab he'd have to ascribe it the state $|000\rangle$, but why would he do this on the basis of the $|00\rangle$ state for the device and system alone? He didn't observe the lab down to the atomic level.

 

[charters]

It does, because it is central to how QBism and Neo-Copenhagenism resolve this point. Why would the friend using the $|00\rangle$ state after his measurement believe the outcome of such an interferometry experiment on the entire lab to have 50:50 odds? To obtain these odds for the entire lab he'd have to ascribe it the state $|000\rangle$, but why would he do this on the basis of the $|00\rangle$ state for the device and system alone? He didn't observe the lab down to the atomic level.

Any other system in the lab (which can be arbitrarily small apart from F) has no significance. It either records the |0> outcome via decoherence (and then is controlled in recombination) or it remains isolated/irrelevant/in its preparation state, and plays a trivial role in the experiment. Interference effects are not predicted based on other subsystems in the lab. They come from the relative phase of the|1> term, same as any double slit or MZI. The only relevant question for predicting interference is if you think the |1> term still exists or was genuinely "collapsed away."

 

[DarMM]

Any other system in the lab (which can be arbitrarily small apart from F) has no significance. It either records the |0> outcome via decoherence (and then is controlled in recombination) or it remains isolated/irrelevant/in its preparation state, and plays a trivial role in the experiment. Interference effects are not predicted based on other subsystems in the lab.

Of course they're not, the superposition is for the entire lab. However I don't see the relevance of this. The question can be simplified as follows. The device showing $0$ implies the Friend's description of the device and system is $|00\rangle$, but why would this imply the absence of the $|111\rangle$ term for Wigner's description of the whole lab?

As I showed in the post I linked to it doesn't even imply its absence in Spekkens toy model.

 

[charters]

Of course they're not, the superposition is for the entire lab. However I don't see the relevance of this

Neither do I, but you brought up that he doesn't "observe the lab down to the atomic level."

why would this imply the absence of the $|111\rangle$ term for Wigner's description of the whole lab?

Because this is the definition of a collapse/state reduction due to F's measurement. There is still a possibility of 1 for Wigner because he lacks information re which collapse outcome obtained. But for anyone who believes a collapse has in fact occured, thereafter there can be no prediction of interference between the 0 and 1 outcomes anymore, so for someone with this belief, there's no guarantee of Wigner getting |+> .

As I showed in the post I linked to it doesn't even imply its absence in Spekkens toy model.

This has HVs instead of collapse, its not the same analysis.

 

[DarMM]

Neither do I, but you brought up that he doesn't "observe the lab down to the atomic level."

Because this is the definition of a collapse/state reduction due to F's measurement

Why does the collapse have to occur on all scales though? The Friend observes his system and device obtaining $0$ and thus updates his state for the system and device. Why would he update the state of the whole lab in the manner you mention. Especially in the realistic case where the lab environment forms most of the state?

This has HVs instead of collapse, its not the same analysis

What difference does this make though in this particular case? Look at what Spekkens model says. Collapse at one level does not imply collapse at all levels. Collapsing the state of the system and device does not mean you should collapse the lab state. Why? Because the lab state concerns a much larger set of variables, including a multitude you have no knowledge of and performed no measurements on.
Further more QM shows this. Trace out the lab environment and one is able form a Boolean lattice around device observables.

So why can't we take the same explanation in QM. Rather than solipsism we see that the superposed state for the entire lab is consistent with definite outcomes for the device, but also encodes statistics for atomic level observations.

 

[charters]

Why would he update the state of the whole lab in the manner you mention

It doesn't matter if he does or doesn't. All that matters is whether you believe, for any given subsystem which *was* measured, does the unobtained outcome for that subsystem still exist in some way, with its proper relative phase, such that it can later on recombine with your outcome. The collapse thesis is no, as saying yes is tacit acceptance of MWI type branching.

the lab state concerns a much larger set of variables, including a multitude you have no knowledge of and performed no measurements on.

Again, the status of any such variables is irrelevant for the prediction of the interference experiment succeeding or failing.

The difference with Spekkens is you can use the HVs, ie the existence of the hidden ontic state can preserve the necessary information from the original preparation state to predict the + outcome only (same basic deal as in Bohm). In collapse, this information is truly, non-unitarily lost.

