Resolution of the Frauchiger-Renner paradox

[Demystifier]

You might not realize you are assuming it, but you are whenever you rely on evidence.

But I never absolutely rely on anything. I always doubt, I always admit that there is a possibility that I'm wrong. The only thing I don't doubt is: I think, therefore I am.

But I have also never seen in the literature any discussion of the implications of it being possible.

Yes you have. The FR paper is an example, as well as all the subsequent papers that analyze the FR paper.

"Measurement" is actually not really the relevant criterion here. The relevant criterion is decoherence. But the concepts of "measurement" and "observation" that we use in science implicitly rely on decoherence (at least if we assume that we and our measuring devices are ultimately quantum systems which must obey the laws of quantum mechanics), and on it being irreversible. The fact that this is not explicitly recognized does not mean it isn't true.

Are you claiming that decoherence is absolutely irreversible, that reversion is not just very difficult but fundamentally impossible? If you have a good argument for this claim, then you should publish it. It would be a very new and important result, contradicting everything we know about decoherence from the existing literature. In the meanwhile, I'll stick with the standard view that reversion of decoherence is just very difficult.

 

[PeterDonis]

Yes you have. The FR paper is an example

I meant they don't discuss the implications in terms of not being able to rely on evidence. I should have been more specific before.

Are you claiming that decoherence is absolutely irreversible

I am saying that extrapolating our current quantum mechanics unchanged to systems with $10^{30}$ or more degrees of freedom might be extrapolating it too far. The implications of being able to reverse decoherence, which is indeed a prediction of our current quantum mechanics, are part of the reason why I say that.

However, as far as this particular thread is concerned, I pointed out the implications in order to argue that the paper you referenced in the OP doesn't actually "resolve" anything about the Frauchiger-Renner scenario, because, as I said, if it is true that decoherence can be reversed, the rule prescribed in that paper cannot be followed--because that rule requires the friend to rely on evidence they are given about whether or not they will be "cat measured" in the future, and, as I have said, if decoherence can be reversed, nobody can rely on evidence. That, in itself, is not an argument that decoherence cannot be reversed. But it is an argument that the implications of the Frauchiger-Renner scenario can't be "resolved" by telling the "friend" to rely on evidence.

 

[Demystifier]

However, as far as this particular thread is concerned, I pointed out the implications in order to argue that the paper you referenced in the OP doesn't actually "resolve" anything about the Frauchiger-Renner scenario, because, as I said, if it is true that decoherence can be reversed, the rule prescribed in that paper cannot be followed--because that rule requires the friend to rely on evidence they are given about whether or not they will be "cat measured" in the future, and, as I have said, if decoherence can be reversed, nobody can rely on evidence. That, in itself, is not an argument that decoherence cannot be reversed. But it is an argument that the implications of the Frauchiger-Renner scenario can't be "resolved" by telling the "friend" to rely on evidence.

I think you see the problem because you think in black or white terms; either friend can rely on evidence or he cannot. By contrast, I think in shades of gray terms. I cannot absolutely rely on anything (except that I think and therefore exist), the best I can do is to rely with more or less confidence. The possibility of FR scenario adds one more reason to question the reliability of evidence, but there are many more. Perhaps the apparatus has a failure, perhaps my research assistant lies to me, perhaps I have schizophrenia, etc. Now you will say that I can use additional evidence to rule out all these other possibilities, but my point is that this additional evidence is also subject to doubt; maybe the apparatus for checking the apparatus also has a failure, etc. Or to be blatantly direct, yes, I think it's possible that someone cat measures my brain right now, but I estimate that probability for that is much smaller than the probability that I'm having a schizophrenic episode right now. And neither of the possibilities worries me much, because I estimate that probability for either of them is very small.

 

[PeterDonis]

I think you see the problem because you think in black or white terms; either friend can rely on evidence or he cannot.

