Resolution of the Frauchiger-Renner paradox

[Demystifier]

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.

I agree it's hard, it takes some effort to see it this way. But they all have in common one crucial thing: There is never a collapse in some objective universal sense.

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?

These theories would be ruled out, precisely because in these theories there is a collapse in an objective sense.

 

[Demystifier]

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


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.


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 $\ket{\psi}_{ab|c}$.

Since RQM is inspired by relativity, let me use an analogy with black holes in general relativity. From the point of view of some observers there is no black hole interior because they don't see it. So they can cut off the interior from their description, and this cut off is analogous to a collapse in QM. But this cut off should be understood as an effective cut off, not as a true cut off. The same observer can reason about what would happen if he or someone else would fall into the black hole, and he could not reason about it correctly if he assumed that the cut off was a true cut off. Similarly, the friend may later be measured by Wigner in a superposition, so if the friend wants to correctly reason about Wigner observations (just as we are reasoning about such stuff here on PhysicsForums, without actually seeing anything like that), the friend must be able to think from a perspective without a collapse. In this sense there is no true collapse, only an effective one, even for the friend.

Or to put in an Orwellian slogan, all observers are equally right, but some observers are more equally right than others. Those who do not cut off the parts of reality they don't see (black hole interiors and non-observed branches of the wave function) are more right than those who do.

 

[Matterwave]

But they all have in common one crucial thing: There is never a collapse in some objective universal sense.

If I squint really really hard... I still can't see how e.g. Copenhagen would lead to this conclusion.

These theories would be ruled out, precisely because in these theories there is a collapse in an objective sense.

Are you claiming the resolution of the Wigner's friend thought experiment rules out objective collapse theories or that you think they will be ruled out by future experiment?

Future experiment, I certainly can't predict, but it seems to me that objective collapse would not lead to any Wigner's friend paradox. The answer would simply be "collapse (almost certainly) happened".

 

[Demystifier]

If I squint really really hard... I still can't see how e.g. Copenhagen would lead to this conclusion.

Well, there are many versions of Copenhagen. Perhaps you have in mind some version where the collapse is objective and caused by something like objective consciousness, in this case you are right that it does not lead to this conclusion. But if you tell me what exactly do you mean by Copenhagen interpretation, I can be more specific.

Are you claiming the resolution of the Wigner's friend thought experiment rules out objective collapse theories or that you think they will be ruled out by future experiment?

Future experiment, I certainly can't predict, but it seems to me that objective collapse would not lead to any Wigner's friend paradox. The answer would simply be "collapse (almost certainly) happened".

I am saying that objective collapse theories predict that the Wigner's friend experiment can't be performed even in principle.

 

[Demystifier]

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

Thanks, that's a very interesting paper, but I disagree with its conclusions. Basically, the authors of the paper require precise rules how to reason correctly. In my view, this boils down to a precise rule which tells you when to apply the collapse rule. In my opinion, it is a too strong demand, there cannot be a precise rule. Let me explain.

Strictly speaking, the collapse rule should never be applied, because there is no such thing as true collapse. However, we still apply it because it makes the analysis simpler. The collapse rule is just a heuristic rule of throwing away irrelevant information, where by "irrelevant information" I mean the branches of the wave function that I don't observe. The rule of thumb is that, if I don't observe it, I will probably never need it in the future, so I can throw it away. But I can never be certain that I will never need it, so throwing it away can be a mistake. And yet, unless I have good reasons to think that I will need it (perhaps because someone told me that Wigner will measure an effect of such a branch and I will be asked to say something about it), for practical purposes it's reasonable to throw it away. There is no precise rule for doing it, and there can't be, but that's how life works.

It is somewhat like deleting junk emails. We have some rules of thumb for deciding which emails are junk, and we delete them without worrying too much. In principle, it can always turn out that some deleted email was in fact relevant. There is no precise rule for deleting junk emails. And yet, we can live with that.

 

[Matterwave]

But if you tell me what exactly do you mean by Copenhagen interpretation, I can be more specific.

