# A A Realization of a Basic Wigner's Friend Type Experiment

#### PeterDonis

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#### StevieTNZ

I will be eager to read posts on this paper, which I was alerted to a few days ago and haven't fully yet read in detail, but can also suggest reading https://arxiv.org/abs/1804.00749 (also official version published, viewable for free, online at Entropy 20, 350, (2018).)

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#### DarMM

Gold Member
So in this experiment we have four observers, let's say Alice, Bob, Zeus and Wigner. Alice and Bob measure an entangled Bell pair in the z-basis:
$$|\pi\rangle = -sin\left(\frac{\theta}{2}\right)|\phi^{+}\rangle + cos\left(\frac{\theta}{2}\right)|\psi^{-}\rangle \\ |\phi^{+}\rangle = \frac{1}{\sqrt{2}}\left(|\uparrow\uparrow\rangle + |\downarrow\downarrow\rangle\right) \\ |\psi^{-}\rangle = \frac{1}{\sqrt{2}}\left(|\uparrow\downarrow\rangle + |\downarrow\uparrow\rangle\right)$$
which causes them to be in the following state from Wigner and Zeus's perspective:
$$|\Pi\rangle = -sin\left(\frac{\theta}{2}\right)|\Phi^{+}\rangle + cos\left(\frac{\theta}{2}\right)|\Psi^{-}\rangle \\ |\Phi^{+}\rangle = \frac{1}{\sqrt{2}}\left(|A_{\uparrow}B_{\uparrow}\rangle + |A_{\downarrow}B_{\downarrow}\rangle\right) \\ |\Psi^{-}\rangle = \frac{1}{\sqrt{2}}\left(|A_{\uparrow}B_{\downarrow}\rangle + |A_{\downarrow}B_{\uparrow}\rangle\right)$$
where the $A_{\downarrow}$ state is the state of Alice's lab had she solely measured an unentangled particle in the $|\downarrow\rangle$ state.

Now Wigner and Zeus perform measurements on Alice and Bob's labs. Wigner for example measuring Alice in either the following basis:
$$\mathcal{Z} = \{|A_{\uparrow}\rangle,|A_{\downarrow}\rangle\}$$
which checks which outcome Alice obtained or he measures Alice in the following basis:
$$\mathcal{X} = \left\{\frac{1}{\sqrt{2}}\left(|A_{\uparrow}\rangle + |A_{\downarrow}\rangle\right), \frac{1}{\sqrt{2}}\left(|A_{\uparrow}\rangle + |A_{\downarrow}\rangle\right)\right\}$$

So essentially by varying these $\mathcal{X}$ and $\mathcal{Z}$ measurements Zeus and Wigner should be able to detect violations of the CHSH inequality.

The contradiction is that from their own perspective Alice and Bob have obtained some definite outcome for their spin measurements, say $z_{1}$ and $z_{2}$. So there is a fact about what Alice and Bob have measured, meaning there is a a definite value Zeus for example will obtain if he measures in the $\mathcal{Z}$ basis. Now if we assume that Zeus and Wigner both measure in the $\mathcal{X}$ basis, we have a set of two $\mathcal{X}$ outcomes and the definite $\mathcal{Z}$ outcomes they would have obtained has they measured in that basis. That's essentially four "elements of reality" or values in each run of the experiment:
$$\left\{\mathcal{Z}_{A},\mathcal{Z}_{B},\mathcal{X}_{A},\mathcal{X}_{B}\right\}$$
Then you'd build a probability distirubition for repeated runs of the experiment $p\left(\mathcal{Z}_{A},\mathcal{Z}_{B},\mathcal{X}_{A},\mathcal{X}_{B}\right)$. However the existence of such a common probability distribution means that one cannot obtain a violation of the Bell inequalities. Hence the contradiction.

