Resolution of the Frauchiger-Renner paradox

[Demystifier]

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).

 

[PeterDonis]

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 on non-classical cat superpositions).

But how can the observer know this? In fact, if the observer cannot use the collapse rule, how can the observer know anything? Anything the observer thinks they "know" could be undone by some unitary operator. The usual argument for invoking the collapse rule is decoherence, but "cat measurements" in the Frauchiger-Renner scenario imply the ability to undo decoherence. Which means the very concept of "measurement" evaporates, since no "measurement result" can ever be irreversibly recorded.

In short, it seems to me that a better resolution of the "paradox" would be to simply point out that the F-R scenario is inconsistent with decoherence.

 

[Morbert]

I argue that the rules of unitary quantum mechanics imply that observers who will themselves be subject to measurements in a linear combination of macroscopic states (“cat” measurements) cannot make reliable predictions on the results of experiments performed after such measurements[...]The two middle outcomes in A’s state should not have occurred according to his predictions based on his states at (6). Yet they do occur, according to the full unitary evolution
of the system, and violate A’s predictions

For posterity: https://www.physicsforums.com/threads/wigners-friend-and-incompatibility.976587/post-6227006

This means we cannot reason about the correlations between the property $F_\uparrow$ (i.e. the friend recording $\uparrow$) after Wigner's measurement, with respect to the property before Wigner's measurement.

 

[Demystifier]

Which means the very concept of "measurement" evaporates, since no "measurement result" can ever be irreversibly recorded.

I think that measurement makes sense even if the record is not irreversible. For example, if I forget the result of my measurement yesterday, that still was a measurement, wasn't it?

 

[PeterDonis]

if I forget the result of my measurement yesterday, that still was a measurement, wasn't it?

You forgetting the result is not the same as reversing the measurement. Even if your memory no longer reliably records the result, there are lots of other irreversible consequences of the decoherence that happened when the measurement was done. Reversing the measurement would mean undoing all of that decoherence and restoring everything to its pre-measurement state.

 

[Demystifier]

You forgetting the result is not the same as reversing the measurement. Even if your memory no longer reliably records the result, there are lots of other irreversible consequences of the decoherence that happened when the measurement was done. Reversing the measurement would mean undoing all of that decoherence and restoring everything to its pre-measurement state.

So what? If a subsystem is reversed, it doesn't mean that the past events in the subsystem did not happen. In the FR scenario the subsystem involves the friend and his laboratory (not the entire universe), and in principle the events in this subsystem can be reversed.

 

[PeterDonis]

If a subsystem is reversed, it doesn't mean that the past events in the subsystem did not happen.

That's not what I said. I said that "reversal" means restoring all affected degrees of freedom to their previous state. That, or its equivalent, is what is claimed to be done to the "friend" in the Frauchiger-Renner scenario. Of course the "reversal" still happens in the forward direction of time; it doesn't mean the past events didn't happen. But it is something much more drastic than just a human forgetting something.

In the FR scenario the subsystem involves the friend and his laboratory (not the entire universe)

I said nothing about the entire universe. I was referring to the F-R scenario. The friend is a human and the laboratory is a complicated macroscopic system. "Reversing" a measurement made by the friend using the laboratory would involve exercising precise control over something like $10^{30}$ degrees of freedom. (And even that assumes that the friend + laboratory can be perfectly isolated during the whole process; allow some photons to be emitted into space and the whole thing is ruined.) Again, much more drastic ("much" as in "many, many, many orders of magnitude") than a human forgetting something.

 

[Demystifier]

@PeterDonis If I understood you correctly, you are explaining why the FR thought is experiment is very very very difficult to perform in practice. I think everyone agrees with that. But the point is that the experiment should be possible in principle. So if quantum mechanics is a fundamental theory that can answer all questions that make sense at least in principle, then it should answer certain questions about the friend in the FR setup. And I think that the paper in the first post answers such questions very convincingly.