I cannot, because I don't know of an exact version of the Copenhagen interpretation to begin with and I am not in the business of clarifying it. But for any incarnation that I am familiar with, I can't squint hard enough to make your statement true. So perhaps if you provided an exact version where your statement is true, I could be enlightened.

I am saying that objective collapse theories predict that the Wigner's friend experiment can't be performed even in principle.

I think I get what you mean here.

 

[Sambuco]

the friend may later be measured by Wigner in a superposition, so if the friend wants to correctly reason about Wigner observations (just as we are reasoning about such stuff here on PhysicsForums, without actually seeing anything like that), the friend must be able to think from a perspective without a collapse. In this sense there is no true collapse, only an effective one, even for the friend.

Or to put in an Orwellian slogan, all observers are equally right, but some observers are more equally right than others.

While what you say isn't "wrong", of course, it's not how things are usually viewed in an $\psi$-epistemic interpretation like QBism or RQM. Let me explain. In RQM, the central role is played by events ("the friend saw spin up"), and the wave function is only (and nothing more than) a way to obtain the transition probabilities between an event whose occurrence is certain and another event whose occurrence is not yet known. In that sense, it's not that Wigner's wave function is more complete than the one assumed by the friend, but rather that it relates different events. The asymmetry between the two observers only has to do with Wigner's ability to perform measurements that involve erasing his friend's memory. When that happens, the friend's perspective ("I saw spin up") no longer exist because the spin up event itself no longer exists, so it wouldn't be correct to use a wave function that is constructed assuming the existence of that event.

Lucas.

 

[Sambuco]

Thanks, that's a very interesting paper, but I disagree with its conclusions. Basically, the authors of the paper require precise rules how to reason correctly. In my view, this boils down to a precise rule which tells you when to apply the collapse rule.

I have to say I've never been a big "fan" of the Frauchiger-Renner no-go theorem because of these kinds of issues. I find local friendliness no-go theorem much clearer.

Strictly speaking, the collapse rule should never be applied, because there is no such thing as true collapse. However, we still apply it because it makes the analysis simpler. The collapse rule is just a heuristic rule of throwing away irrelevant information, where by "irrelevant information" I mean the branches of the wave function that I don't observe.

Continuing somewhat with what I said in the previous post, I think part of the discussion surrounding the Frachiger-Renner no-go theorem revolves around how to circumvent it without assuming the existence of a wave function that is more real than all the others. In interpretations like many-worlds or Bohmian mechanics, the contradiction posed by the theorem is straightforward resolved, as you describe. In $\psi$epistemic interpretations, I think the solution lies rather in denying the asumption of absoluteness of observed events.

It is somewhat like deleting junk emails. We have some rules of thumb for deciding which emails are junk, and we delete them without worrying too much. In principle, it can always turn out that some deleted email was in fact relevant. There is no precise rule for deleting junk emails. And yet, we can live with that.

I have to say you have a special gift for making really good analogies!

Lucas.

 

[Demystifier]

I have to say I've never been a big "fan" of the Frauchiger-Renner no-go theorem because of these kinds of issues. I find local friendliness no-go theorem much clearer.

Same with me.

I have to say you have a special gift for making really good analogies!

Thanks!
That's my way of thinking, in terms of analogies. That's probably the reason why I prefer the Bohmian interpretation, because this interpretation itself can be viewed as an analogy with classical mechanics (in the Hamilton-Jacobi formulation).

 

[Morbert]

In case anyone is interested: The FR paradox analyzed with the consistent histories formalism.

https://arxiv.org/abs/1907.10095

 

[Demystifier]

Let me further develop my analogy with junk emails and explain what would be the analogies of various interpretations of QM. This may be useful for developing intuition about various interpretations.