Matt Pusey discusses Copenhagen versus Spekkens in the context of Wigner's Friend a little in this short editorial: https://www.nature.com/articles/s41567-018-0293-7?WT.feed_name=subjects_quantum-mechanics

Spekkens is really not helpful to this issue. His idea is psi-epistemic within the ontological models framework, not pure epistemic, and he solves Wigners Friend basically the same way as Bohm. Another way to see the difference is QBism/Bub has no PBR theorem problem, but Spekkens does. So these are disjoint interpretations with different weak points.

 

[DarMM]

See my next post as well.

Another way to see the difference is QBism/Bub has no PBR theorem problem, but Spekkens does

What do you mean by "Spekkens does"?
I assume you don't mean the toy model has a PBR theorem problem.
Acausal/Retrocausal ontic models also don't have a PBR theorem problem since they are outside the ontological model framework within which the theorem is proved and it's usually models like these that Leifer, Spekkens and others are working on.

The difference with Spekkens is you can use the HVs, ie the existence of the hidden ontic state can preserve the necessary information from the original preparation state to predict the + outcome only

I don't quite agree with this. What the toy model has is that collapse at one scale does not permit collapse at a lower scale. Thus the removal of epistemic states involving $1$ at the higher level does not imply their loss in the state for the whole lab.
Since after decoherence we can give the macroscopic variables a Boolean lattice structure after the Friend's measurement why can't we follow this "collapse at one level and not another" in Copenhagen style models?

 

[DarMM]

I think we can resolve this based on your previous post.
QBism and Copenhagen views by saying there is no ontic state are not saying there is nothing beneath the quantum epistemic states, but rather that what lies beneath cannot be modeled mathematically. "The world is not a mechanism" as one of the QBist authors Ruediger Schack has said. So they think that like Spekkens model the level beneath the epistemic states is holding the "details" as you mentioned as being necessary. The difference is that in Spekkens model these can be described with mathematical variables, but in these views they cannot.

So it's really a choice between assuming "transcendent" elements of reality beneath the quantum formalism come to your rescue, multiple worlds, nonlocality, or some form of retro/acausality.

 

[DarMM]

Woops last point. There is also the option of holding a Copenhagen style view but just rejecting the existence of superobservers as Peres and Omnès do.

 

[charters]

I think we can resolve this based on your previous post.
QBism and Copenhagen views by saying there is no ontic state are not saying there is nothing beneath the quantum epistemic states, but rather that what lies beneath cannot be modeled mathematically. "The world is not a mechanism" as one of the QBist authors Reudiger Schack has said. So they think that like Spekkens model the level beneath the epistemic states is holding the "details" as you mentioned as being necessary. The difference is that in Spekkens model these can be described with mathematical variables, but in these views they cannot.

So it's really a choice between assuming "transcendent" elements of reality beneath the quantum formalism come to your rescue, multiple worlds, nonlocality, or some form of retro/acausality.

Yes, agreed. Or you accept you have a "single user" theory or (as you mention) you deny superobservers somehow.

 

[DarMM]

Perfect. Thanks for the discussion @charters , always worthwhile with yourself.

 

[charters]

Perfect. Thanks for the discussion @charters , always worthwhile with yourself.

Same to you!

 

[DarMM]

Or, if Friend's state is only valid up to Wigner's choice to do a recombination experiment, at which point Friend has to switch to using Wigner's state (this being one of Baumann & Brukner's ideas to resolve the tension), then Friend is admitting they need MWI or HV type reasoning, at least in some cases/for some predictions. At this point, they might as well just apply this full time, since it will work in all cases

I was just rereading some of Brukner's papers including this one. Brukner himself holds a view that's a form of Copenhagen/QBism so I wanted to see what he was saying.

It seems to be that he thinks Wigner's friend type situations call for a generalisation of the Born rule. This Born rule allows one to compute probabilities like $p(k|j)$, i.e. that the superobserver sees outcome $k$ given that the observer see outcome $j$.

So before we listed the "outs" for a Copenhagen view regarding Wigner's friend as:

1. The necessary info to prevent a contradiction is hidden in the unmodelable layer of the world. It basically takes the solution to be like Spekkens approach, but replaces the HVs.
2. Facts are relative to the observer. More accurately their environment. A quantum system can imprint itself differently in different classical environments in a way that makes reasoning about their combination inconsistent. This is the approach QBism seems to take, a relativisation of classical facts.
3. There are no superobservers. Peres and Decoherent history authors take this approach. Bub uses a form of this as well.