 

[Morbert]

@PeterDonis If I understood you correctly, you are explaining why the FR thought is experiment is very very very difficult to perform in practice. I think everyone agrees with that. But the point is that the experiment should be possible in principle. So if quantum mechanics is a fundamental theory that can answer all questions that make sense at least in principle, then it should answer certain questions about the friend in the FR setup. And I think that the paper in the first post answers such questions very convincingly.

"in principle" might need to be qualified here as pertaining to a non-relativistic quantim mechanical universe, as physicists like Roland Omnes argue that relativity renders such measurements impossible in principle as well as in practice. [edit] - see chapter 7 in "The Interpretation of Quantum Mechanics"

With this caveat in mind, what the paper shows is that if a universe is nonrelativistic and contains superobservers making measurements on ordinary observers, in measurement bases corresponding macroscopic state superpositions, then the ordinary observers cannot make reliable records of measurements on microscopic systems.

 

[Demystifier]

then the ordinary observers cannot make reliable records of measurements on microscopic systems.

Yes, but this sentence alone does not say how observers should cope with that, i.e. how they should apply QM.

 

[PeterDonis]

If I understood you correctly, you are explaining why the FR thought is experiment is very very very difficult to perform in practice.

That's one way of viewing it. But another way of viewing it is that we have no evidence that performing it is even possible in principle. Claiming that it is requires extrapolating our current capability for precise control of quantum degrees of freedom over about 30 orders of magnitude. In other words, it requires believing that our current theory of quantum mechanics is a true fundamental theory, not an approximation to something else which is valid within our current domain of experimental capability but is not valid when extrapolated that far.

You appear to agree with this:

if quantum mechanics is a fundamental theory

Yes, if. But Frauchiger and Renniger, as far as I can tell, make no such qualification. Nor do other physicists who agree with them. They appear to be claiming that their scenario is possible, with no caveat that that's only true if QM, in the form in which we currently have it, turns out to be a truly fundamental theory.

 

[PeterDonis]

this sentence alone does not say how observers should cope with that, i.e. how they should apply QM.

One obvious way would be to question whether these ordinary "observers" even deserve to be called that, since our ordinary concept of "observer" presupposes that "observers" can make reliable records of their observations.

Another obvious point is to question whether, if F-R are correct about "ordinary observers", there can even be any such "superobservers" at all. Wigner, in their scenario, is just a human, just like his friend. Someone else could come and do the same unitary operations on Wigner that Wigner does on his friend. If such operations are possible, then the whole conceptual basis of QM evaporates, since we cannot reliably infer anything from what we currently call "observations"--after all, someone else could come along and perform a unitary operation on us that invalidates them. Nothing would be immune to this. But then what justifies us using QM as a theory in the first place? Our basis for believing it is that we have run lots of experiments and gotten certain results that match QM predictions. But if F-R are correct, that basis is invalid.

 

[Demystifier]

Yes, if. But Frauchiger and Renniger, as far as I can tell, make no such qualification. Nor do other physicists who agree with them. They appear to be claiming that their scenario is possible, with no caveat that that's only true if QM, in the form in which we currently have it, turns out to be a truly fundamental theory.

The point of the FR gedanken experiment is to better understand quantum theory per se, not to predict what will actually happen in an experiment that is practically impossible to perform.

 

[PeterDonis]

The point of the FR gedanken experiment is to better understand quantum theory per se, not to predict what will actually happen in an experiment that is practically impossible to perform.

I'm not sure I see the point if that's all it is. Nor am I sure that Frauchiger and Renner, and other proponents of their thought experiment, would agree that that's all it is.

In any case, my reason for pointing these things out in this particular thread is that, as I said in post #2, to me it undermines the argument given in the paper cited in the OP. That argument depends on the friend "knowing" something, but if FR's scenario is taken as it is given, the friend cannot reliably "know" anything. Nor can anyone. To me that amounts to a reductio ad absurdum of the FR thought experiment itself. But obviously not everyone agrees with that assessment.

 

[Demystifier]

but if FR's scenario is taken as it is given, the friend cannot reliably "know" anything.

