What Is the Frauchiger-Renner Theorem?

[Demystifier]

Richard Healey has the best exposition:
https://arxiv.org/abs/1807.00421

Concerning the Masanes's argument, that is the "Third Argument" in the Healey's paper, it seems to me that the crucial assumption responsible for the appearance of inconsistency is the assumption of Lorentz invariance. Would you agree? If so, and given that the assumption of Lorentz invariance is closely related to the assumption of locality, isn't the "Third Argument" just a restatement of the good old Bell theorem that the existence of unique objective outcomes in QM is incompatible with locality?

 

[DarMM]

Concerning the Masanes's argument, that is the "Third Argument" in the Healey's paper, it seems to me that the crucial assumption responsible for the appearance of inconsistency is the assumption of Lorentz invariance. Would you agree? If so, and given that the assumption of Lorentz invariance is closely related to the assumption of locality, isn't the "Third Argument" just a restatement of the good old Bell theorem that the existence of unique objective outcomes in QM is incompatible with locality?

Just to let you know I need to do some thinking on this, there are others who have said similar and it seems to be a subtle observation. 2-3 days I estimate, I don't want to just blurt out a lazy response.

 

[RUTA]

See also:
On Formalisms and Interpretations
Veronika Baumann, Stefan Wolf
https://arxiv.org/abs/1710.07212

I detail in The Quantum Mystery of Wigner's Friend how Baumann and Wolf's paper bears on FR's paper.

 

[David Byrden]

I don't think that there is a difference between knowledge "in the mind" and knowledge "contained in the environment".

Here's an example showing the difference; an uneducated person is told that we're firing particles at two slits (Young's experiment). In his mind, he knows that each particle will pass through a single slit. But the environment knows that they pass through both slits.
The environment wins out, and it forms interference patterns.

 

[DarMM]

Modern interpretatiions of QM acknowledge that the state of a quantum system is relative to the observer.

Well some do. It's not a universal feature of all modern interpretations.

But Agent F doesn't know what the system state is.
She knows it in her mind, to be sure, but her environment doesn't contain knowledge of it, acquired through the Wave Function.

So, all that she really can say, is that she measured "spin up".

You're basically saying that all the agent can say is their own personal experience of the outcome occurred? Even after being told the initial state and the exact way the experiment will be performed, you're saying they could still just assign "some" random state inconsistent with that information? If the quantum state forms an objective description of the statistics of the experiment then:
$$\sqrt{\frac{1}{3}}\left(|\downarrow,h\rangle + |\downarrow,t\rangle + |\uparrow,t\rangle\right)$$
is the only valid state for them to use, the correct one.

If on the other hand, there is no such thing as $|\psi\rangle$ and it's just in the agent's head and subjective to their situation, i.e. they could pick any $|\psi\rangle$ and just use the observation "spin is up" to update it via Lüders Rule, then you are rejecting the "objective" part of Assumption 1 I gave in the OP.

You're just assuming an interpretation that gets out of the contradiction from the beginning, it's not a flaw in the argument.

The actual flaw in the Frauchiger-Renner paper is that they don't notice they have an assumption about observer's not being entangled with each other from a superobserver's perspective. This is sort of the more developed version of Scott Aaronson's issue with the paper and is given more coverage in Richard Healey's paper.

To be clear, the contradiction FR find can be escaped by:

1. Saying QM is a single-user subjective theory, like Relational QM or QBism
2. Saying QM will be wrong in certain experiments (this seems to be the response of some Bohmians)
   
3. Multiple Worlds, like the Everett interpretation
4. Wave functions objectively undergo collapse as a physical process
5. Accept that Observers can be entangled, they're not purely classical like basic Copenhagen, i.e. accept that even after a measurement you could always be on the Quantum side of a very powerful Observer's Heisenberg cut. There isn't a pure Quantum-Classical divide.

The problem is FR don't mention the assumption that permits (5.) as a way out.

The Masanes's version removes (5.) as a way out, but introduces an alternate way out:
5*. Not all unitaries are reversible in principle.

 

[atyy]

I don't. Do you?

Hmmm, I don't know. I haven't had the time to read it carefully. It does seem to me as mistaken as Ballentine's argument that Copenhagen is wrong, and ignores previous work like Hay and Peres's https://arxiv.org/abs/quant-ph/9712044.

 

[1977ub]

I don't think that there is a difference between knowledge "in the mind" and knowledge "contained in the environment". After all, the state of the mind is in fact a state of the brain described by a wave function of the brain.

If one has a problem with other minds, then other people don't have minds. This is not a contradiction of anything empirical. Also it may be that each particle goes through one slit or the other and something mysterious keeps a tally to make it as if it had gone through both, no?

