Evolution of the Renner et al Wigner-like paradox

[Demystifier]

In the first version of their arxiv preprint, Frauchiger and Renner argued that only the many word interpretation of QM was consistent.
https://arxiv.org/abs/1604.07422v1

In the second version, the famous one published in Nature Communications, they radically changed their conclusions. They argued that there are 3 categories of consistent QM interpretations, depending on which of the 3 natural assumptions is denied. One of those assumptions is the existence of a single outcome, so the many world interpretation was interpreted as the interpretation that denies that assumption.
https://arxiv.org/abs/1604.07422v2

Now in the most recent arxiv paper (published in Contemporary Physics), Renner (together with Nurgalieva) changes his opinion again. This time they argue that in fact many worlds do not deny the existence of a single outcome, so there are only two types of quantum interpretations, depending on whether they deny the assumption Q or C. Denying Q is denial that the quantum Born rule can be applied to any system, even if that system is a macroscopic observer. Denying C is denial that conclusions by different agents must be mutually consistent. It seems to me that those two types of interpretations roughly coincide with ontological interpretations (which propose existence of an objective reality) and non-ontological interpretations.
https://arxiv.org/abs/2106.05314

Given that Renner et al change their opinion so often, should we take them seriously? Does their change of opinion converge to something? If yes, to what?

 

[Fra]

Does their change of opinion converge to something? If yes, to what?

Qbism + something new?

/Fredrik

 

[EPR]

Given that Renner et al change their opinion so often, should we take them seriously? Does their change of opinion converge to something? If yes, to what?

From the paper:

"Here we propose a gedankenexperiment where quantum theory is applied to model an experimenter who herself uses quantum theory. We find that, in such a scenario, no single-world interpretation can be logically consistent. "A Superobserver can mend the single-world interpretation.

 

[Fra]

"Assumption C. An agent can use conclusions obtained by admitting the view of another agent
..
A notable exception is QBism, which rejects Assumption C. Rather, QBism holds that an “agent will have to decide on a case by case basis” whether or not they adopt another agent’s conclusions [47]."
-- https://arxiv.org/abs/2106.05314

[47] Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend
"We have shown that the paradoxa found by these authors disappear if the friend analyses the experiment as an action she performs on the world outside herself, which includes Wigner. These thought experiments thus illustrate what we have called a quantum Copernican principle: when two agents take actions on each other, each agent has a dual role as a physical system for the other agent."
-- https://arxiv.org/pdf/2008.03572.pdf

/Fredrik

 

[gentzen]

Given that Renner et al change their opinion so often, should we take them seriously?

No, we should no longer take them seriously!

Their initial argument has been analysed by many different people, and there is widespread agreement that their argument does not prove what they claim. They even react to some of those analyses in their paper:

In a much-noticed comment [74] about the FR paradox, Aaronson argued that, due the detrimental effect of the measurements that are applied to Alice and Bob’s labs, these agents can no longer remember the statements they derived. His conclusion was that the contradiction arising inthe FR thought experiment may be avoided simply by declaring that an agent’s inferences obtained from Q become void once the agent has lost their memory. (A similar argument has been given in [64], see Ftn. 11, and in [75].)

Such a declaration would however be hard to justify. The timing of the individual steps in the FR experiment is chosen such that no agent is required to remember statements (...) after a measurement has been applied to their lab. ... This amounts to dismissing quantum-theoretic predictions that an agent makes at present on the grounds that the agent’s brain will at some later time deteriorate

Of course such a declaration can be justified, erasing memory is exactly what happens in the sleeping beauty paradox. Craig Gidney (Strilanc) is spot on when he fills this and other details to Aaronson's argument in The Frauchinger-Renner Paradox is a Sleeping Beauty Problem.

 

[PeterDonis]

erasing memory

It's worse than just "erasing memory". The scenarios being considered in all these discussions require the ability to reverse decoherence. But if the ability to reverse decoherence exists, then there can never be any such thing as a "measurement" as that term is used in the basic math of QM, because the basic math of QM assumes that a "measurement" irreversibly records a result. (Note that this is true even in the many worlds interpretation--decoherence tells you when worlds "split" in the MWI, so if decoherence can be reversed, there is no longer splitting of "worlds" in the MWI and the whole basis for making the MWI consistent with our actual observations is destroyed.)

In other words, all of these discussions rely on an assumption that contradicts basic QM. And since you can derive any conclusion you like from a contradictory set of premises, it's no wonder that so many incompatible conclusions have been derived in this area.

 

[Fra]

Of course such a declaration can be justified

Maybe, but I think it would required a non-trivial radical modification of the theory that nees to be qualified?