This is very similar to Masanes's version of the Frauchiger-Renner argument. Creating a situation where the superobservers should see CHSH violations, but the existence of definite objective outcomes for the observers implies a common probability distribution in contradiction to the CHSH inequalities. This common probability distribution is created by using a "trick" that allows outcomes for all four Bell measurements in a single run. Masanes uses reversibility to obtain this, Brukner uses counterfactuals to include the values $\mathcal{Z}$ would have definitely had had it been measured.

However the problem both have is that this inclusion isn't really valid.

In Masanes case reversing the measurement is either impossible (some versions of Copenhagen) or simply undoes the CHSH correlations he needs (other versions of Copenhagen).

In this experiment's case the problem is that, although given a specific outcome for Alice's measurement then Wigner's measurement of $\mathcal{Z}$ should produce a value in line with that outcome, if Wigner doesn't measure $\mathcal{Z}$ then it has no outcomes and thus shouldn't be included in the list of outcomes. QM does not allow you to include counterfactuals like this.

This is simply an unintuitive aspect of the Quantum/Classical cut. The macroscopic degrees of freedom of a device might show $\uparrow$ as the result of measurement, but that doesn't mean you can consider a measurement of the device's atoms in the $\mathcal{Z}$ basis to already have the value $A_{\uparrow}$. Unless somebody actually performs the measurement there is no such value.

This is actually the same kind of thinking that leads to Many Worlds type observations that my measurement of definite outcomes is in some contradiction with a superobserver's assigning a superposed state to me. All the Frauchiger-Renner type arguments are basically trying to push a contradiction out of this. However there really seems there isn't a contradiction. Somebody can assign a superposed state to me despite my seeing a definitive outcome and it neither implies multiple worlds nor that my outcomes are private/subjective. It's just that the superobserver's state assignment refers to the statistics of superobservables that have yet to be measured.

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#### RUTA

So essentially by varying these $\mathcal{X}$ and $\mathcal{Z}$ measurements Zeus and Wigner should be able to detect violations of the CHSH inequality.

The contradiction is that from their own perspective Alice and Bob have obtained some definite outcome for their spin measurements, say $z_{1}$ and $z_{2}$. So there is a fact about what Alice and Bob have measured, meaning there is a a definite value Zeus for example will obtain if he measures in the $\mathcal{Z}$ basis. Now if we assume that Zeus and Wigner both measure in the $\mathcal{X}$ basis, we have a set of two $\mathcal{X}$ outcomes and the definite $\mathcal{Z}$ outcomes they would have obtained has they measured in that basis. That's essentially four "elements of reality" or values in each run of the experiment:
$$\left\{\mathcal{Z}_{A},\mathcal{Z}_{B},\mathcal{X}_{A},\mathcal{X}_{B}\right\}$$
Then you'd build a probability distirubition for repeated runs of the experiment $p\left(\mathcal{Z}_{A},\mathcal{Z}_{B},\mathcal{X}_{A},\mathcal{X}_{B}\right)$. However the existence of such a common probability distribution means that one cannot obtain a violation of the Bell inequalities. Hence the contradiction.

This is very similar to Masanes's version of the Frauchiger-Renner argument. Creating a situation where the superobservers should see CHSH violations, but the existence of definite objective outcomes for the observers implies a common probability distribution in contradiction to the CHSH inequalities. This common probability distribution is created by using a "trick" that allows outcomes for all four Bell measurements in a single run. Masanes uses reversibility to obtain this, Brukner uses counterfactuals to include the values $\mathcal{Z}$ would have definitely had had it been measured.
I haven’t reproduced all the calculations yet, I’ve been too busy, but I will definitely do so and report back. Having read the paper, I suspect DarMM is correct, though.

First, this cannot possibly be a true Wigner’s friend experiment, since the friends are not screened off, i.e., they and their labs are interacting extensively with Wigner and Zeus’s labs, so decoherence will certainly render them “classical.” QM behavior does not follow from mere ignorance. Imagine for example that I scatter photons off electrons in a twin-slit experiment and use those photons to create “which-slit” information. If I merely hide the electron detector screen from my view and let my friend watch it, do you believe my friend will see an interference pattern? Of course not, but that’s exactly what they’re doing here.

