# Insights The Quantum Mystery of Wigner's Friend - Comments

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#### Greg Bernhardt

RUTA has updated this Insight

#### nikkkom

"The second assumption of FR is that there is only one outcome for a quantum measurement, so Xena doesn’t measure both heads and tails and send both versions of state s."

Which sounds obviously false to me.
We assume that Schrödinger's cat can indeed exist in superposition of states.
IOW: the cat indeed observes (nee "measures") both possible states of the radioactive atom. And then cat "sends" both signals (in the form of being in superposition itself) to the observing scientist.

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#### RUTA

"The second assumption of FR is that there is only one outcome for a quantum measurement, so Xena doesn’t measure both heads and tails and send both versions of state s."

Which sounds obviously false to me.
We assume that Schrödinger's cat can indeed exist in superposition of states.
IOW: the cat indeed observes (nee "measures") both possible states of the radioactive atom. And then cat "sends" both signals (in the form of being in superposition itself) to the observing scientist.

View attachment 234106
You have grasped the problem exactly -- by saying Xena only measures one outcome in one world, we've excluded the possibility that a future measurement by Zeus in an eigenbasis differing from that for $\hat{x}$ can in any way bear on Wigner's $\hat{y}$ measurement outcome, which we know doesn't work for entangled states. Look at the simple example of polarized light. If the light is polarized in x and I make a measurement in y (intensity would correspond to probability here), I get zero. But, if someone else measures in x + y before I measure in y, then when I do a y measurement I get a non-zero result. Eq. 4 in my Insight (Healey's Eq (13)) is fine as long as Zeus and Wigner only measure $\hat{x}$ and $\hat{y}$, respectively. That's consistent with classical probability theory. In Hardy's axiomatization of QM, there is only one difference between classical and quantum probability theory -- in quantum theory every Hilbert space basis rotated from the original measurement eigenbasis represents another measurement. That's certainly not true for discrete classical physics (e.g., coin flips). So, if we want classical probability theory modeled via quantum probability theory we're going to have to accept something unusual, e.g., rewriting history or accepting that Wigner's measurement of Yvonne's measurement outcome differs from Yvonne's recorded measurement outcome. Even my solution requires we give up our cherished ant's-eye explanation, which required an entire book to defend. Something we believe to be true is going to have to be sacrificed in whatever new model of objective reality we finally embrace.

#### John McAndrew

I'm under the impression that Wigner's Friend is a rip-off of Everett's argument in his PhD thesis for a universal wave function.

#### bhobba

Mentor
We assume that Schrödinger's cat can indeed exist in superposition of statesView attachment 234106
Such as assumption is false. Because it is entangled with the radioactive source it is in a mixed state - not a superposition. It is the essence of de-coherence - which I must emphasize does not solve the measurement problem just shifts the emphasis a bit. There have been many posts explaining this. I have explained it a different way as well - but will just limit my objection to the simple calculation that shows its in a mixed state - not a superposition.

Ruta's reply and reference to Hardy is excellent though IMHO - but not really dependent on being in a superposition.

Thanks
Bill

#### RUTA

I'm under the impression that Wigner's Friend is a rip-off of Everett's argument in his PhD thesis for a universal wave function.
From what I’ve read (I’m no historian) FR is a variation of many other such thought experiments, e.g., Everett and Wigner.

There is an interesting Quanta article on this https://www.quantamagazine.org/frauchiger-renner-paradox-clarifies-where-our-views-of-reality-go-wrong-20181203/

I was surprised that some people believe there will prove to be a limit on the applicability of QM.

Here is Leifer’s closing statement in that article: “It’s likely that we are making some implicit assumption about the way the world has to be that just isn’t true. Once we change that, once we modify that assumption, everything would suddenly fall into place. That’s kind of the hope. Anybody who is skeptical of all interpretations of quantum mechanics must be thinking something like this. Can I tell you what’s a plausible candidate for such an assumption? Well, if I could, I would just be working on that theory.”

#### Demystifier

2018 Award
Here is Leifer’s closing statement in that article: “It’s likely that we are making some implicit assumption about the way the world has to be that just isn’t true. Once we change that, once we modify that assumption, everything would suddenly fall into place. That’s kind of the hope. Anybody who is skeptical of all interpretations of quantum mechanics must be thinking something like this. Can I tell you what’s a plausible candidate for such an assumption? Well, if I could, I would just be working on that theory.”
In the paper linked in my signature I argue that this implicit assumption (that just isn't true) is that relativistic QFT is fundamental. Once we change that (which is rather natural from condensed-matter point of view), everything in Bohmian mechanics suddenly falls into place.