No, that's not the issue. Once again, it's not a question of ordinary ways that people forget things or that evidence is not always reliable. Those have nothing to do with reversing decoherence. Reversing decoherence is a fundamentally different way for evidence to be unreliable. I've already explained why I think that and I don't think I can add anything further.

 

[Demystifier]

No, that's not the issue. Once again, it's not a question of ordinary ways that people forget things or that evidence is not always reliable. Those have nothing to do with reversing decoherence. Reversing decoherence is a fundamentally different way for evidence to be unreliable. I've already explained why I think that and I don't think I can add anything further.

At least we know where we disagree. But let us try to understand each other in a different way. Suppose that we model observers by using only classical physics. Would a possibility of reversal in the classical phase space be a fundamentally different way for evidence to be unreliable, compared to ordinary ways that people forget things or that evidence is not always reliable?

 

[PeterDonis]

Suppose that we model observers by using only classical physics. Would a possibility of reversal in the classical phase space be a fundamentally different way for evidence to be unreliable, compared to ordinary ways that people forget things or that evidence is not always reliable?

Since the effects of such a reversal, assuming classical physics (and therefore a fully deterministic time reversible model), would be to undo everything that happened during the period that got reversed, yes, I would say this is a fundamentally different way for evidence to be unreliable.

Note, however, that classical physics does not contain any operation that would actually do such a reversal. It contains pairs of solutions that are time reverses of each other, but does not contain any way of switching between them in mid-stream, so to speak. So there is no analogue in classical physics to the kinds of "reverse decoherence" unitary operations that the Frauchiger-Renner scenario uses.

 

[Demystifier]

Since the effects of such a reversal, assuming classical physics (and therefore a fully deterministic time reversible model), would be to undo everything that happened during the period that got reversed, yes, I would say this is a fundamentally different way for evidence to be unreliable.

Fine. And assuming classical physics, do you think that such reversal is possible in principle? (I'm not talking about reversal of the whole Universe, but about reversal of the friend and his classical laboratory.) And if it possible in principle, does it mean that we cannot do science? Or if you say that it is not possible in principle, can you explain why it is not possible?

 

[PeterDonis]

assuming classical physics, do you think that such reversal is possible in principle?

I thought I already answered that in post #36, second paragraph.

 

[Demystifier]

I believe I understand now the Wigner friend type experiments very well. It's really much simpler than usually presented in the literature. Consider a situation in which unitarity implies that the friend F is in a superposition, say
$$|{\rm F\;\;sees\;\;up}\rangle + |{\rm F\;\;sees\;\;down}\rangle$$
(By the "friend" F we mean a system sufficiently complex to detect definite outcomes. Without loosing on generality we can think of it as a human being. All other objects such as the measured particle with spin up or down, the apparatus, and the environment confined to the F's laboratory are not essential, because they can all be absorbed into a redefinition of "F".) The friend F himself sees only one of those possibilities, so from his point of view there is no superposition. But suppose that Wigner W has an advanced technology by which he can demonstrate that F is really in the superposition. How to reconcile these two perspectives, without falling into a logical contradiction?

It's actually not so difficult, we just need to accept that, in one way or another, there are two levels of description. At some global level there is no collapse, that's the level suitable for Wigner, while at another local level we can describe it as some kind of effective collapse, that's the level suitable for the friend alone. This may look rather vague, but specific interpretations of QM make it more precise. Each interpretation makes it more precise in its own way, so let us discuss it briefly.

Many worlds:
Both branches of F exist, but from the perspective of any particular branch it looks as if only that branch exists.

Bohmian:
Both branches of the wave exist, but only one branch is filled with actual particles.

Statistical ensemble (Ballentine):
There is no true collapse. F sees definite outcomes, but the statistical ensemble interpretation does not specify how exactly to describe it. Yet it insists that it should not be described by a true collapse. At best, collapse can be used as a rule of thumb associated with an update of information about definite outcomes.