Second, if DarMM is correct in his analysis I quoted here (again, I suspect he is), then this is really an instantiation of the Quantum Liar Experiment. Read my Insight on that and you’ll see what I mean.

I have a student working with me on this for his senior project. Once we have it all analyzed and properly critiqued, I’ll post something here.

#### RUTA

We need to be careful about the names of the participants. In the paper cited in post #1, Alice and Bob replace Wigner and Zeus, so we have Alice and Bob measuring their friends' labs. I attached Fig 2 from their paper.

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#### eloheim

First, this cannot possibly be a true Wigner’s friend experiment, since the friends are not screened off, i.e., they and their labs are interacting extensively with Wigner and Zeus’s labs, so decoherence will certainly render them “classical.” QM behavior does not follow from mere ignorance. Imagine for example that I scatter photons off electrons in a twin-slit experiment and use those photons to create “which-slit” information. If I merely hide the electron detector screen from my view and let my friend watch it, do you believe my friend will see an interference pattern? Of course not, but that’s exactly what they’re doing here.
I don't think this criticism of the experiment is warranted, from how I take the paper, at least. IMO it spawns from too literal an expectation for the Wigner's friend gedanken experiment aspect of it. It's more like a formal proof of concept, using single photons and a setup where everything can be kept coherent up until the final macroscopic measurement result of each trial is produced. I believe this is separate from any issues it has with assuming counterfactuals.

#### Demystifier

2018 Award
All these experiments and no-go theorems are compatible with Bohmian mechanics in which an observer independent reality exists.

#### RUTA

I don't think this criticism of the experiment is warranted, from how I take the paper, at least. IMO it spawns from too literal an expectation for the Wigner's friend gedanken experiment aspect of it. It's more like a formal proof of concept, using single photons and a setup where everything can be kept coherent up until the final macroscopic measurement result of each trial is produced. I believe this is separate from any issues it has with assuming counterfactuals.
The criticism is very fair. The experiment is missing the essential point of Wigner's friend, i.e., the friend (measurement and recording device) must be screened off. Indeed, the entire collection of outcomes is compatible with a single, self-consistent (per QM) observer independent reality contrary to their claim. So, this is not even a proof of principle. See the two slides attached from Brukner and Renner's talks, respectively, at the APS March Meeting two weeks ago. Until someone can screen off a measurement, Wigner's friend has not been instantiated in fact or principle.

Again, this experiment is an instantiation of the Quantum Liar Experiment precisely as I explain in this Insight. Alice and Bob are doing measurements X and Y on an entangled system stemming from a particular form of psi (eigen function in Z). Alice and Bob's results in X and Y violate a Bell inequality implying no definite value for Z. But, without psi (in Z), the Bell results couldn't obtain. That's the experiment they should reference.

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#### Demystifier

2018 Award
Sober comments on the experiment: http://dailynous.com/2019/03/21/philosophers-physics-experiment-suggests-theres-no-thing-objective-reality/?fbclid=IwAR1kIJPwbYiZh7ZedZiEogcshXf1R-aPW4WEA-Nmp6vzS0MWJgKWiC5qJxc

In particular, Sean Carroll said the following:
"There is a long tradition in science journalism—and one must admit that the scientists themselves are fully culpable in keeping the tradition alive—of reporting on experiments that (1) verify exactly the predictions of quantum mechanics as they have been understood for decades, and (2) are nevertheless used to claim that a wholesale reimagining of our view of reality is called for. This weird situation comes about because neither journalists nor professional physicists have been taught, nor have they thought deeply about, the foundations of quantum mechanics."

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#### DarMM

Gold Member
I haven’t reproduced all the calculations yet, I’ve been too busy, but I will definitely do so and report back. Having read the paper, I suspect DarMM is correct, though.