This is similar what I implied by "something new" in post 2. After all, even Qbism has to eventually "handle" the disagreement between agents as they start to interact. It's not like it would make any sense to consider qbist agents that never interacts, or never are required to face the inconsistencies. But I think that requires serious modification of QM.

/Fredrik

 

[gentzen]

This is similar what I implied by "something new" in post 2. After all, even Qbism has to eventually "handle" the disagreement between agents as they start to interact.

Maybe Qbism and other theories will eventually have to "handle" disagreements between agent. However, the Frauchinger-Renner argument does not provide such a disagreement. Maybe my "teaser" of Craig Gidney's analysis was too short or misleading, but if you read it, you will understand how he makes the error in the argument extremely obvious (and how this can be seen as a more elaborated version with more details of Aaronson's objection, and how it addresses the dismissal of Aaronson's analysis in the new paper).
Not sure whether you heard of the sleeping beauty problem before. The point is that the agent (i.e. Alice and Bob) is woken up two times, but his memory gets erased after being woken up the first time. The Frauchinger-Renner argument just obscures the fact that Alice and Bob are in a similar situation.

 

[PeterDonis]

even Qbism has to eventually "handle" the disagreement between agents as they start to interact

Unless decoherence can be reversed, there can never be any disagreement between agents as they start to interact. With decoherence, agents that interact will always find that the measurement results they have observed are consistent with each other.

 

[Demystifier]

But if the ability to reverse decoherence exists, then there can never be any such thing as a "measurement" as that term is used in the basic math of QM, because the basic math of QM assumes that a "measurement" irreversibly records a result.

In principle I disagree. Even the conventional decoherence theory predicts that the system will spontaneously turn back to the initial state after a very long quantum Poincare recurrence time. Sure, this time is many many orders of magnitude larger than the age of the Universe, so for practical purposes we can say that decoherence is irreversible. But the point is that reversibility is not impossible in principle, it's only impossible in practice. In other words, standard QM does not require that measurement is irreversible in principle, only in practice. (Just like standard thermodynamics, when viewed from the point of view of statistical physics, does not require that violation of the 2nd law is impossible in principle, only in practice.)

So in a thought experiment I think it's perfectly justified to consider what would happen under conditions which are possible in principle. Reversing measurement is such a condition.

 

[martinbn]

Is there a Poincare like theorem in this context?

 

[Demystifier]

Is there a Poincare like theorem in this context?

https://en.wikipedia.org/wiki/Poincaré_recurrence_theorem#Quantum_mechanical_version

 

[martinbn]

https://en.wikipedia.org/wiki/Poincaré_recurrence_theorem#Quantum_mechanical_version

For time-independent quantum mechanical systems with discrete energy eigenstates, a similar theorem holds.

So, in general no such theorem?

 

[gentzen]

So, in general no such theorem?

Well, if the Hamiltonian is allowed to change with time, then of course you won't have a recurrence theorem.

The part with the discrete energy eigenstates is less obvious, because even if they are discrete, you still need detailed arguments involving approximations. And it is not obvious why such approximations should not also be possible in the case with continuous energy eigenstates. But maybe the argument became too technical in that case for a wikipedia article.

 

[martinbn]

Well, if the Hamiltonian is allowed to change with time, then of course you won't have a recurrence theorem.

The part with the discrete energy eigenstates is less obvious, because even if they are discrete, you still need detailed arguments involving approximations. And it is not obvious why such approximations should not also be possible in the case with continuous energy eigenstates. But maybe the argument became too technical in that case for a wikipedia article.

Of course, my question was genuine. I am just curious. The references given also treat only the case of discrete energy eigenstates.

 

[gentzen]

Of course, my question was genuine. I am just curious. The references given also treat only the case of discrete energy eigenstates.

You are right, I was a bit annoyed by your suggested conclusion. The discrete energy eigenstates probably arise as a simple way to translate the "bounded orbits" parts of the classical theorem into the quantum domain:

The theorem is then: If a flow preserves volume and has only bounded orbits, then for each open set there exist orbits that intersect the set infinitely often.

I don't know whether the "discrete energy eigenstates" translation of "bounded orbits" is the most appropriate one, or whether another technical condition would capture its meaning even more faithful. But on an intuitive level, it is indeed closely related, because the bound states are the ones which cannot escape completely from the influence of a potential, and those are also the states that end up with a discrete spectrum in the analysis of explicitly given (i.e. sufficiently well defined) quantum systems.

 

[Demystifier]

So, in general no such theorem?

No, but the classical recurrence theorem is also not general, it's only valid if the system has only bounded orbits.