To this Brukner seems to be adding that scenarios like Wigner's friend require a modification of the Born rule and that it is this modification as a genuine mathematical feature of the formalism that points to (2) being the correct answer (given a Copenhagen style view of course).

 

[charters]

To this Brukner seems to be adding that scenarios like Wigner's friend require a modification of the Born rule and that it is this modification as a genuine mathematical feature of the formalism that points to (2) being the correct answer (given a Copenhagen style view of

I guess I think this is just careful speech to avoid explicitly saying what Friend would really be doing here - in using unitary V (in appendix A to Baumann & Brukner) she is very clearly making her prediction of Wigner's outcome based on the expectation that her obtained outcome path will overlap with, recombine with, and interfere with the unobtained outcome path in her initial measurement. Making the prediction requires treating the obtained and unobtained outcomes as both still relevant after the alleged collapse, which undermines the notion of the collapse altogether.

The admission that unitary V is necessary for Friend's prediction undermines believing in collapse, given a definition of the term that is reasonably close to the standard textbook account and/or close to how (imo) most people use and understand the concept.

 

[DarMM]

So then I would have a slight question before more reading.

Earlier you said there was a flaw in Bub's view. What is it given that Bub does believe in total collapse, i.e. that the other element of the superposition is completely gone leading him to derive:
$$p(ok|t_{L}) = 0$$
for the FR experiment.

 

[charters]

So then I would have a slight question before more reading.

Earlier you said there was a flaw in Bub's view. What is it given that Bub does believe in total collapse, i.e. that the other element of the superposition is completely gone leading him to derive:
$$p(ok|t_{L}) = 0$$
for the FR experiment.

In https://arxiv.org/abs/1804.03267 Bub says (where annoyingly he calls one of the superobservers "Friend"):

"There is another option, which is to reject assumption (ii)—not by restricting the universality of the unitary dynamics or any part of quantum mechanics, but by interpreting the quantum state probabilistically rather than representationally in the sense of §3. Quantum probabilities don’t quantify incomplete knowledge about an ontic state, but reflect the irreducibly probabilistic relation between the non-Boolean microlevel and the Boolean macrolevel, expressed through the intrinsic randomness of events associated with the outcomes of quantum measurements. On this option, what the Frauchiger-Renner argument shows is that quantum mechanics, as it stands without embellishment, is self-contradictory if the quantum state is interpreted representationally. The conclusion is avoided if we interpret the state probabilistically, with respect to a Boolean frame defined with respect to an “ultimate measuring instrument” or “ultimate observer.” In a situation, as in the Frauchiger-Renner argument, where there are multiple candidate observers, there is a question as to whether Alice and Bob are “ultimate observers,” or whether only Wigner and Friend are “ultimate observers.” The difference has to do with whether Alice and Bob perform measurements of the observables A and B with definite outcomes at the Boolean macrolevel, or whether they are manipulated by Wigner and Friend in unitary transformations that entangle Alice and Bob with systems in their laboratories, with no definite outcomes for the observables A and B. What actually happens to Alice and Bob is different in the two situations."

The problem is, if measurement induced collapse is a thing, then every human being must consider *him or her self* an ultimate observer in all cases. Nothing else is consistent with experience. So, Alice thinks she is an ultimate observer even when Wigner thinks she isn't. This is what causes the single user limitation, and Bub doesn't avoid this, despite claiming he does.

 

[DarMM]

My reading of Bub was more that when Alice is an observer then she is to everybody, Wigner cannot consider her not an observer due to the difference in the FR probabilites of $\frac{1}{4}$ vs $\frac{1}{12}$. In other words he is saying any application of FR on a real human being would give $\frac{1}{4}$. Alice and Bob can't be observers and Wigner still use the superposed state. If Wigner does use the superposed state then Alice and Bob are not observers. This would not happen for actual human observers.

 

[charters]

Alice and Bob can't be observers and Wigner still use the superposed state. If Wigner does use the superposed state then Alice and Bob are not observers. This would not happen for actual human observers.

But he says: "There is another option, which is to reject assumption (ii)—not by restricting the universality of the unitary dynamics or any part of quantum mechanics"

You are however restricting QM. You are saying Wigner can't use unitary QM if doing so means he'd have to unitarily recombine a human, because the internal human already made a Boolean macrolevel measurement.