Suppose I receive two emails, E1 and E2. E1 starts with "Dear Demystifier", clearly this one is relevant to me. E2 starts with "Dear John", clearly this one is not relevant to me, this is a junk email. But suppose that Wigner is a superuser on the email server, who can read both emails and extract some useful information from a combination of both emails. And suppose that I, as ordinary user, cannot physically delete the junk email. How to interpret this?

Objective collapse:
The computer recognizes that E2 starts with "Dear John", and physically deletes it. After that, not even Wigner can see it.

Many worlds:
Both emails exist, but from the perspective of each email it looks as if only that email exists.

Bohmian:
Both emails exist, but the computer recognizes that E1 starts with "Dear Demystifier" and puts a mark "relevant" on E1, which reminds me that only E1 is relevant. The mark objectively exists too.

Statistical ensemble:
If I am going to fully read an email, the probability that it will be E2 is zero. The probability that Wigner will read E2 (together with E1) is 100%.

QBism:
It's really about readers, not about emails. Email is just an abstract idea describing what a reader sees and subjectively considers relevant.

Relational:
E1 is not relevant by itself, it is relevant relative to the reader called Demystifier. Likewise, E2 is relevant relative to John. Both E1 and E2 are relevant relative to Wigner.

Copenhagen (Bohr's version):
Emails do not describe what exists, but what we can say about things that exist. Since E2 is relevant to Wigner but not to me, the Wigner's and my perspectives are complementary.

Consistent histories:
It's a formalization of the idea of complementarity. Me and Wigner are using different, mutually incompatible, frameworks.

Instrumental (shut up and read):
If you want to know what I find relevant, ignore E2. If you want to know what Wigner finds relevant, take both E1 and E2 into account.

I believe it is now much easier to understand why all the interpretations, except the objective collapse "interpretation", really say the same, but in a different way.

 

[gentzen]

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.

In case anyone is interested: The FR paradox analyzed with the consistent histories formalism.

https://arxiv.org/abs/1907.10095

We show that the supposedly contradictory conclusion of the argument requires computing probabilities in a family of histories that does not satisfy the consistency condition, i.e., an invalid family of histories for the theory.

Sounds more like Bohr's "this a meaningless question" to me than Bohr's complementarity.

Actually, I think Demystifier interprets "complementarity" diiferent from the meaning intended by Bohr.

Copenhagen (Bohr version):
... 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.

I think, the "real" complementarity is deeper but more complicated to understand.
For example, there is a Bohr version of Copenhagen, and a Heisenberg version. The consistent histories interpretation seems to correspond more to Bohr's version of Copenhagen, than to Heisenberg's. But Morbert once argued for a more Heisenberg like version of consistent histories, which really could work. And Bohr's point with complementarity is that those alternative versions are also important, and also contain an important part of the truth about the underlying phenomena.

 

[Morbert]

But Morbert once argued for a more Heisenberg like version of consistent histories, which really could work.

You'd have to refresh my memory here.

Omnes says complementarity follows from the formalism:
"It should be stressed first of all that this approach brings nothing new concerning the reality of quantum properties. Complementarity is still there and even more so, because it is now a trivial consequence of the history construction" -- Roland Omnes
https://www.pas.va/content/dam/casinapioiv/pas/pdf-volumi/scripta-varia/sv99/sv99-omnes.pdf

In a similar spirit, Hohenberg says the single framework rule "is the precise mathematical statement of Bohr’s complementarity." https://arxiv.org/abs/0909.2359

I've always loosely thought of consistent histories as complementarity applied to closed systems.

 

[gentzen]

I've always loosely thought of consistent histories as complementarity applied to closed systems.

Of course people want to make clear sense of Bohr's obscure words. So they are happy to write things like:

This basic assumption is consistent with Bohr’s complementarity principle, but it is formulated without recourse to measurement or to the existence of a classical regime and it is therefore more general and can be more precisely formulated than Bohr’s complementarity principle.

But the problem with Bohr is that he is obscure for a very specific reason: He only wants to say correct things. So if you remove the obscurity, often you also remove the depth and the correctness.

You'd have to refresh my memory here.

I will look for it, and post a link.