 

[DarMM]

ignores previous work like Hay and Peres's

I had a read of Hay and Peres's paper, what aspect of it do they ignore. The subject topic is similar, but I don't see them ignoring anything there.

It does seem to me as mistaken as Ballentine's argument that Copenhagen is wrong

What part seems mistaken?

 

[Demystifier]

Just to let you know I need to do some thinking on this, there are others who have said similar and it seems to be a subtle observation. 2-3 days I estimate, I don't want to just blurt out a lazy response.

I made some additional thinking too and now I think I know exactly what is wrong with the Healey's "Third Argument". In the critique of the Frauchiger and Renner’s argument, Healey correctly objects that this argument rests on the unjustified assumption of intervention insensitivity. But in the "Third Argument", Healey argues that the "Third Argument" does not assume the intervention insensitivity, and therefore that the "Third Argument" is correct. I think it's wrong. I think the "Third Argument" also uses the assumption of intervention insensitivity and is therefore incorrect.

Let me explain. The main culprit is Eq. (31). Healey does not explain how exactly this inequality is obtained, but as far as I can see, this inequality is nothing but a variant of CHSH inequality (see e.g. https://en.wikipedia.org/wiki/CHSH_inequality). On the other hand, it is well known that CHSH inequality is a consequence of the assumption of non-contextuality (which in the literature is usually justified by the assumption of locality). Hence the contradiction derived by Healey seems to originate from the assumption of non-contextuality, which is more-or-less the same as the assumption of intervention insensitivity. Since this assumption is unjustified, the "Third Argument" seems wrong.

 

[stevendaryl]

In my effort to understand what exactly was proved by the Frauchiger and Renner argument, I have come to the conclusion that what they show is impossible is not something that anybody believed, anyway. I already said this, but I feel that it's worth repeating:

The way I described it is through the $\leadsto$ relation: That should actually have a subscript, $\psi$, because it's relative to an initial state.

I write $(A, \alpha) \leadsto_\psi (B, \beta)$ to mean: If a measurement of observable $A$ in state $\psi$ produces result $\alpha$, then it is certain that a later measurement of $B$ will produce result $\beta$. This is the sort of reasoning using in EPR experiments. With anti-correlated spin-1/2 twin pairs, if Alice measures the spin of her particle along axis $\vec{a}$ and gets result $\alpha = \pm \frac{1}{2}$ and later Bob measures the spin of his particle along that same axis, he will get result $-\alpha$ with certainty.

So the FR argument just seems to me to be the claim that the $\leadsto$ relation is not transitive:

If $(A, \alpha) \leadsto (B, \beta)$ and $(B, \beta) \leadsto (C, \gamma)$, it's not necessarily true that $(A, \alpha) \leadsto (C, \gamma)$.

It's hard to see why anyone would think it was transitive. A measurement potentially modifies the state, so with a chain of measurements,

1. Initially, the state is $\psi$
2. A measurement of $A$ produces result $\alpha$.
3. Now, the state is $\psi' \neq \psi$
4. A measurement of $B$ produces result $\beta$.
5. But we don't have $(B, \beta) \leadsto_{\psi'} (C, \gamma)$ so we can't conclude that a measurement of $C$ will produce result $\gamma$.

(Note: the statement $(A, \alpha) \leadsto (B, \beta)$ must assume that there is no interference in the state that is relevant to the measurement of $B$ that takes place after the measurement of $A$. Going back to the EPR case, obviously, if between Alice's measurement and Bob's measurement, someone interacts with Bob's particle, then it will no longer be guaranteed that his result will be anticorrelated with Alice's)

If I'm not missing something, then it seems to me that the thing proved impossible by the argument is not something that anyone would believe, anyway.

Now, I think that an argument for transitivity could be made in certain circumstances. The measurement of $A$ may change the state, but in a way that is irrelevant to the final measurement of $C$. But that requires a separate argument, it seems to me.

 

[DarMM]

If I'm not missing something, then it seems to me that the thing proved impossible by the argument is not something that anyone would believe, anyway.

I don't think you are missing anything. As you say $\leadsto_\psi$ simply couldn't be transitive (in slightly different language this paper points out what you do: http://philsci-archive.pitt.edu/15552/).

I think the only thing blocked by the result are certain forms of Copenhagen where you say observers/measuring devices are completely classical, where they'd say you should be able to use a transitive form of $\leadsto_\psi$ or something like it. However I don't think forms of Copenhagen this strong made much sense anyway, since although it is fine for the observer to treat themselves as classical, asking that superobservers treat observers as classical is essentially just objective collapse.

However your objection doesn't seem to apply to Masanes's version. Though perhaps it has other problems as @Demystifier mentions.