Mentor

#### RUTA

Even though this response is billed as "according to BM", as you say, the key analysis, in particular in section 3, does not appear to me to require adopting BM as an interpretation; it's based solely on observations about quantum states.
I’m not an expert in BM, so I believed them when they said keeping the “empty” components of the wavefunction was necessary in BM and those components are the key for getting the OK-OK piece at the end.

#### PeterDonis

Mentor
I believed them when they said keeping the “empty” components of the wavefunction was necessary in BM and those components are the key for getting the OK-OK piece at the end.
Calling the components "empty" is specific to BM, yes--it means the actual particle trajectories don't lie in those components. But including those components in the wave function up until the final measurement is not specific to BM; that's just standard QM. Basically the point the paper is making is that predicting a nonzero probability for the {ok, ok} result requires interference between two macroscopically different states of the "inside the lab" observers; but the reasoning that leads to the "paradox" that the {ok, ok} result should be impossible given the observations of the "inside the lab" observers is based on the implicit assumption that no such interference takes place. That point is independent of any interpretation of QM, as far as I can see.

#### RUTA

Calling the components "empty" is specific to BM, yes--it means the actual particle trajectories don't lie in those components. But including those components in the wave function up until the final measurement is not specific to BM; that's just standard QM. Basically the point the paper is making is that predicting a nonzero probability for the {ok, ok} result requires interference between two macroscopically different states of the "inside the lab" observers; but the reasoning that leads to the "paradox" that the {ok, ok} result should be impossible given the observations of the "inside the lab" observers is based on the implicit assumption that no such interference takes place. That point is independent of any interpretation of QM, as far as I can see.
I agree, that equation with the OK-OK piece is not unique to BM. Did you see this paper https://arxiv.org/abs/1710.07212 ? They show that the apparent contradiction in FR is due to conflating inequivalent QM formalisms: standard QM and the relative-state formalism.

#### DarMM

Gold Member
I agree, that equation with the OK-OK piece is not unique to BM. Did you see this paper https://arxiv.org/abs/1710.07212 ? They show that the apparent contradiction in FR is due to conflating inequivalent QM formalisms: standard QM and the relative-state formalism.
https://arxiv.org/abs/1611.01111

Is that QM has three formalisms, Objective collpase, No-collapse (relative state) and subjective collapse. The FR scenario is a situation where the first two give different predictions and the third is inconsistent, unless you restrict QM to being a single user theory.

EDIT: I said follow up, but the date is earlier. Did I make a mistake or was it a retrocausal influence?

#### PeterDonis

Mentor
https://arxiv.org/abs/1611.01111

Is that QM has three formalisms, Objective collpase, No-collapse (relative state) and subjective collapse.
I hadn't seen either of these papers, I'll take a look. On their face they seem to be claiming that "QM" is not in fact a single theory (i.e., a single mathematical system for making predictions) but at least two (perhaps three if @DarMM is correct). That claims seems like it could stand a lot of examination.

#### RUTA

https://arxiv.org/abs/1611.01111

Is that QM has three formalisms, Objective collpase, No-collapse (relative state) and subjective collapse. The FR scenario is a situation where the first two give different predictions and the third is inconsistent, unless you restrict QM to being a single user theory.
As they say, the difference between interpretations becomes apparent in Wigner’s-friend-type experiments. The reason is that you have assumed the availability of classical information for screened off entites during interference and classical information constitutes “scientific fact.” So, what’s going on “behind the curtain” to account for the QM outcomes is no longer “behind the curtain.”

#### DarMM

Gold Member
perhaps three if @DarMM is correct
Look for the terms "objective collapse", "no-collapse" and "subjective-collapse" in their papers. I find the 2016 paper I linked a bit clearer.

#### RUTA

Look for the terms "objective collapse", "no-collapse" and "subjective-collapse" in their papers. I find the 2016 paper I linked a bit clearer.
Here is a paragraph in the Conclusion of their 2016 paper:

The Wigner’s-friend experiment can (in principle) discriminate between two competing quantum formalisms describing a measurement — the unitary relative-state formalism and the non-unitary measurement update rule. A specific combination of these two formalisms, together with the assumption regarding possible communication, gives a contradiction. We do, however, not regard a formalism to necessarily imply a particular interpretation like “many worlds” or “collapse.” We believe that the contradiction above does, therefore, not disqualify a particular interpretation of quantum mechanics.