 

[PeterDonis]

standard QM does not require that measurement is irreversible in principle, only in practice

I would say that with standard QM it is impossible to test whether measurement is irreversible in principle, if you insist on asking the question. But that doesn't mean standard QM is fine with measurement not being irreversible; it isn't. If measurement is not irreversible, standard QM as a theory breaks down--it becomes inconsistent with observation. (And possibly inconsistent period, depending on which interpretation you adopt.) So we need some other theory to tell us what happens if measurement is no longer irreversible. We can't use standard QM.

https://en.wikipedia.org/wiki/Poincaré_recurrence_theorem#Quantum_mechanical_version

Which, as noted, is only valid for a time-independent Hamiltonian. Which does not apply to any real system. Real Hamiltonians are not time-independent.

 

[PeterDonis]

the classical recurrence theorem is also not general, it's only valid if the system has only bounded orbits.

A similar restriction applies to the quantum version also, does it not? At least if relativity is taken into account? For example, in any real situation, some of the degrees of freedom that get entangled during decoherence will be low energy photons sent off to infinity. Those degrees of freedom are gone; they're never coming back. So the system is effectively unbounded. I believe the quantum recurrence theorem would also be invalid under such conditions.

 

[Fra]

Maybe Qbism and other theories will eventually have to "handle" disagreements between agent. However, the Frauchinger-Renner argument does not provide such a disagreement. Maybe my "teaser" of Craig Gidney's analysis was too short or misleading, but if you read it, you will understand how he makes the error in the argument extremely obvious (and how this can be seen as a more elaborated version with more details of Aaronson's objection, and how it addresses the dismissal of Aaronson's analysis in the new paper).
Not sure whether you heard of the sleeping beauty problem before. The point is that the agent (i.e. Alice and Bob) is woken up two times, but his memory gets erased after being woken up the first time. The Frauchinger-Renner argument just obscures the fact that Alice and Bob are in a similar situation.

I admit I didn't read or check all the claims in the paper in detail, on quick reading the most obvious things that seems suspicous from my perspective is the assumption C in post 4. Perhaps their argument is wrong, but I am inclined to think their conclusion is right. But for perhaps other reasons, I intuitively can not see how quantum theory as it stands is possibly consistent as a universal theory of intrinsic inference. There are lots of details in this that just doesn't make sense to me. It seems clear that as QM relies on classical agents, and that these agents are able to in a fairly trivial manner make observer equivalence manifest. But the tension in this picture will grow out of hand as the systems get very complex, and the interactions between the classical agents probably need to be explained better. I certainly dont' have any explicit arguments, and I also don't know the the motives for the papers is, if it IS to find some proof of what may be intutively true or not. IF so, they have my symphaty and i can not blame them for changing their mind between papers. A solid proof would be NICE, as it would convince people also that don't see the problem of current theory intuitively from their interpretation.

/Fredrik

 

[Fra]

Unless decoherence can be reversed, there can never be any disagreement between agents as they start to interact. With decoherence, agents that interact will always find that the measurement results they have observed are consistent with each other.

I realized that what i had in mind is not part of regular qbism.

(What I meant was the idea of possible disagreements, just in order to understand and explain the process which produces a consistent asymptotic agent population. And thus to distinguish between regular expected evolution as per law, and the slower evolution of law itself, relative to the agent, and as long as the law itself is evolving, no theory may be 100% consistent, so paradoxally I think that any agent doing a proper intrinsic inference would have to LIVE with and handle small inconsistencies. The question is how to understand and make sense of a system where "inconsistences" are bound to exist. Another way of putting it is. It seems intutiviely inconsistent to think that you can LEARN without ever beeing wrong, and it's hard to upfront to constrain your "errors" to a predefined statespace, as it will grow as you learn more)

/Fredrik

 

[atyy]

Given that Renner et al change their opinion so often, should we take them seriously? Does their change of opinion converge to something? If yes, to what?

That depends on your interpretation of https://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf.

 

[Demystifier]

Which, as noted, is only valid for a time-independent Hamiltonian. Which does not apply to any real system. Real Hamiltonians are not time-independent.

By "real" Hamiltonians you obviously mean effective Hamiltonians that can be manipulated in a laboratory. Fundamental Hamiltonians, like that of the Standard Model, are time independent.

 

[Demystifier]

For example, in any real situation, some of the degrees of freedom that get entangled during decoherence will be low energy photons sent off to infinity. Those degrees of freedom are gone; they're never coming back. So the system is effectively unbounded. I believe the quantum recurrence theorem would also be invalid under such conditions.

Yes. But then again, one may suppose that the Universe is not actually infinite (it does not contradict any observed fact), in which case the system is bounded in principle (even if still unbounded for practical purposes).