 

[DarMM]

The main culprit is Eq. (31). Healey does not explain how exactly this inequality is obtained, but as far as I can see, this inequality is nothing but a variant of CHSH inequality (see e.g. https://en.wikipedia.org/wiki/CHSH_inequality). On the other hand, it is well known that CHSH inequality is a consequence of the assumption of non-contextuality

Eq. 31 comes about via an assumption of objective outcomes, i.e. actual objective facts about the four measurements exist. Do trillions of runs of the Masanes experiment and there will be a frequency distribution from the data $p(a,b,c,d)$. Via Fine's theorem this gives the inequality quoted for the marginals and ultimately one has the contradiction.

Or in brief the contradiction is QM is saying that the $E(i,j)$ should break the CHSH inequality, but the fact that they are marginals of the distribution for the ontic/objective device clicks means they shouldn't break the inequality.

This is avoided in a normal CHSH experiment because you can only get outcomes for a pair of variables in a single run, not all four as here. Hence the $E(i,j)$ are simply the probabilities predicted by QM. Reversing the measurements in Masanes thought experiment however causes them to also be marginals of a classical (i.e. Kolmogorov) probability distribution.

The QBist way out of this is that $p(a,b,c,d)$ is simply meaningless, there are no distributions for objective facts, only facts for agents. Since nobody can experience all of $a,b,c,d$, it is meaningless to speak of $p(a,b,c,d)$.

Retrocausal theories permit one of the marginals, e.g. $E(a,d)$, to deviate significantly from QM allowing consistency between the marginals and $p(a,b,c,d)$.

Interested to hear your thoughts.

 

[Demystifier]

Eq. 31 comes about via an assumption of objective outcomes, i.e. actual objective facts about the four measurements exist.

I don't see how Eq. (31) comes from that assumption alone. I would like to see an explicit derivation. I will check the Fine's paper and comment it later.

 

[Demystifier]

I don't see how Eq. (31) comes from that assumption alone. I would like to see an explicit derivation. I will check the Fine's paper and comment it later.

I checked the Fine's paper and now I am even more convinced that I am right. Eq. (31) in the Healey's paper is
$$|corr(a,b)+corr(b,c)+corr(c,d)-corr(a,d)|\leq 2$$
after which he writes: "Note that no locality assumption is required to derive this inequality here, since it is mathematically equivalent to the existence of a joint distribution over the actual, physical outcomes whose existence has been assumed [17]."

The Ref. [17] is the paper by Fine. The central result is the Fine's Theorem 7 which says:
"Observables $A_1$ , ... ,$A_n$ satisfy (the joint distribution condition) if and only if all pairs commute."
To apply this to Eq. (31) above, the relevant "pairs" are pairs of spin operators in different directions. But spin operators in different directions do not commute, so Theorem 7 implies that the joint distribution condition is not satisfied. Hence the quoted Healey's claim above that the "existence of a joint distribution ... has been assumed" is simply an expression of a wrong assumption. It looks as if Healey have not understood the content of Ref. [17] that he cites as an alleged support of his claim. It's not only that Ref. [17] does not support his claim, but just the opposite, it explains why his claim after Eq. (31) is wrong.

 

[DarMM]

Please note I'm not too certain about this myself...

It looks as if Healey have not understood the content of Ref. [17] that he cites as an alleged support of his claim

Just to be clear, this would mean many people don't understand the content of Fine's theorem as Healey's exact presentation of the argument has been used by Matt Leifer and Matthew Pusey. That's not to say you are wrong, just telling you the "scope" of the error if you are right.

To apply this to Eq. (31) above, the relevant "pairs" are pairs of spin operators in different directions. But spin operators in different directions do not commute

Okay, but is this not just another presentation of the contradiction, i.e. we have two results:

1. The $E(i,j)$ are the probabilities predicted by QM.
2. The $E(i,j)$ are marginals of a distribution $p(a,b,c,d)$, coming from simply the occurrence of the four outcomes in each run.

I agree that (2.) then implies the observables would commute, which is wrong. However to me that is simply the contradiction stated another way:

1. Given the experimental set up, they are marginals
2. As marginals they have to commute
3. However from QM they obviously don't commute
4. Thus a contradiction

I don't see the fact that they need to commute as contradicting Healey, as the contradiction is between conditions on them from being marginals conflicting with their properties from QM.

In a way the whole point of Masanes set up is to force the existence of $p(a,b,c,d)$ to give these contradictions.

Hence the quoted Healey's claim above that the "existence of a joint distribution ... has been assumed" is simply an expression of a wrong assumption

It's a fact of the experiment I would have said, $a,b,c,d$ occur in a single run, thus there must be a frequency of their occurance $p(a,b,c,d)$. How could there not be?

