# I Frauchiger & Renner: There's a Mistake, Right?

#### tomdodd4598

Hey there!

I was recently pointed to this thought experiment, claiming an apparent 'contradiction' involving the various predictions of the observers.

Now, this has been discussed on PF quite recently, but I found the discussion rather hard to follow. I've read the paper, the PF discussion, and tried to just do the maths myself. There is also a section on Wikipedia that goes through it and helpfully spells out the full state in the various bases. I'll just copy the statements here:

Statement 1 by F1: "If I get t, I know that W2 will measure plus"
Statement 2 by F2: "If I get up, I know that F1 had measured t"
Statement 3 by W1: "If I get minus, I know that F2 had measured up"
Statement 4 by W2: "If I get minus, I know that there exists one round of the experiment in which W1 also gets minus"

Statement 4 seems to be correct. Even statements 1 to 3 individually look fine to me, but I may be wrong. I can only conclude that there is an issue with combining the first three statements to make the conclusion that if W1 gets minus, W2 will measure plus, because this is clearly not true from just looking at the state, but I can't put my finger on it.

So my question is specifically whether this is the source of the paradox, and if so, why?

EDIT: So I went through the PF thread again and this post by stevendaryl seems to agree with this lack of transitivity from statement 3 through to 1. However, I still don't think I understand why this is the case.

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#### DarMM

They use a counterfactual that contradicts the fact that the observers are entangled. See section 3 of this paper:
https://arxiv.org/abs/1807.00421

If we call the two superobservers Wigner and Zeus and the observers Alice and Bob, the contradiction is that Zeus predicts he should always observe "fail" when measuring Bob due to reasoning about Alice's measurement.

However his reasoning about Alice uses an measurement from Wigner on Alice and since Alice and Bob are entangled this invalidates the conclusions about Bob because due to the entanglement the measurement on Alice changes Bob's state.

Another way of saying it is that they mix quantum and classical reasoning and Bub's paper discusses how if you use either totally classical reasoning (observers on classical side of superobserver's cut) or totally quantum reasoning (quantum side of cut) there are no contradictions.

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#### tomdodd4598

Ok, so the idea is that although F1, F2 and W1 can each legitimately make those statements themselves, any given one of them can't chain them together because the state of the system is different after each of the measurements (from an 'observer-dependent collapse' point of view), which invalidates the certainty of the transitivity of the conclusions because each of them are statements about the state before any measurements have occurred?

#### tomdodd4598

Thanks for this - I think he explains it very nicely!

#### Demystifier

2018 Award
Thanks for this - I think he explains it very nicely!
Explanations by Scott Aaronson are always worth reading. He is always deep, simple and right to the point at the same time.

#### RUTA

Aaronson misses a key point that I highlight in The Quantum Mystery of Wigner's Friend, i.e., one of the friends is allowed to send information to their environment and yet is still treated as quantum, i.e., is still screened off. I like Aaronson's use of the Hardy state though, it does get to another interesting question about Wigner's friend, i.e., what does a recording device such as a brain record while being screened off? And what happens to that recording upon measurement by Wigner? Aaronson says Alice's measurement will "scramble Charlie's brain." So, Aaronson is assuming Charlie's brain has recorded 0 or 1 while screened off and that Alice's measurement forces it to end up in some superposition of 0 and 1. Who knows what a screened off brain will experience, but Aaronson's belief is akin to Lazarovici & Hubert (cited in my Insight):
the macroscopic quantum measurements performed by [Alice] and [Bob] 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.

#### PeterDonis

Mentor
one of the friends is allowed to send information to their environment and yet is still treated as quantum, i.e., is still screened off.
I think it's even more basic than this. A system like a brain, or even more a human as a whole, can't possibly maintain quantum coherence even within itself: thermal noise is way too large for that. So even if you put a person in an isolation box that completely prevented any interaction with their environment, they would still be a decoherent system all by themselves and you could not treat them as being in a pure quantum state the way these papers are trying to.