This is the GRW type of answer, and it is a sensible one. But its not universally unitary, so I can't say Bub is clearly arguing for this. Ultimately this is because I think the root problem is he's trying to have his cake and eat it too, and not accepting he has to just bite one of the 3 F&R bullets/accept some downside. So, whatever plausible view you ascribe to him, there will be some remark inconsistent with that view, where he denies its necessary implications.

 

[DarMM]

I agree which is what confuses me, it seems to me that it is a restriction of QM because in his view there clearly is a macro level where events actually occur as he says and where superposition doesn't seem to be valid. I haven't seen much commentary on the paper, so I'm willing to believe there might be something I haven't understood. Currently though what you say seems true. When he says "universally" he seems to mean "can be applied to any micro/macro interaction" not "can be applied to anything".

What do you think of Renato Renner's view (referenced in Bub's most recent paper) that MWI bites two bullets, rejecting single world and inter-agent consistency?

 

[charters]

What do you think of Renato Renner's view (referenced in Bub's most recent paper) that MWI bites two bullets, rejecting single world and inter-agent consistency?

I think F&R came up with a very nice framework - the choice to give up Q, C, or S - but I think they misdiagnose some interpretations, and this problem got worse between the 2015 and 2018 papers.

To me, the whole issue only needs the basic Wigner's friend scenario, not the extended version. Then, there is simply one material question: after Wigner (attempts to) perform the recombination step of the interference experiment, does he see (A) 100% |+> or (B) 50/50 |+> and|->?

If both W and F agree on (A), then F is accepting that something (e.g., an MWI copy or a pilot wave) persists on the unobtained path after her measurement. This is what giving up S means: for maximum predictive accuracy, F is required to still keep track of unobtained measurement outcomes, especially their relative phases, just in case recombination is attempted in the future. There's no inescapable duty to treat these unobtained as literal "other worlds". F just can't act like they've been "collapsed away" such that they have 0 ongoing empirical significance, if she wants to always recover Wigner's unitary prediction.

If both parties agree on answer (B), then W is giving up universally unitary QT, ie giving up assumption Q, and technically introducing a modification to the Schrodinger eq.

If W and F don't agree on (A) or (B) - yet agree it is reasonable that they can disagree on this point - they give up C.

So, since in MWI the two certainly can agree on the empirical question, I can't see why they'd also have to give up C, which is defined by the absence of agreement.

 

[DarMM]

So, since in MWI the two certainly can agree on the empirical question, I can't see why they'd also have to give up C, which is defined by the absence of agreement

The state supporting it is given on p.15-16 of Bub's paper if you want to see Renner's argument. The elements behind his argument wouldn't occur in a basic Wigner's friend, so I don't think there's anything in that case that would force MWI to give up C. It only seems to occur in extended Wigner's friend scenarios.

 

[charters]

The state supporting it is given on p.15-16 of Bub's paper if you want to see Renner's argument. The elements behind his argument wouldn't occur in a basic Wigner's friend, so I don't think there's anything in that case that would force MWI to give up C. It only seems to occur in extended Wigner's friend scenarios.

None of the Bub papers I have saved have 15+ pages. Link?

 

[DarMM]

Woops, that should have been eq.15-16 on p.11-12 here:
https://arxiv.org/abs/1907.06240

 

[charters]

Woops, that should have been eq.15-16 on p.11-12 here:
https://arxiv.org/abs/1907.06240

That's where we started this back and forth/what I wanted to call your attention to. See my comment #109. Basically I think he is just wrong about what information W-bar can obtain on a given run. He is making a basic complementarity error.

 

[DarMM]

In the step between (16) and (17) I thought what was happening is that it displays the results of $W$ and $\bar{W}$ using modal logic after getting their superobservable results rather than them obtaining the results of $F$ and $\bar{F}$.

Of course I think the problem is that using such logic isn't valid in QM at all in any interpretation.

 

[charters]

In the step between (16) and (17) I thought what was happening is that it displays the results of $W$ and $\bar{W}$ using modal logic after getting their superobservable results rather than them obtaining the results of $F$ and $\bar{F}$.

Of course I think the problem is that using such logic isn't valid in QM at all in any interpretation.

But there's no logical inference by which you can get specific F outcomes just from the Ws knowing their ok/fail outcomes. The ok/fail outcomes are equivalent to W "inserting the second beamsplitter" to close the interferometer, which means both the |ok> and |fail> paths are interfering combinations of F's paths along both the heads/tails or up/down paths, as appropriate.