$p(a,b,c,d)$ is not coming from QM as such, just a fact of objective experimental outcomes existing.

 

[DarMM]

I don't see how Eq. (31) comes from that assumption alone. I would like to see an explicit derivation. I will check the Fine's paper and comment it later.

If there are objective facts about the outcomes, then there is a distribution of those outcomes $p(a,b,c,d)$, the $E(i,j)$ then are marginals of this distribution and thus obey the inequality.

As above yes this would require them to commute, either this or the obeying of the CHSH inequality contradicts their QM behaviour, i.e. noncommuting and breaking the CHSH inequality.

 

[DarMM]

Leifer presenting Masanes's version:

@39:44

@41:55 the slide with $p(a,b,c,d)$ distribution is shown. It simply exists because the outcomes exist as Leifer says.

 

[Demystifier]

Just to be clear, this would mean many people don't understand the content of Fine's theorem as Healey's exact presentation of the argument has been used by Matt Leifer and Matthew Pusey. That's not to say you are wrong, just telling you the "scope" of the error if you are right.

Well, I am not sure about Pusey, but Leifer is one of those who think that the FR theorem is essentially correct and relevant. On the other hand, Healey thinks that FR theorem is not correct because it uses an unjustified assumption of non-contextuality, which he calls "intervention insensitivity". All I'm saying is that Eq. (31) also contains the assumption of non-contextuality (aka intervention insensitivity) so the Third Argument is wrong for essentially the same reason as the FR theorem.

 

[Demystifier]

If there are objective facts about the outcomes, then there is a distribution of those outcomes $p(a,b,c,d)$, the $E(i,j)$ then are marginals of this distribution and thus obey the inequality.

Ah, now I think I better understand the error in the Third Argument. The error is in the assumption that Eq. (31) is the same as Eq. (32). But it is not. The quantity $corr(a,b)$ in (31) is not the same as $E(a,b)$ in (32). The quantity $corr(a,b)$ in (31) is indeed a marginal of $p(a,b,c,d)$, but $E(a,b)$ in (32) is something else. The probability distribution $p(a,b,c,d)$ is obtained under a very specific measurement procedure that includes undoing previous measurements, while $E(a,b)$ describes a correlation obtained under a different, more ordinary, measurement procedure that does not include undoing previous measurements. The assumption that $E(a,b)$ is the same as $corr(a,b)$ corresponds to the assumption that it is not important how exactly something is measured, which is the same as the assumption of intervention insensitivity. Hence Eq. (32) would follow from (31) if intervention insensitivity was true. But intervention insensitivity is not true, so (32) does not follow from (31). Eqs. (31) and (33) are both correct, but there is no contradiction because Eq. (32) is not correct.

 

[DarMM]

Well, I am not sure about Pusey, but Leifer is one of those who think that the FR theorem is essentially correct and relevant.

Not that I've seen, in his lectures and talks he uses Masanes's version, not the actual FR result, although he still calls it "Frauchiger-Renner (Masanes version)". See the video I posted or this set of slides:
http://mattleifer.info/wordpress/wp-content/uploads/2009/04/FQXi20160818.pdf
(Slide 12)

Pusey can be seen using Masanes version here:

@18:38 he starts talking about it, @19:17 he mentions how it is not the actual FR result, but Masanes's version.

 

[DarMM]

The quantity $corr(a,b)$ in (31) is not the same as $E(a,b)$ in (32). The quantity $corr(a,b)$ in (31) is indeed a marginal of $p(a,b,c,d)$, but $E(a,b)$ in (32) is something else. The probability distribution $p(a,b,c,d)$ is obtained under a very specific measurement procedure that includes undoing previous measurements, while $E(a,b)$ describes a correlation obtained under a different, more ordinary, measurement procedure that does not include undoing previous measurements.

I don't see how this could be true, although I might be missing something. $E(a,b)$ and $corr(a,b)$ would occur before the reversal and seem identical.

So $corr(a,b)$ is the correlation between Alice and Bob's result. Let's displace the reversals to be 1,000 years after their measurments (for both of them), $corr(a,b)$ is then just the correlation between Alice and Bob's measurements on an entangled pair. I don't see how it could differ from $E(a,b)$, it can't involve a different quantum state or measurement operators as far as I can see and the set up is the same, except that a reversal awaits them in the far future, but I don't know of anything in the quantum formalism that means you should use a different state or measurement operator in such a case. When the measurement occurs it seems to me everything is the same.

If I'm wrong, which changes, the state or the operators, both? If the state how is it that the entangled particle pair themselves are affected?

 

[Demystifier]

I don't see how this could be true, although I might be missing something. $E(a,b)$ and $corr(a,b)$ would occur before the reversal and seem identical.