QBism:
The primitive entities are the conscious agents, while the wave functions are only tools for thinking. The agent F uses the collapsed wave to describe his own observations, while the agent W uses the superposition. If F wants to think about observations of W, he can do that, but then he must use the superposition.

Relational (Rovelli):
We cannot say that F collapsed for himself, because collapse is only an effective description relative to something else (very much the same way velocity in classical physics makes sense only as relative to something else). So we may say, for instance, that the left brain hemisphere of F is entangled with his right brain hemisphere, so the left one collapses relative to the right one, and the right one collapses relative to the left one.

Copenhagen (Bohr version):
Physics does not tell us what nature is, but what we can say about nature. For that purpose, we use QM for microscopic stuff and classical physics for macroscopic stuff. Thus there is a cut after which we use a classical description. But the cut is not universal, F uses one cut (when he only talks about his own observations), W uses another. The descriptions by F and W are complementary.

Consistent histories:
The consistent histories interpretation can be viewed as a formalization of the Bohr's notion of complementarity. Any system can be described in many different frameworks, but the frameworks are "complementary" to each other, meaning that one should not combine conclusions obtained from different frameworks. In one framework there is (something that can effectively be described as) collapse of F, in another framework there isn't.

Instrumental (shut up and calculate):
When you want to know what F will see, use collapse. When you want to know what W will see, use the superposition.

We see that all the interpretations say basically the same, although in different ways. The global view with the superposition is somehow more "fundamental", or more "general", while the collapse is only an effective collapse, only suitable to describe what F sees without caring about a more global description such as that by W.

 

[javisot]

Consider a situation in which unitarity implies that the friend F is in a superposition, say
$$|{\rm F\;\;sees\;\;up}\rangle + |{\rm F\;\;sees\;\;down}\rangle$$
The friend F himself sees only one of those possibilities, so from his point of view there is no superposition. But suppose that Wigner W has an advanced technology by which he can demonstrate that F is really in the superposition. How to reconcile these two perspectives, without falling into a logical contradiction?

I find this part strange: imagine I have the technology to confirm that I live in "many worlds"—it would be paradoxical if, having confirmed that I live in many worlds, I could still explain the same thing using a single-world interpretation.

 

[Demystifier]

I find this part strange: imagine I have the technology to confirm that I live in "many worlds"—it would be paradoxical if, having confirmed that I live in many worlds, I could still explain the same thing using a single-world interpretation.

What do you mean by "I", and what do you mean by "many worlds"? The F does not see that F lives in a superposition. Only W can see that F lives in a superposition. And neither of them does not need to interpret the superposition in terms of "many worlds", the "many worlds" is only one of the interpretations, while there are many other interpretations that I briefly discussed in the previous post. If the many world interpretation is not intuitive to you, choose an interpretation that is. Interpretations are just tools for intuitive thinking.

 

[javisot]

Consider a situation in which unitarity implies that the friend F is in a superposition, say
$$|{\rm F\;\;sees\;\;up}\rangle + |{\rm F\;\;sees\;\;down}\rangle$$
The friend F himself sees only one of those possibilities, so from his point of view there is no superposition.

Up to this point, you could be talking about the many-worlds interpretation. The cat is both alive and dead (many worlds), but from its perspective, it does not experience those other worlds.

But suppose that Wigner W has an advanced technology by which he can demonstrate that F is really in the superposition.

Next, you state that W can demonstrate that F falls under the Many-Worlds interpretation—that is, W asserts that F is described by Many-Worlds and that the other interpretations are invalid.

How to reconcile these two perspectives, without falling into a logical contradiction?

You simply can't, a contradiction is guarantees,

isn't it?