#### StevieTNZ

I think it's even more basic than this. A system like a brain, or even more a human as a whole, can't possibly maintain quantum coherence even within itself: thermal noise is way too large for that. So even if you put a person in an isolation box that completely prevented any interaction with their environment, they would still be a decoherent system all by themselves and you could not treat them as being in a pure quantum state the way these papers are trying to.
FAPP, though. In principle it can be in a pure quantum state and described as such. When people ask why the macroscopic world exists, often in relation to the measurement problem, it seems to me the obvious answer is "measurement has taken place". Does that take place before we see the world in consciousness or then? That's up for discussion, debate and experimental testing.

#### PeterDonis

Mentor
In principle it can be in a pure quantum state and described as such.
"In principle" if you accept a particular interpretation (or one of a certain set of interpretations) of QM. Not all interpretations are committed to this.

Experimentally, we have no evidence that a human being, or any indeed ordinary macroscopic object, can be in a pure quantum state. That combined with the fact that there are different, mutually inconsistent interpretations of QM, should make us careful about making "in principle" claims like this.

#### RUTA

When I speak of in principle, I refer to the formalism of QM by itself ... Apparently all interpretations of where collapse occurs give different predictions
That's certainly the case for collapse (standard) versus no-collapse (relative-state) formalisms as Bub explains in a forthcoming paper (see The Quantum Mystery of Wigner's Friend for an explanation of Bub).

#### PeterDonis

Mentor
When I speak of in principle, I refer to the formalism of QM by itself
Just writing down, for example, the kets $|\text{dead}\rangle$ and $|\text{alive}\rangle$ for Schrodinger's cat, which the formalism says you can do, does not mean any actual cat will behave in an actual experiment the way the formalism says. It is worth noting that Schrodinger's original cat thought experiment was not intended to show that cats actually could be put in superpositions like that, but to be a reductio ad absurdum of the claim that any system whatever could be described accurately by the QM formalism.

Regarding macroscopic superposition, I refer to this thread
Yes, there can be Bose-Einstein condensates of macroscopic size. Those are the kinds of systems that experiments indicate can be in a macroscopic superposition. But those are not "ordinary" macroscopic objects; you have to give them very special treatment, and they have to have very special composition. You couldn't do those experiments with an ordinary rock, let alone a human being: neither one would form a Bose-Einstein condensate at any temperature, no matter how low.

#### StevieTNZ

That's certainly the case for collapse (standard) versus no-collapse (relative-state) formalisms as Bub explains in a forthcoming paper (see The Quantum Mystery of Wigner's Friend for an explanation of Bub).
I'll need to recheck the correspondence I had with Chalmers, but I believe from what he said it holds for both stances.

#### RUTA

I'll need to recheck the correspondence I had with Chalmers, but I believe from what he said it holds for both stances.
I'm not sure if you mean those different approaches can give different predictions or that they can't. But, you can see from the calculations in my Insight that they do in fact give different answers in this case.

#### zonde

Gold Member
I found one answer to Wigner's friend paradox that seems very satisfying to me.
It is based on statement that Wigner's measurement in superposition basis is necessarily an interference measurement. That would mean that to perform this measurement we need ensemble of indistinguishable Wigner's friend laboratories (or at least two simultaneous laboratories). Each laboratory has recorded either one or the other measurement outcome, so they are distinguishable. So in order to perform interference (Wigner's) measurement we have to mix them in such a way that we can not tell any more from which particular experimental run the laboratory came (like erasing which-way information for particles). That way all the Wigner's friends can have objective measurement records, all the Wigners can perform their measurements with unique outcomes but we have no idea how to pair particular Wigner with particular Wigner's friend (like we don't know through which slit the particle came).

#### StevieTNZ

I found one answer to Wigner's friend paradox that seems very satisfying to me.
It is based on statement that Wigner's measurement in superposition basis is necessarily an interference measurement. That would mean that to perform this measurement we need ensemble of indistinguishable Wigner's friend laboratories (or at least two simultaneous laboratories). Each laboratory has recorded either one or the other measurement outcome, so they are distinguishable.
The part I have placed in bold I would question.

And I've yet to check the correspondence I've had with David Chalmers.

#### StevieTNZ

So I checked our email correspondence and he refers to different predictions to where "collapse of the wave function" takes place in align with QM formalism (i.e. linear at all times).

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