So $corr(a,b)$ is the correlation between Alice and Bob's result. Let's displace the reversals to be 1,000 years after their measurments (for both of them), $corr(a,b)$ is then just the correlation between Alice and Bob's measurements on an entangled pair. I don't see how it could differ from $E(a,b)$, it can't involve a different quantum state or measurement operators as far as I can see and the set up is the same, except that a reversal awaits them in the far future, but I don't know of anything in the quantum formalism that means you should use a different state or measurement operator in such a case. When the measurement occurs it seems to me everything is the same.

If I'm wrong, which changes, the state or the operators, both? If the state how is it that the entangled particle pair themselves are affected?

I was slightly sloppy by writing $a,b$ when I meant $i,j$. Let me explain all this once again, more carefully.

Let me first make a purely logical analysis, without much physical insight. Basically, there are 3 potentially reasonable but mutually exclusive possibilities:
a) $corr(i,j)=E(i,j)$ for all $i,j$, (31) and (32) are wrong, while (33) is true.
b) $corr(i,j)=E(i,j)$ for all $i,j$, (31) and (32) are true, while (33) is wrong.
c) $corr(i,j)\neq E(i,j)$ for some $i,j$, (31) and (33) are true, while (32) is wrong.
Which of those 3 possibilities do you think is correct?

Now physically, my chain of reasoning is the following:
- Eq. (33) is standard QM, which I think is consistent. After all, (33) can be thought of as a violation of the CHSH inequality, which has been confirmed experimentally. Hence I exclude b).
- Eq. (31) is standard probability theory stemming from the existence of joint probability $p(a,b,c,d)$, so it must be right. Hence I exclude a).
- What remains is c), which requires to explain why exactly $corr(i,j)\neq E(i,j)$ for some $i,j$. My answer is that they are different because they correspond to different measurement procedures. $corr(i,j)$ corresponds to a thought experiment in which the joint probability $p(a,b,c,d)$ exists. $E(i,j)$ corresponds to an actual experiment in which (33) is true, in which case Fine (and others) proved that the joint probability does not exist. If $corr(i,j)$ was the same as $E(i,j)$ for all $i,j$, then it would mean that the joint probability both exists and doesn't exist, which would be a logical contradiction. Hence it must be that $corr(i,j)\neq E(i,j)$ for some $i,j$.

Concerning your last question, almost any measurement changes the state of the system. That's called quantum contextuality. The exact mechanism of this change is a matter of interpretation. In practice it can usually be described by "collapse", but in the case of a thought experiment that includes undoing previous measurements, the collapse postulate must be replaced by something else. One possibility is the Bohmian interpretation, which clearly distinguishes the change of the wave function from change of the particles themselves. Both change in the Bohmian interpretation, but since it is formulated in the Schrodinger picture, the observable operators do not change. For more conceptual details about the Bohmian interpretation see my "Bohmian mechanics for instrumentalists" linked in my signature below.

One additional comment. Experiment that corresponds to Eq. (33) can be described by a collapse, while experiment that corresponds to Eq. (31) cannot be described by a collapse. That's another evidence that those are two very different experiments, which is why $corr(i,j)$ and $E(i,j)$ are physically different for some $i,j$.

 

[DarMM]

I quote you thrice, but the main point of this comment is the response to the last quote. The rest might make more sense in light of it.

Let me first make a purely logical analysis, without much physical insight. Basically, there are 3 potentially reasonable but mutually exclusive possibilities:
a) $corr(i,j)=E(i,j)$ for all $i,j$, (31) and (32) are wrong, while (33) is true.
b) $corr(i,j)=E(i,j)$ for all $i,j$, (31) and (32) are true, while (33) is wrong.
c) $corr(i,j)\neq E(i,j)$ for some $i,j$, (31) and (33) are true, while (32) is wrong.
Which of those 3 possibilities do you think is correct?

It's not so much that I think any of them are right or wrong. It's that in this set up you can derive all three under the given assumptions, which is impossible as they can't be all right and thus the contradiction. So you have to forgo an assumption. Which one depends on your interpretation.

In a given interpretation you might take various ones to be wrong, e.g. QBism has (31) and (32) being wrong, Retrocausal theories would have $corr(i,j) \neq E(i,j)$ in some cases, i.e. at least one marginal does not match quantum predictions. What I have heard is that Bohmians would also take $corr(i,j) \neq E(i,j)$ (mentioned in the talk by Pusey)

- What remains is c), which requires to explain why exactly $corr(i,j)\neq E(i,j)$ for some $i,j$. My answer is that they are different because they correspond to different measurement procedures. $corr(i,j)$ corresponds to a thought experiment in which the joint probability $p(a,b,c,d)$ exists. $E(i,j)$ corresponds to an actual experiment in which (33) is true, in which case Fine (and others) proved that the joint probability does not exist. If $corr(i,j)$ was the same as $E(i,j)$ for all $i,j$, then it would mean that the joint probability both exists and doesn't exist, which would be a logical contradiction. Hence it must be that $corr(i,j)\neq E(i,j)$ for some $i,j$.