 

[PeterDonis]

Consider a situation in which unitarity implies that the friend F is in a superposition, say
$$|{\rm F\;\;sees\;\;up}\rangle + |{\rm F\;\;sees\;\;down}\rangle$$

It's not that simple. The friend has made a measurement, so he's entangled with something. So the state is really something like (I'll ignore normalization throughout this post):

$$\ket{\uparrow} \ket{\text{Friend sees up}} + \ket{\downarrow} \ket{\text{Friend sees down}}$$

And if we take decoherence into account, so that the entanglement has spread to the environment, we have

$$\ket{\uparrow} \ket{\text{Friend sees up}} \ket{E}_\uparrow + \ket{\downarrow} \ket{\text{Friend sees down}} \ket{E}_\downarrow$$

where the $E$ kets include all of the environment degrees of freedom.

The issue here isn't really one of how existing QM interpretations account for this. It's that, for Wigner to be able to make the observations he's claimed to make, he would have to be able to reverse the decoherence. He would have to be able to make a measurement in a basis whose eigenstates were something like

$$\ket{\uparrow} \ket{\text{Friend sees up}} \ket{E}_\uparrow + \ket{\downarrow} \ket{\text{Friend sees down}} \ket{E}_\downarrow$$

and

$$\ket{\uparrow} \ket{\text{Friend sees up}} \ket{E}_\uparrow - \ket{\downarrow} \ket{\text{Friend sees down}} \ket{E}_\downarrow$$

which would reveal the interference between the alternatives--but the whole point of decoherence is that that's no longer possible. And AFAIK no interpretation of QM says it is; indeed, since the development of decoherence theory, decoherence has been the main way that all QM interpretations account for measurements being irreversibly recorded. Frauchiger-Renner are claiming (whether they realize it or not) that all of that can be discarded--but that throws away all known QM interpretations.

 

[Demystifier]

@PeterDonis
I don't think that any of this what you mentioned is essential.

1. The entanglement with the particle with spin doesn't change much. For example, F can eat that particle and then it becomes a part of F.

2. Adding environment also doesn't change much because F himself can be described as his brain + his other body parts, and the other body parts can be interpreted as environment around the brain. So putting additional environment around the whole body of F doesn't make any qualitative change.

3. In Wigner-friend-type thought experiments it is not essential to reverse the decoherence. The FR experiment uses a reversal of decoherence, but some experiments don't. More importantly, any experiment of this type with a reversal of decoherence is equivalent to a version of the same experiment without reversal, as explained in https://arxiv.org/abs/2308.16220 Sec. II.E. So the reversal of decoherence is just a technicality, which is not essential for understanding the core problem of the Wigner friend.

 

[Demystifier]

You simply can't, a contradiction is guarantees,

isn't it?

No. The interpretations that I discuss in the post explain why there is no contradiction. If you don't see how the contradiction is avoided in the many worlds interpretation, try other interpretations.

 

[PeterDonis]

1. The entanglement with the particle with spin doesn't change much. For example, F can eat that particle and then it becomes a part of F.

In the sense that F already has a huge number of degrees of freedom, and entangling with one more doesn't really matter, I suppose this is true. But I don't think it means my argument is irrelevant. See below.

2. Adding environment also doesn't change much because F himself can be described as his brain + his other body parts, and the other body parts can be interpreted as environment around the brain. So putting additional environment around the whole body of F doesn't make any qualitative change.

This just admits that F himself is already an "environment", i.e., F himself already contains a large number of untrackable degrees of freedom, so F can already decohere himself. (Similar remarks would apply to other similar experimental subjects like Schrodinger's cat.) Again, I suppose this is true, but I don't think it makes my argument irrelevant. See below.

3. In Wigner-friend-type thought experiments it is not essential to reverse the decoherence. The FR experiment uses a reversal of decoherence, but some experiments don't. More importantly, any experiment of this type with a reversal of decoherence is equivalent to a version of the same experiment without reversal, as explained in https://arxiv.org/abs/2308.16220 Sec. II.E. So the reversal of decoherence is just a technicality, which is not essential for understanding the core problem of the Wigner friend.