First, this cannot possibly be a true Wigner’s friend experiment, since the friends are not screened off, i.e., they and their labs are interacting extensively with Wigner and Zeus’s labs, so decoherence will certainly render them “classical.” QM behavior does not follow from mere ignorance. Imagine for example that I scatter photons off electrons in a twin-slit experiment and use those photons to create “which-slit” information. If I merely hide the electron detector screen from my view and let my friend watch it, do you believe my friend will see an interference pattern? Of course not, but that’s exactly what they’re doing here.

Second, if DarMM is correct in his analysis I quoted here (again, I suspect he is), then this is really an instantiation of the Quantum Liar Experiment. Read my Insight on that and you’ll see what I mean.

I have a student working with me on this for his senior project. Once we have it all analyzed and properly critiqued, I’ll post something here.
I think the resolution is easy to see in your view.

We have Alice and Bob's friends called $1$ and $2$, large classical systems providing the context for an exchange of angular moment, this angular momentum being represented by the observables $z_1$ and $z_2$. Then we have Alice and Bob, even larger classical systems providing the context for exchanges of quantities related to the atomic structure of Alice and Bob's friends, the superobservables $\left\{\mathcal{X}_i,\mathcal{Z}_i\right\}$.

The contradiction claimed in Brukner's paper (and followed in this experiment) is that Alice and Bob's friends' measurements of $z_1$ and $z_2$ immediately imply a value for the superobservables $\mathcal{Z}_1$ and $\mathcal{Z}_2$, since the result of such a measurement is guaranteed from the $z_1$ and $z_2$ values. Thus if the superobservers measure $\mathcal{X}_1$ and $\mathcal{X}_2$ we have a joint measurement of all four, which ultimately contradicts CHSH.

However in the Relational Blockworld this is instantly avoided. If the superobservers aren't set up correctly to provide the context for $\mathcal{Z}_1, \mathcal{Z}_2$ then those values just don't exist. Yes had the context been set up correctly the $z_1, z_2$ values from the observer context would imply those of the superobserver $\mathcal{Z}_i$ context with certainty. However if you measure $\mathcal{X}_i$ you simply do not provide the context for $\mathcal{Z}_i$ regardless of how determined/fixed it would have been if you had. Thus there is no measurement of all four superobservables, indeed such a context is impossible.

Similar remarks hold for Copenhagen.

In essence yes a Quantum Liar experiment, but thinking the superobserver counterfactual somehow is valid to include because when its context is present it logically follows (i.e. Probability is 1) from an observer fact.

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#### DarMM

Gold Member
To be fair to the experimenters Brukner and the experiment don't intend to include Bohmian Mechanics or Many-Worlds which are discussed a good bit in that article. Although those interpretations do provide a good refutation of the article title and media headlines. The paper should have been called something like:
"Experimental investigation of Objective Reality in Single World Local Interpretations with Global Unitarity"
since the interpretations in bold are Brukner's target.

These are interpretations that want to retain the validity of QM at all scales (no spontaneous collapse like GRW), have one world and are local. So Copenhagen style interpretations (Consistent Histories, Ignorance Ensemble, Bub/Healey) or retrocausal and acausal ones.

However of course Brukner's theorem doesn't affect such interpretations since it assumes the existence of a superobservable context that is never realized.

Frauchiger-Renner attempts to target such interpretations as well, but doesn't succeed either.

I think it is simply the case that there is no contradiction between locality, one world and an observer being modeled as being in a superposition. All these variations of Wigner's friend keep trying to do this and not succeeding. The outcome for me is more just emphasizing interesting aspects of Copenhagen or acausal views rather than refuting them.

#### Demystifier

2018 Award
The paper should have been called something like:
"Experimental investigation of Objective Reality in Single World Local Interpretations with Global Unitarity"
Yes. But then nobody would care.

#### vanhees71

Gold Member
All these experiments and no-go theorems are compatible with Bohmian mechanics in which an observer independent reality exists.
Hm, involving photons, I'd be very careful with statements about Bohmian interpretations. Particularly for photons at least I've seen no convincing Bohmian setup yet.