Note the bolded part as I believe that's exactly it. Hidden variable theories like Bohmian Mechanics and Retrocausal theories have exactly $corr(i,j)\neq E(i,j)$. As you say otherwise you'd have $p(a,b,c,d)$ both existing and not existing. However that is the point of the theorem. The given assumptions require it to both exist and not exist, thus something is wrong with them. Hopefully this will make more sense after the following...

Concerning your last question, almost any measurement changes the state of the system. That's called quantum contextuality. The exact mechanism of this change is a matter of interpretation. In practice it can usually be described by "collapse", but in the case of a thought experiment that includes undoing previous measurements, the collapse postulate must be replaced by something else. One possibility is the Bohmian interpretation, which clearly distinguishes the change of the wave function from change of the particles themselves. Both change in the Bohmian interpretation, but since it is formulated in the Schrodinger picture, the observable operators do not change. For more conceptual details about the Bohmian interpretation see my "Bohmian mechanics for instrumentalists" linked in my signature below.

One additional comment. Experiment that corresponds to Eq. (33) can be described by a collapse, while experiment that corresponds to Eq. (31) cannot be described by a collapse. That's another evidence that those are two very different experiments, which is why $corr(i,j)$ and $E(i,j)$ are physically different for some $i,j$

I'm aware of these things, but I think what you are missing is the assumptions. I completely agree that they are different experiments and thus it is not unreasonable to ascribe $corr(i,j)\neq E(i,j)$. However what you are doing is secretly filling in the explanatory logic of an interpretation like Bohmian mechanics. For interpretations obeying the assumptions of the theorem there is no reason for $corr(i,j)\neq E(i,j)$.

This isn't a contradiction of all interpretations, but ones obeying all four of Masanes assumptions. In interpretations obeying those assumptions there is no reason that $corr(i,j) \neq E(i,j)$, in fact for them it is necessary that $corr(i,j) = E(i,j)$ and thus as you said perfectly in those interpretations "the joint probability both exists and doesn't exist". Which means they're self contradictory.

Interpretations like Bohmian Mechanics can naturally have $corr(i,j) \neq E(i,j)$ and thus the theorem has no relevance to them. Of course Masanes's proof can't show something nonsensical like $p(a,b,c,d)$ exists and doesn't exist at the same time. You're reasoning in physically logical terms that it must be that $corr(i,j)\neq E(i,j)$, but this isn't a proof about what is actually physically true, it's a proof about how some interpretations are ultimately self-contradictory.

Let's look at a type of nterpretation that falls victim to the no-go result, they have:

1. Observations are facts, i.e. if you were labelling events in spacetime you could assign something like $\sigma_z = \frac{\hbar}{2}$ to a spin measurement in a spacetime region. You don't need a pair like $(\sigma_z = \frac{\hbar}{2}, Measuring Entity)$. So the particle "had +-spin" as a simple universal fact, not "it manifested +-spin to Agent X".
   
   This means $p(a,b,c,d)$ exists
2. Quantum Theory is universal with no restrictions. This means I can describe Observers with quantum states and superpositions and they can be unitarily reversed like anything else.
   
   This permits the reversals of the measurements.
3. No hidden variables that permit differences from QM.
   So I cannot fall back on the contextual mechanics of some underlying theory to permit $corr(i,j) \neq E(i,j)$. Of course it is this assumption that is rejected by Bohmian Mechanics. Healey and Masanes don't really say this, it's just built into "QM is always right".
4. $\psi$ is not real, just ones knowledge/beliefs/etc. So collapse has no physical content, which prevents the "out" you have in the final paragraph.

Your ways out require $\psi$-collapse being physically real or additional variables, these interpretations don't have either. (Note "No Collapse" in Healey's paper)

Basically you're finding fault with the proof because it results in a contradiction about $p(a,b,c,d)$ and saying some assumptions must be wrong. However as I said, yes indeed, that's the point of the proof, one of the premises must be wrong. However they are all premises of Classic Copenhagen.

Thus if you want to be a Copenhagenist, or other similar interpretations, you need to jettison $p(a,b,c,d)$'s existence. You need to be perspectival. As Leifer and Pusey say, Observations are not facts.

 

[David Byrden]

Are we still talking about the FR paper now? I'm losing track.