I'll look at the paper you referenced. My initial response is that without reversal of decoherence, Wigner's frield type thought experiments are pointless. We already know things like Mach-Zehnder interferometers work. If you're going to say that you can make an MZI out of a system with $10^{30}$ degrees of freedom by maintaining its quantum coherence for long enough, well, I think I'm entitled to be skeptical, but in any case such a system, by construction, can't have observed anything. So what is all the fuss about?

The fuss over Wigner's friend is because the friend is claimed to have observed something--and then we supposedly say how QM lets Wigner do something that seems paradoxical in the light of that. But "observed" requires decoherence--the irreversible (at least FAPP) recording of a result. If you don't have that, whatever you're doing, it doesn't seem to me to be what Wigner's friend experiment proponents think they're doing.

Again, I'll look at the reference. Maybe they address concerns like these somehow.

 

[Demystifier]

But "observed" requires decoherence--the irreversible (at least FAPP) recording of a result.

In the context of Wigner type experiments, decoherence is not reversed during some time during which the friend thinks "I have observed a definite outcome", but it is reversed later.

 

[PeterDonis]

any experiment of this type with a reversal of decoherence is equivalent to a version of the same experiment without reversal, as explained in https://arxiv.org/abs/2308.16220 Sec. II.E.

I don't think the meaning of "without reversal" in that section addresses the issue I'm raising. The alternative they describe there is basically that, instead of applying the unitary operator that reverses the decoherence directly, they make a measurement that detects interference between the decoherent branches--i.e., the kind of measurement I described in post #43. Technically I guess you could say that this isn't literally reversing the decoherence, but it amounts to the same thing: making use of interference between decoherent branches (since you have to know what, precisely, those interference terms are in order to apply the unitary operator that reverses the decoherence, just as you have to to make the measurement that detects the interference).

But interference between decoherent branches is exactly what can't be there if the branches are going to represent actual observed results. If the interference is still there, the branches aren't actually decohered.

 

[Demystifier]

But interference between decoherent branches is exactly what can't be there if the branches are going to represent actual observed results. If the interference is still there, the branches aren't actually decohered.

I don't think that the notion of "actual" decoherence makes sense. To explain what I mean, let us model the friend F as F=B+R, where B stands for brain, and R for the rest of his body. Let us assume that F is isolated from all other environments. Then decoherence means that B is entangled with R, so B is in the mixed state. But the full friend F=B+R is in the pure state. In other words, decoherence happens at the level of B, not at the level of F. Interference is still there in F, but not in B. In this sense there is no such thing as "actual" decoherence because there is a sufficiently big closed system, in this case F, which is still in superposition. And yet, this "non-actual" decoherence is sufficient for B to observe definite brain "outcomes". Later, after B saw a definite outcome, Wigner manipulates F. If Wigner could manipulate only B, then he could not reverse decoherence, not even in principle. But it is assumed that Wigner can manipulate the whole F, which is why he can reverse decoherence.

 

[PeterDonis]

Let us assume that F is isolated from all other environments.

Of course if you assume away the possibility of information leaking out, then no information leaks out and you can claim that the idealized, imaginary isolated system F can't "actually" decohere.

In the actual world, if nothing else, every real physical system emits photons, some of which escape never to return.

decoherence means that B is entangled with R, so B is in the mixed state. But the full friend F=B+R is in the pure state.

As I understand it, that's not what decoherence means in the actual decoherence literature. Decoherence in the actual decoherence literature, as I understand it, means that F has become entangled with environmental degrees of freedom outside of F which are untrackable (like photons escaping to infinity), so you can no longer assign a pure state to F. If you have any system of interest in your experiment that you can still assign a pure state to, then decoherence hasn't yet happened.

this "non-actual" decoherence is sufficient for B to observe definite brain "outcomes"

No, you can't just claim this, because this is precisely the point at issue. Has F actually observed any definite outcome when he's in an entangled superposition? Even when actual decoherence hasn't happened?