#### DarMM

Gold Member
Here is a paragraph in the Conclusion of their 2016 paper:
They do consider a third formalism, subjective collapse, as a combination of the first two (though maybe formalism is the wrong word for it).

However the actual way out of the contradiction is rejecting being a multi-user theory as QBism does, then you can use subjective collapse.

#### Demystifier

2018 Award
Even though this response is billed as "according to BM", as you say, the key analysis, in particular in section 3, does not appear to me to require adopting BM as an interpretation; it's based solely on observations about quantum states.
I agree. Perhaps the crucial insight in this paper is contained in the following quote:
"The contradiction derived by Frauchiger and Renner simply arises from the fact that one experimentalist, F̄ , uses the wrong quantum state to make predictions about the outcome of a later measurement. Her wrong assumptions may be (subjectively) justified if she doesn’t know about the very special procedure that W̄ carries out on her laboratory. But this – to put it bluntly – is her problem, not a problem with Bohmian mechanics or quantum theory in general."

#### RUTA

I agree. Perhaps the crucial insight in this paper is contained in the following quote:
"The contradiction derived by Frauchiger and Renner simply arises from the fact that one experimentalist, F̄ , uses the wrong quantum state to make predictions about the outcome of a later measurement. Her wrong assumptions may be (subjectively) justified if she doesn’t know about the very special procedure that W̄ carries out on her laboratory. But this – to put it bluntly – is her problem, not a problem with Bohmian mechanics or quantum theory in general."
You guys seem to be knowledgeable about BM. Does this response to Wigner's friend in that paper follow for BM as they claim?

the macroscopic quantum measurements performed by [Zeus] and [Wigner] are so invasive that they can change the actual state of the respective laboratory, including the records and memories (brain states) of the experimentalists in it.

#### Demystifier

2018 Award
You guys seem to be knowledgeable about BM. Does this response to Wigner's friend in that paper follow for BM as they claim?
It follows from QM itself, or more precisely from any interpretation of QM (including BM) that takes Schrodinger equation seriously, as an equation valid not only for microscopic systems but also for macroscopic ones.

#### RUTA

It follows from QM itself, or more precisely from any interpretation of QM (including BM) that takes Schrodinger equation seriously, as an equation valid not only for microscopic systems but also for macroscopic ones.
I think the subjective formalism (like Healey's) would say no changes to memories or records occur. Rather, people just disagree with each other. Here is a quote from Healey:
So one could argue that whatever Wigner says about his outcome (more carefully, whatever Zeus measures Wigner’s outcome to be) is not a reliable guide to Wigner’s actual outcome. In particular, even if Zeus takes Wigner’s outcome to have been OK (because that’s what he observes it to be in a hypothetical future measurement on W) Wigner’s actual outcome might equally well have been FAIL.
Personally, this strikes me exactly as it did Renner (this excerpt from the Quanta article):
“If you want to maintain the Copenhagen type of view, it seems the best move is towards this perspectival version,” Leifer said. He points out that certain interpretations, such as quantum Bayesianism, or QBism, have already adopted the stance that measurement outcomes are subjective to an observer.

Renner thinks that giving up this assumption entirely would destroy a theory’s ability to be effective as a means for agents to know about each other’s state of knowledge; such a theory could be dismissed as solipsistic. So any theory that moves toward facts being subjective has to re-establish some means of communicating knowledge that satisfies two opposing constraints.

#### Demystifier

2018 Award
I think the subjective formalism (like Healey's) would say no changes to memories or records occur. Rather, people just disagree with each other.
Perhaps, but I would say that such approaches do not take the Schrodinger equation seriously. If the wave function describes only a subjective knowledge of an agent, then all the stuff about which the agent knows nothing (and there is certainly a lot of such stuff) is not described by the Schrodinger equation. In fact it is not described by anything, because in subjective approaches the agent cannot describe something that he does not have a knowledge about. The wave function of the Universe, which makes sense in approaches (like BM and MWI) in which the Schrodinger equation is taken seriously, does not make any sense in subjective approaches.

Is there a wave function of the Moon when the agent knows nothing about the Moon? Subjective approaches say no, other approaches say yes.

"The Quantum Mystery of Wigner's Friend - Comments"

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