I don't know how many times their error needs to be explained before everybody "gets" it.
Here, let me try to put it in simple terms. This is essentially what FR wrote:

Agent F says "I just got a qubit from Agent /F and measured it as UP. I will assume she's in a classical state. It must be TAILS".

And this is a corrected version:

Agent F says "I just got a qubit from Agent /F and measured it as UP. Since she's isolated from me, I will allow her to be in a superposition. Therefore she could be either TAILS or OK"

There. That's the whole thing solved, explained, finished and done with.

 

[DarMM]

Are we still talking about the FR paper now? I'm losing track.

We're talking about Masanes version, which works a bit differently.

Are we still talking about the FR paper now? I'm losing track.

I don't know how many times their error needs to be explained before everybody "gets" it.
Here, let me try to put it in simple terms. This is essentially what FR wrote:

Agent F says "I just got a qubit from Agent /F and measured it as UP. I will assume she's in a classical state. It must be TAILS".

And this is a corrected version:

Agent F says "I just got a qubit from Agent /F and measured it as UP. Since she's isolated from me, I will allow her to be in a superposition. Therefore she could be either TAILS or OK"

There. That's the whole thing solved, explained, finished and done with.

Maybe it's not because we don't "get it", perhaps your approach is wrong. It's been explained to you why this is wrong. If $F$ models $\bar{F}$ in superposition then they use the state:
$$\sqrt{\frac{1}{3}}\left(|\downarrow,h\rangle + |\downarrow,t\rangle + |\uparrow,t\rangle\right)$$

Thus if they measure $|\uparrow\rangle$ they can conclude $\bar{F}$ saw $|t\rangle$. That's just standard QM. To refute this you've said something about "knowledge in the environment" that doesn't seem part of QM. If the above was a typical particle state there's no way you'd conclude the second particle was in a superposition, so I genuinely don't understand your objection.

Also Masanes version doesn't use any of this, so even if this objection were valid it says nothing about Masanes version covered in Healey's paper.

 

[Demystifier]

Basically you're finding fault with the proof because it results in a contradiction about p(a,b,c,d) and saying some assumptions must be wrong. However as I said, yes indeed, that's the point of the proof, one of the premises must be wrong. However they are all premises of Classic Copenhagen.

I agree with everything you said in the great and very clear post above, except that I am not convinced that the bold sentence quoted above is true. What exactly is "Classic Copenhagen"? Is there a standard QM textbook in which it is unambiguously clear they all really are the premises? I ask this because it still looks to me as if the theorem (either FR or the Masanes version of it) rules out an "interpretation" that nobody seriously believed in the first place.

 

[Demystifier]

Also Masanes version doesn't use any of this, so even if this objection were valid it says nothing about Masanes version covered in Healey's paper.

In addition, the Masanes version is technically much simpler, so it is much easier to see the forest for the trees.

 

[DarMM]

I agree with everything you said in the great and very clear post above, except that I am not convinced that the bold sentence quoted above is true. What exactly is "Classic Copenhagen"? Is there a standard QM textbook in which it is unambiguously clear they all really are the premises? I ask this because it still looks to me as if the theorem (either FR or the Masanes version of it) rules out an "interpretation" that nobody seriously believed in the first place.

By Classic Copenhagen I mean roughly what Bohr, Heisenberg, etc thought. They're not consistent with each other or even themselves at different times, so in truth there is no "Copenhagen interpretation", but I mean roughly an interpretation following the list below which most of them would have held. Wasn't sure what to call, especially since there is no single Copenhagen interpretation, should have been clearer.

Before I go digging into Bohr's papers and those of the old Copenhagen group, I would just like to narrow the search for what you want. Which do you think Bohr for example didn't hold:

1. Observations are objective events, not agent experiences
2. There are no hidden variables, i.e. QM is complete
3. QM may be universally applied to any system (note this is not the same as saying there is no Heisenberg cut)
4. The wavefunction is not an ontic object

From my reading of him he said all four. I just want to know which one you think he didn't say, or what form of Copenhagen do you have in mind that denies one of these four statements and which one? Haag for example says something I believe in Local Quantum Physics, though I have to check that when I'm at my books.

To clarify does it need to be a textbook that says it, most textbooks are very operational and say nothing about the reality of $\psi$ for example. Would Omnés book "The Interpretation of Quantum Theory" count even though its not a "textbook" designed to teach QM?

Again most of the Foundations community would be wrong on this, they all seem to say it invalidates Classic Copenhagen, see Leifer's lectures I linked to before.

 

[DarMM]

In addition, the Masanes version is technically much simpler, so it is much easier to see the forest for the trees.

I 100% agree on this!