Note that the Wigner's Friend scenario, where Wigner makes a measurement that reveals that F is in an entangled superposition, cannot answer this question, because the very operation Wigner does destroys any information that might have enabled us to test it!

 

[Demystifier]

Has F actually observed any definite outcome when he's in an entangled superposition? Even when actual decoherence hasn't happened?

Yes he has, that's my main point. The brain B has observed a definite outcome, because B decohered due to interaction and entanglement with R (the rest of F's body). For that purpose, it is not necessary that the whole of F decoheres due to interaction and entanglement with something outside of F.

Moreover, some interpretations of QM claim that the environment does not even need to have many degrees of freedom. For example, if the whole universe contains only two entangled particles, say in the state $|a_1>|b_1>+|a_2>|b_2>$, then the Rovelli's relational interpretation claims that the state of the first particle is in a definite state $|a_1>$ or $|a_2>$. But this definiteness is not absolute, it's relative with respect to the other particle. The whole system of two particles is still in superposition.

 

[PeterDonis]

The brain B has observed a definite outcome, because B decohered due to interaction and entanglement with R (the rest of F's body).

But B also has to be entangled with things outside of F's body--the information about what B observed has to come from somewhere. So what you are calling "F" actually has to be more than just the friend's body; it has to be the friend's entire lab, including what they're experimenting on, all the apparatus, and everything else associated with it--anything that is involved in the overall interaction, however small a part it plays.

I realize that, in terms of the number of degrees of freedom involved, this is not a very large change--compared to the change from qubits. But that's part of my point--humans and their experimental labs are not qubits.

some interpretations of QM claim that the environment does not even need to have many degrees of freedom.

Yes, I know. I think those interpretations are, to say the least, using the term "environment" in an extremely unusual way.

To put my basic position in a nutshell: when Schrodinger originally published his cat thought experiment, he did not intend it as what we might now call PR for quantum mechanics. He intended it as a reductio ad absurdum of the belief that QM could be a fundamental theory of everything. I view Wigner's Friend scenarios in much the same way. Yes, if you take QM literally and treat it as a fundamental theory of everything, and assume that humans and our experimental labs are in principle just like qubits, the only difference is scale, you get outlandish stuff like this (much more outlandish than the usual counterintuitive things QM has forced us to accept because we've done the experiments to confirm them). That, to me, is a good reason not to take QM literally and treat it as a fundamental theory of everything, and not to believe that humans and our experimental labs are just like qubits.

 

[Demystifier]

Let me make some side remarks on decoherence.

In the actual world, if nothing else, every real physical system emits photons, some of which escape never to return.

That's why, in actual experiments, systems are cooled down close to absolute zero, so that photon emission is reduced to minimum, thus making decoherence negligible.

As I understand it, that's not what decoherence means in the actual decoherence literature. Decoherence in the actual decoherence literature, as I understand it, means that F has become entangled with environmental degrees of freedom outside of F which are untrackable (like photons escaping to infinity), so you can no longer assign a pure state to F. If you have any system of interest in your experiment that you can still assign a pure state to, then decoherence hasn't yet happened.

It depends on which literature you read. In the literature that models actual experiments that's right. But in the theoretical literature that deals with fundamental principles, that's not exactly what is meant by decoherence. In the context of the Wigner friend thought experiment such more theoretical literature is of course more relevant.

 

[PeterDonis]

That's why, in actual experiments, systems are cooled down close to absolute zero, so that photon emission is reduced to minimum, thus making decoherence negligible.

Yes, and for qubits, that works fine. Doing it with humans and a whole experimental lab, well, that's something else again.

in the theoretical literature that deals with fundamental principles, that's not exactly what is meant by decoherence.

Well, of course if you insist on the theoretical possibility of doing something like a Wigner's Friend experiment, you have to define "decoherence" differently, so it's something you can reverse (or the equivalent, like making the kind of measurement I described in post #43), but you can still trade on the connotations of "decoherence" as meaning the friend actually measured something and got a result. To me that's sleight of hand. But obviously many researchers in the field don't agree.

