# Measurement results depend on the observer

In today’s arXiv appeared a nice paper by Časlav Brukner, my former PhD supervisor. Its central claim is that one cannot have observer-independent measurement results in quantum mechanics, which I bet you disagree with. But if you think a bit more about it, you shouldn’t: which interpretation, after all, allows one to have observer-independent measurement results? Old-style Copenhagen definitely allows that1, but it’s hard to find a living defender of old-style Copenhagen. Bohmian mechanics also allows that, and actually has living defenders, but it is a minority interpretation, and always appealed more to philosophers than to physicists. Collapse models also allow that, but they are on the verge on being experimentally falsified, and were never popular to start with.

What about the mainstream interpretations, then? In Časlav’s neo-Copenhagen interpretation the measurement results are observer-dependent (otherwise this would be a rather schizophrenic paper). In QBism they are explicitly subjective2, as almost everything else. In Many-Worlds there isn’t a single observer after a measurement, but several of them, each with their own measurement result.

How can this be? Časlav’s argument is as simple as it gets in quantum foundations: Bell’s theorem. In its simple version, Bell’s theorem dashes the old hope that quantum mechanics could be made deterministic: if the result of a spin measurement were pre-determined, then you wouldn’t be able to win the CHSH game with probability higher than $3/4$, unless some hidden action-at-a-distance was going on. But let’s suppose you did the measurement. Surely now the weirdness is over, right? You left the quantum realm, where everything is fuzzy and complicated, and entered the classical realm, where everything is solid and clear. So solid and clear that if somebody else does a measurement on you, their measurement result will be pre-determined, right?

Well, if it were pre-determined, than people doing measurements on people doing measurements wouldn’t be able to win the CHSH game with probability higher than $3/4$, unless some hidden action-at-a-distance was going on. But if quantum mechanics holds at every scale, then again one can win it with probability $\frac{2+\sqrt{2}}{4}$.

This highlights the fundamental confusion in Frauchiger and Renner’s argument, where they consider which outcome some observer thinks that another observer will experience, but are not careful to distinguish the different copies of an observer that will experience different outcomes. I’ve reformulated their argument to make this point explicit here, and it works fine, but undermines their conclusion that in single-world but not many-world theories observers will make contradictory assertions about which outcomes other observers will experience. Well, yes, but the point is that this contradiction is resolved in many-world theories by allowing different copies of an observer to experience different outcomes, and this recourse is not available in single-world theories.

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### 5 Responses to Measurement results depend on the observer

1. Ruth Kastner says:

Just a note that not all collapse models are ad hoc versions that depart from standard QM, like GRW. The Transactional Interpretation is a collapse model that is empirically equivalent to ‘standard’ QM (except that, unlike unitary-only QM, it predicts that measurements have results). It can do this because it’s based on the direct-action theory of fields. For quantitative details, see for example: https://arxiv.org/abs/1709.09367 and for an explicit derivation of the Born Rule in TI, see https://arxiv.org/abs/1711.04501

2. Daniel Tung says:

Would love to know your opinion of this paper: https://arxiv.org/abs/2012.05712
It shows how, if there are ontic states beneath quantum states, such states must be relative to observers.
So this together with the recent Nature paper (https://www.nature.com/articles/s41567-020-0990-x), which is in the same vein as Brukner of your blogpost, says that reality is in some sense observer dependent, whether it is observable or non-observable (ontic states).

3. Mateus Araújo says:

I’m not a fan of your paper. The informal conclusion in the abstract is clearly false. Clearly Wigner and his Friend can assign the same ontic state to the physical systems in the lab, namely the quantum state $\frac1{\sqrt2}(\ket{+}\ket{F_+}+\ket{-}\ket{F_-})$. You exclude that by assumption in the setup, demanding the Friend to assign an ontic state to either $\ket{+}$ or $\ket{-}$. Why would the Friend to that? It clearly contradicts the quantum mechanical description of the setup.

More generally, I don’t think reality is in any sense observer dependent. Measurement results are, as defended by Brukner and Bong et al., but reality is not made of measurement results. Reality is made of quantum states, and these are objective and observer independent.

4. Daniel Tung says:

Hi Mateus, thanks for the comment!

The paper works within the ontological model framework, where quantum states are epistemic states over an ontic state space.
The usual argument of the Wigner’s friend scenario is that since the friend only sees one outcome, she will assign either $\ket{+}_S\ket{F_+}$ or $\ket{-}_S\ket{F_-}$ to the lab (IF she can assign a quantum state to herself, which is not true for some interpretations).
In such cases the no-go result is obvious.
The paper shows that the no-go result is true even when the friend does not assign a quantum state to herself (but she still has an ontic state), only to the system she measures. This is the standard and common application of quantum theory to the scenario, just like Wigner’s original treatment.

Therefore, the paper does not refute MWI, where the friend assigns the same pure state to the lab as Wigner, as mentioned in your comment.

But I have a question for MWI: which pure state the friend should assign to the lab, if she does not contact to anyone outside the lab? Infinitely many pure states of the lab are consistent with her observations, which differs by a phase between the two terms $\ket{+}_S\ket{F_+}$ and $\ket{-}_S\ket{F_-}$. All such states seem applicable.
Similarly, how do we know which pure state is the true universal pure state in MWI?

5. Mateus Araújo says:

I don’t think interpretations that forbid you from assigning a quantum state to yourself are worth talking about.

As for your question, usually one assumes that the initial quantum state and the dynamics are known in the Wigner’s friend scenario, so one should assign that quantum state. More generally, if you make a single measurement of a quantum state, the only thing that you know about it is that it was not orthogonal to the projector you measured. This is true for any interpretation.

As for the true universal pure state, there is no hope finding that out, for pretty much the same reasons you’ll never find out the state of the entire universe even in classsical GR.