 

[atyy]

By Classic Copenhagen I mean roughly what Bohr, Heisenberg, etc thought. They're not consistent with each other or even themselves at different times, so in truth there is no "Copenhagen interpretation", but I mean roughly an interpretation following the list below which most of them would have held. Wasn't sure what to call, especially since there is no single Copenhagen interpretation, should have been clearer.

Before I go digging into Bohr's papers and those of the old Copenhagen group, I would just like to narrow the search for what you want. Which do you think Bohr for example didn't hold:

1. Observations are objective events, not agent experiences
2. There are no hidden variables, i.e. QM is complete
3. QM may be universally applied to any system (note this is not the same as saying there is no Heisenberg cut)
4. The wavefunction is not an ontic object

From my reading of him he said all four. I just want to know which one you think he didn't say, or what form of Copenhagen do you have in mind that denies one of these four statements?

To clarify does it need to be a textbook that says it, most textbooks are very operational and say nothing about the reality of $\psi$ for example. Would Omnés book "The Interpretation of Quantum Theory" count even though its not a "textbook" designed to teach QM?

Again most of the Foundations community would be wrong on this, they all seem to say it invalidates Classic Copenhagen, see Leifer's lectures I linked to before.

So what is wrong with Scott Aronson's objection?

 

[DarMM]

So what is wrong with Scott Aronson's objection?

He doesn't deal with Masanes's version.

 

[atyy]

He doesn't deal with Masanes's version.

OK, so basically the first 2 versions of the theorem are wrong?

For te Masanes version, I would count myself a believer in classic Copenhagen (ie, QM is formally complete), but also believe in hidden variables - I dare say many older physicists take this position - Dirac, Messiah, Bell, possibly even Landau & Lifshitz - because it has generally been assumed that Copenhagen has a measurement problem, the most important problem in foundations - not these horrible fake problems that Frauchiger and Renner solve.

 

[DarMM]

OK, so basically the first 2 versions of the theorem are wrong?

Not wrong, but the set of interpretations eliminated by them is almost null and I believe nobody held them outside of those who don't think much about Foundations. I don't think they have much content for serious interpretations.

For te Masanes version, I would count myself a believer in classical Copenhagen (ie, QM is formally complete), but also believe in hidden variables - I dare say many older physicists take this position - Dirac, Messiah, Bell, possibly even Landau & Lifshitz - because it has generally been assumed that Copenhagen has a measurement problem, the most important problem in foundations - not these horrible fake problems that Frauchiger and Renner solve.

What "fake problems" are you talking about?

You start off talking about Masanes's version and then switch back to Frauchiger-Renner. Are the fake problems with Masanes or the original Frauchiger-Renner.

As I said, like Healey I believe that the original FR papers have little force, but like most of the foundations community I think Masanes's version is a serious result. If Masanes's version has "fake problems" I'd like to hear them.

 

[atyy]

Not wrong, but the set of interpretations eliminated by them is almost null and I believe nobody held them outside of those who don't think much about Foundations. I don't think they have much content for serious interpretations.

Well, those are equivalent FAPP (as stevendaryl said, one can be charitable). Anyway, I'm glad I haven't spent much time with the first 2 FR versions.

What "fake problems" are you talking about?

You start off talking about Masanes's version and then switch back to Frauchiger-Renner. Are the fake problems with Masanes or the original Frauchiger-Renner.

As I said, like Healey I believe that the original FR papers have little force, but like most of the foundations community I think Masanes's version is a serious result. If Masanes's version has "fake problems" I'd like to hear them.

Fake problems in the sense that they are, as you say, completely irrelevant. Given the bad track record of this theorem, I'm going to wait before investing time in the Masanes version. However, I would like to know how that accounts for the view that QM is only formally complete, but not de facto complete because of the measurement problem. I think many would count this a variety of classic Copenhagen - Dirac, Messiah, Bell, possibly L&L. Demystifier himself is, I think, a proponent of this version of classic Copenhagen: https://www.physicsforums.com/insights/stopped-worrying-learned-love-orthodox-quantum-mechanics/.

 

[DarMM]

Given the bad track record of this theorem, I'm going to wait before investing time in the Masanes version.

Just to be clear Masanes's version is almost as old as the FR result itself. The FR result had problems recognised almost immediately, Masanes has yet to have any pointed out.

I don't think it can be judged as poor based on the track recorded of a related theorem. They're not the same result.

Although I understand your weariness.

The rest of your post requires a longer answer which I'll only have time for over the weekend. To help though what do you mean by "formally complete". That it isn't self-contradictory, even though it leaves somethings unexplained like measurement?

Also do you take a perspectival view of Copenhagen, i.e. the measurement outcomes aren't fully objective but associated with the agent observing them, relational to some degree.