 

[Demystifier]

That depends on your interpretation of https://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf.

Yes, when I was thinking about Renner et al, I was thinking about that story too.

 

[martinbn]

Yes. But then again, one may suppose that the Universe is not actually infinite (it does not contradict any observed fact), in which case the system is bounded in principle (even if still unbounded for practical purposes).

I am not sure about this. A spatially finite universe that is expanding forever is not really a bounded system. At the very least the volume changes all the time. If the expansion is fast enough a light pulse in some direction will never return from the other side back to us.

 

[Demystifier]

A spatially finite universe that is expanding forever

I had in mind a universe that does not expand forever.

 

[martinbn]

I had in mind a universe that does not expand forever.

That does contradict observations.

 

[Demystifier]

That does contradict observations.

No. Observations show that universe expands now, but not that it will expand forever. For instance, if dark energy (responsible for accelerated expansion) is dynamical and time dependent, then it's possible that expansion will stop one day.

 

[gentzen]

By "real" Hamiltonians you obviously mean effective Hamiltonians that can be manipulated in a laboratory. Fundamental Hamiltonians, like that of the Standard Model, are time independent.

Maybe PeterDonis is thinking more about the expansion of the universe, which was also brought up by martinbn?
However, martinbn's "I am just curious" is interesting in this context: Can we allow some harmless form of time dependence, like a time periodic Hamiltonian? In the classical version, it looks like this case is automatically included in the time independent version. For the quantum version, this is less obvious, at least I don't see how. But I guess it is still true nevertheless, i.e. I guess that the theorem can also be proved for time periodic Hamiltonians.

 

[msumm21]

Given that Renner et al change their opinion so often, should we take them seriously?

I once read the first paper you cited. If I recall correctly it took the same approach as many Wigner's friend type experiments that I personally don't like. They assume an experimenter in a lab measures something and remembers a definite outcome, but doesn't collapse the wave function. I realize there may be some interpretations that allow this, but doesn't every experiment known to man appear to violate this assumption? If so, any contradictions derived on top of this assumption may just as well be due to this assumption as whatever else they claim.

 

[Fra]

They assume an experimenter in a lab measures something and remembers a definite outcome, but doesn't collapse the wave function.

Which agents wave function do you mean is not collapsed? Wigners wavefunction of the lab+friend, when the friend in in the lab makes a measurement or something else?

/Fredrik

 

[msumm21]

Which agents wave function do you mean is not collapsed? Wigners wavefunction of the lab+friend, when the friend in in the lab makes a measurement or something else?

If I recall correctly, they assumed the wave function is not collapsed, according to actors that didn't directly do the measurement themselves (i.e. Wigner in the original experiment).

Why not go with a simple explanation that agrees with all experiments--when a person measures a qubit it's collapsed? Even if that person wasn't me, or conducted the experiment in a different room/lab. If I don't know the measurement result, then I'd consider it a mixed state.

 

[Fra]

If I recall correctly, they assumed the wave function is not collapsed, according to actors that didn't directly do the measurement themselves (i.e. Wigner in the original experiment).

Yes, but the point of the argument (trying to prove inconsistect) is that if QM is to have universal validity. Then the collapse of the the friend + lab, must have a unitary description from the other agent when isolated.

Then tension seems to be that QM requires a classical context to be formulated. Which means that classical observers has to be able to trust each other. but as one what pushes this, to extremes, by proposing that the classical agents are part of a quantum system, things break down.

Instead of getting stuck on the details, this is not suprising to me, and it suggests that we need somehow a reconstruction, or perhaps a new way to understand QM. Perhaps perfect consistency is impossible, their third paper also mentions Gödels incompleteless. Intuitively learning, is NOT a deductive process, nor is science, so it seems that somewhere therer is a bound to exist a bleeding edge. All we need to do is have it under control I think.

As I see it, trying to illuminate potential problem doesn't have the purpose to trash something that obviously works, but hopefully to help see how to move on and extend it.

/Fredrik

 

[msumm21]

Yes, but the point of the argument (trying to prove inconsistect) is that if QM is to have universal validity. Then the collapse of the the friend + lab, must have a unitary description from the other agent when isolated.

I guess it depends on how you interpret the laws of QM and "universal validity," but to me the easiest way to read rule 7 is that the state is collapsed after any measurement, not just my measurements. Also seems more universal (to me). (Despite the ambiguity in "measurement," I think we all agree that a human measuring something and getting a definite result qualifies.)

Said another way, it seems awkward for me to think that measurements behave one way when I perform them, but a different way when you perform them.

So if a contradiction is derived by assuming this "awkward" fact, then I want to blame it on this fact.