 

[Demystifier]

To put my basic position in a nutshell: when Schrodinger originally published his cat thought experiment, he did not intend it as what we might now call PR for quantum mechanics. He intended it as a reductio ad absurdum of the belief that QM could be a fundamental theory of everything. I view Wigner's Friend scenarios in much the same way. Yes, if you take QM literally and treat it as a fundamental theory of everything, and assume that humans and our experimental labs are in principle just like qubits, the only difference is scale, you get outlandish stuff like this (much more outlandish than the usual counterintuitive things QM has forced us to accept because we've done the experiments to confirm them). That, to me, is a good reason not to take QM literally and treat it as a fundamental theory of everything, and not to believe that humans and our experimental labs are just like qubits.

Ok, now your point of view is clear, and it's a perfectly legitimate point of view. But it is also legitimate to take the opposite point of view and take QM literally. The Wigner friend thought experiments take this point of view. My comments on this thread are also all made from this what-if-QM-is-really-fundamental? point of view. But you have every right to look at it from a different point of view. And maybe your point of view is correct. Nevertheless, I think it's interesting to investigate the what-if-QM-is-really-fundamental? perspective to see how far we can go with that.

 

[Matterwave]

Nevertheless, I think it's interesting to investigate the what-if-QM-is-really-fundamental? perspective to see how far we can go with that.

When you use the words "QM" here, are you attaching an interpretation? E.g. that MWI/BM should be fundamental.

 

[Demystifier]

When you use the words "QM" here, are you attaching an interpretation? E.g. that MWI/BM should be fundamental.

No. See my post #39 in which I explain how all interpretations say essentially the same, but in a different way.

 

[Matterwave]

We see that all the interpretations say basically the same, although in different ways.

It is very hard for me to read it this way. Your descriptions in this post of what the different interpretations say, at face value, seem to say very different things.

You have also (I presume intentionally) not included objective collapse theories in the list which are (as the name suggests) highly opinionated on what actually happens (namely... collapse). Do you think these theories will simply be ruled out by experiment eventually or you simply did not want to discuss them for the purposes of this thread?

 

[Sambuco]

Since I am a "relational guy" I would like to clarify a few points about how RQM deals with Wigner's friend experiment.

We cannot say that F collapsed for himself, because collapse is only an effective description relative to something else

The description is correct, but I would remove the word "effective," as it suggests that there is another, more fundamental state than the one assigned by the friend after measuring the particle's spin. The relational interpretation denies this because it assumes that all quantum states are equally valid, representing only different perspectives.

For example, if the whole universe contains only two entangled particles, say in the state |a1>|b1>+|a2>|b2>, then the Rovelli's relational interpretation claims that the state of the first particle is in a definite state |a1> or |a2>. But this definiteness is not absolute, it's relative with respect to the other particle. The whole system of two particles is still in superposition.

RQM assumes that there is no "view from nowhere", so all states are "relative states". Therefore, if the universe consisted only of two entangled particles, the superposition state you described would be meaningless. Since all quantum states represent the information that one physical system possesses about another, for your state to have (physical) meaning, a third particle would be needed, in which case your state would be $\ket{\psi}_{ab|c}$.

Lucas.

 

[Sambuco]

Brilliant paper https://arxiv.org/abs/2202.04203v2 recently published in Nature Communications (open access) https://www.nature.com/articles/s41467-024-47170-2 resolves and demystifies the Frauchiger-Renner paradox associated with the Wigner friend problem. The resolution of the paradox, in short, is that the observer should not use the collapse rule if she knows that she herself will be cat measured (i.e., measured in a basis of non-classical cat superpositions).

Since I don't think anyone has mentioned it before, I'm sharing this paper where Del Rio and Renner respond to Polychronakos' work.

Lucas.