I disagree. Wigner can tell the friend in advance, by classical channels, that he will measure him, so if the friend trusts Wigner that he is not lying, he knows that he will be measured. Of course, it depends on trust, but that may be enough for practical purposes. The issue is how to use QM in practice under certain conditions. Since this kind of knowledge has a Bayesian character, a QBist may find it particularly appealing, but one does not need to be a strong QBist to apply this reasoning in practice.

 

[martinbn]

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).

How is this resolving and demystifying anything? It simply declares that in some cases you cannot use the Born rule.

 

[PeterDonis]

Wigner can tell the friend in advance, by classical channels, that he will measure him

But someone else could then come in and do a unitary operation on the friend that would undo the change that Wigner induced in the friend by doing this. And the friend would have no way of knowing that this had not happened.

Or, for that matter, someone else could do a unitary operation on Wigner that removed Wigner's "knowledge" of what he had told the friend, so that Wigner no longer "cat measures" the friend.

Once you introduce the possibility of doing these kinds of operations on observers, you can no longer just help yourself to the assumption that any information is ever stored reliably.

 

[Demystifier]

But someone else could then come in and do a unitary operation on the friend that would undo the change that Wigner induced in the friend by doing this. And the friend would have no way of knowing that this had not happened.

Or, for that matter, someone else could do a unitary operation on Wigner that removed Wigner's "knowledge" of what he had told the friend, so that Wigner no longer "cat measures" the friend.

Once you introduce the possibility of doing these kinds of operations on observers, you can no longer just help yourself to the assumption that any information is ever stored reliably.

So what? Someone mean could do various nasty things do deceive scientists, but it doesn't stop scientists from doing their job based on trust that this probably does not happen. For example, maybe all my copies of QM textbooks are non-reliable because there is a world conspiracy against me, so I always get a version of the textbook with many false claims, so my understanding of QM is totally wrong. Maybe, but so what? I trust that this isn't the case, so I do science as if this is isn't the case. The same is with the possibility you describe above.

 

[Morbert]

Yes, but this sentence alone does not say how observers should cope with that, i.e. how they should apply QM.

From the paper:

Could perhaps observer A modify his application of quantum mechanical rules to account for measurements that he knows will happen to him? Sadly, in general no. To do so, A should know the exact state of the full system before he performs any measurements, as well as the precise measurement that will be performed on him afterwards. With anything short of this full information, A can make no reliable predictions, even probabilistic ones.

Perhaps our only hope would be to evolve into exotic beings that register superpositions of macroscopically distinct states as the new pointer states, so that our bases line up with whatever bases the higher beings are observing us in.

 

[Morbert]

An adjascent discussion is had here by Gell-Mann and Hartle: https://arxiv.org/pdf/gr-qc/9404013 (section IV), where hypothetical observers operating in complementary descriptions of the universe are explored.

 

[PeterDonis]

So what?

So if scenarios like the one Frauchiger and Renner describe are possible, the trust you describe is not justified, because you cannot trust that the mean, nasty things have not happened. You cannot trust anything you think you know. You cannot trust that you can draw inferences from whatever "data" you think you have, not even with the caveat that of course there is some probability of error.

I understand that in a practical sense, we are going to keep on doing science as if none of the above is the case. My point is that doing that implicitly assumes that scenarios like the one Frauchiger and Renner describe are not possible. The whole thing is just an abstract curiosity that cannot be relevant to any actual science we actually do.

 

[iste]

the trust you describe is not justified, because you cannot trust that the mean, nasty things have not happened. You cannot trust anything you think you know. You cannot trust that you can draw inferences from whatever "data" you think you have

But things playing a similar role to this are possible in any scientific context. This has been a running theme in epistemology and philosophy of science since Hume. Even falsification isn't safe from these kind of threats.

 

[PeterDonis]

things playing a similar role to this are possible in any scientific context. This has been a running theme in epistemology and philosophy of science since Hume.

It's one thing to make an abstract philosophical observation about the limits of our ability as humans to have confidence in our knowledge.

It's quite another thing to make a specific prediction based on a specific scientific theory that, if taken seriously as it is made, invalidates the very basis on which that specific scientific theory was built.

The latter is what I am saying is being done in the Frauchiger-Renner scenario.