#### Demystifier

2018 Award
Hm, involving photons, I'd be very careful with statements about Bohmian interpretations. Particularly for photons at least I've seen no convincing Bohmian setup yet.
How about the version of Bohmian mechanics (linked in my signature below) in which photon does not have a trajectory?

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#### kimbyd

Gold Member
2018 Award
This is actually the same kind of thinking that leads to Many Worlds type observations that my measurement of definite outcomes is in some contradiction with a superobserver's assigning a superposed state to me. All the Frauchiger-Renner type arguments are basically trying to push a contradiction out of this. However there really seems there isn't a contradiction. Somebody can assign a superposed state to me despite my seeing a definitive outcome and it neither implies multiple worlds nor that my outcomes are private/subjective. It's just that the superobserver's state assignment refers to the statistics of superobservables that have yet to be measured.
It directly implies multiple worlds.

The multiple worlds interpretation is merely the statement that the wavefunction never truly collapses: it only appears to do so. The "multiple worlds" are merely the different branches of the wavefunction that no longer interact to any significant degree. In this specific situation, the "multiple worlds" comes in in the following way:

Observer A observes a definite effect.
Observer B interprets Observer A as being in a superposition of two states.

As long as you have a quantum mechanical system that behaves in the above way, the many worlds interpretation is intrinsic to that system's description.

Granted, it doesn't necessarily imply one single many-worlds interpretation (there are many), but it does imply many worlds, as the only consistent interpretation of observer B's view of the world is that observer A is in a superposition of "measured state 1" and "measured state 2".

#### DarMM

Gold Member
As long as you have a quantum mechanical system that behaves in the above way, the many worlds interpretation is intrinsic to that system's description.
No it isn't. It's only the case if you ascribe an ontic status to the quantum state and add no additional variables. In an epistemic view one observer can have another in superposition without multiple worlds being involved.

#### kimbyd

Gold Member
2018 Award
No it isn't. It's only the case if you ascribe an ontic status to the quantum state and add no additional variables. In an epistemic view one observer can have another in superposition without multiple worlds being involved.
The other observer in a superposition is experiencing multiple worlds by definition. That's what the term means.

#### DarMM

Gold Member
The other observer in a superposition is experiencing multiple worlds by definition. That's what the term means.
Superposition does not mean "experiencing multiple worlds", it's a form of statistics. What textbook are you getting that definition from?

Superposition doesn't have to mean "being in both states at once". In an epistemic view it simply means you have a chance of being found in either, just as in a state from Kolmogorov probability.

#### kimbyd

Gold Member
2018 Award
Superposition does not mean "experiencing multiple worlds", it's a form of statistics. What textbook are you getting that definition from?

Superposition doesn't have to mean "being in both states at once". In an epistemic view it simply means you have a chance of being found in either, just as in a state from Kolmogorov probability.
The observer in a superposition sees a single outcome of their observation, and does not interact with the part of the wavefunction where they see the alternative outcome.

That's textbook multiple worlds. That's all it is.

#### DarMM

Gold Member
The observer in a superposition sees a single outcome of their observation, and does not interact with the part of the wavefunction where they see the alternative outcome.

That's textbook multiple worlds. That's all it is.
Well it's the Many World's view of observer superposition, but nothing about observer superposition requires a Many Worlds view, i.e
$$\frac{1}{\sqrt{2}}\left(|A\rangle + |B\rangle\right)$$

Where A and B are observer states, doesn't have to mean the observer actually is in both states, it only means so in many worlds.

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#### microsansfil

Superposition doesn't have to mean "being in both states at once". In an epistemic view it simply means you have a chance of being found in either, just as in a state from Kolmogorov probability.
How would you interpret the fact that a quantum computer uses the principle of superposition of quantum mechanics to perform an immense number of calculations in parallel ?

/Patrick

"A Realization of a Basic Wigner's Friend Type Experiment"

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