 

[Demystifier]

My point is that doing that implicitly assumes that scenarios like the one Frauchiger and Renner describe are not possible. The whole thing is just an abstract curiosity that cannot be relevant to any actual science we actually do.

And my point is that, to keep doing science as we are used to, it is not necessary to assume that such scenarios are absolutely impossible. It is sufficient to assume that they are very unlikely. Just as it is very unlikely but not absolutely impossible, for instance, that the 2nd law of thermodynamics will be violated in a macroscopic system.

 

[PeterDonis]

to keep doing science as we are used to, it is not necessary to assume that such scenarios are absolutely impossible. It is sufficient to assume that they are very unlikely.

But on what basis are you assuming this? If such scenarios are possible at all, we cannot say anything about their unlikelihood based on any evidence we have, because such scenarios invalidate any evidence we have.

Just as it is very unlikely but not absolutely impossible, for instance, that the 2nd law of thermodynamics will be violated in a macroscopic system.

False analogy, because a violation of the second law would not invalidate the evidence on which we rely to justify our belief that such violations are very unlikely.

 

[Demystifier]

But on what basis are you assuming this? If such scenarios are possible at all, we cannot say anything about their unlikelihood based on any evidence we have, because such scenarios invalidate any evidence we have.

Yes we can. We have a lot of evidence that quantum systems can relatively easily be manipulated in the needed way (cat measured and reversed) when they contain a small number of degrees of freedom. We also have evidence that they can be manipulated so when they have a bit more degrees of freedom, but not longer so easily. By extrapolation, we can infer that such manipulations should be possible even for macroscopic quantum systems (like a Wigner's friend), but should be very difficult.

 

[PeterDonis]

We have a lot of evidence

Which, if the F-R scenario is possible, we cannot trust. That's the point I have been making. It is no answer to this to argue based on evidence.

By extrapolation

It isn't a matter of "extrapolation" in itself. It's a matter of maintaining quantum coherence vs. decoherence happening. One could say that maintaining coherence gets more difficult as the number of degrees of freedom goes up. But it's not that simple either. For the concepts of "measurement" and "observer" as they are used in QM to work at all, decoherence has to be irreversible, at the very least, when a measurement or an observer is involved. That is what we have to assume for us to be able to do science. It's not enough to assume that it's "very difficult" to reverse it in such cases. It has to be impossible. At least, that's what the F-R scenario tells us: if we let it be possible for measurements and observers, those concepts no longer work the way they have to for us to do science.

 

[Demystifier]

Which, if the F-R scenario is possible, we cannot trust.

I think we are here discussing epistemology, not physics. There are many other possible scenarios by which I cannot trust anything I think I know. One such possibility is that I have schizophrenia, so anything I think I know could be a delusion. How is the possibility of FR scenario different from the possibility of schizophrenia scenario?

 

[Demystifier]

For the concepts of "measurement" and "observer" as they are used in QM to work at all, decoherence has to be irreversible, at the very least, when a measurement or an observer is involved. That is what we have to assume for us to be able to do science. It's not enough to assume that it's "very difficult" to reverse it in such cases. It has to be impossible.

No, we don't need to assume this to do science. I do not assume this and yet I do science. In fact, I have never seen in the literature than anybody claims that reversal of decoherence is impossible when a measurement is involved, AFAIK there is a consensus that it is very very difficult, but not absolutely impossible. Do you know a reference claiming that it is absolutely impossible?

 

[PeterDonis]

I think we are here discussing epistemology, not physics.

I would say Frauchiger and Renner brought epistemology into it when they made claims about being able to undo an observation made by the friend.

How is the possibility of FR scenario different from the possibility of schizophrenia scenario?

Because schizophrenia can be established by observation and evidence. But you cannot establish by observation and evidence that no "Wigner" with the capability of undoing decoherence has performed such an operation on you.

I do not assume this and yet I do science.

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

I have never seen in the literature than anybody claims that reversal of decoherence is impossible

Nor have I. But I have also never seen in the literature any discussion of the implications of it being possible. It is simply an issue that appears to have been ignored. That doesn't mean it isn't an issue.

when a measurement is involved

"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.