Tuesday, March 12, 2019

Six photons claimed to prove that Wigner, his friend have irreconcilable views

Can a doable experiment prove that the objective reality doesn't exist?

Here's a rare example of the media hype that leads the reader to a basically correct conclusion about quantum mechanics.

As I have often argued, quantum mechanics fundamentally requires the description of the phenomena to be observer-dependent. An observer must know what he observes, what the result is, and the answers to these questions are in principle subjective. Consequently, the wave function or the density matrix, its collapse, and the precise predictions of the future measurements are subjective or observer-dependent, too. There is no way to objectively label phenomena as measurements or non-measurements and there is no viable way (and no way that would be compatible with relativity) to make the collapse of the wave function – describing the change of the observer's knowledge – as an objectively real collapse.

Wigner's friend experiment is the simplest thought experiment that shows the point. In that thought experiment (which is now claimed to become a real experiment), Eugene Wigner observes a lab in which his friend observes a quantum experiment. For the friend, the collapse occurs as soon as the friend sees something. But for Wigner himself who hasn't observed the particle inside, the system keeps on evolving as a superposition in which all options have nonzero amplitudes and are capable of reinterfering.

Today, the MIT Technology review promoted an Italian experimental paper:
A quantum experiment suggests there’s no such thing as objective reality (MIT)

Experimental rejection of observer-independence in the quantum world (quant-ph arXiv February 2019)
Massimiliano Proietti and 7 co-authors have performed an experiment with six photons.

It's not the "basic" Wigner's friend setup but an "extended" one. For that setup, one may derive a Bell-like inequality – assuming that the perceptions of both people are real – and this Bell-like inequality is violated by the quantum mechanical predictions and has been shown to be violated by 5 sigma in the Italian experiment. OK, I call it "Italian" because of some surnames but their affiliations are in Edinburgh, Grenoble, and Innsbruck – no Italy.

I still don't understand how it's possible – a "contradiction" between the people's perspective is only possible when the interference between the "not yet collapsed" options is actually measured which will never be possible in practice, I think. But they must make some "more classical" assumptions about the interpretation of the experiment and this is being experimentally violated. I am going to look at the details, after a day with the monster group.

At any rate, in principle, the conclusion is surely correct. In the Wigner's friend setup, the descriptions of the phenomena by the two people must be fundamentally distinct and impossible to unify into one "collective" let alone "objective" description. Different observers have different lists of observations with their generally different results, and therefore generally different predictions for the future and different microscopic descriptions what happened.

P.S.: The inequality they test and violate isn't really a Bell's inequality but a Clauser-Horne-Shimony-Holt inequality (equation 2) which is derived assuming an objective probability distribution. When the variables \(A_x,B_y\) take values in \(a,b\in \{-1,+1\}\), then the average values\[

\langle A_x B_y\rangle = \sum_{a,b} ab\cdot P(A_x\!=\!a,B_y\!=\!b)

\] obey the CHSH inequality (yes, you have heard about CHSH before)\[

\langle A_1 B_1\rangle + \langle A_1 B_0\rangle + \langle A_0 B_1\rangle - \langle A_0 B_0\rangle \leq 2.

\] OK, they seem to assume that all the photons' degrees of freedom are described by pure states according to both observers. This seems wrong to me. The observation of the photons by Wigner's friend creates an entanglement with the degrees of freedom in the friend's body, so the state of the photons themselves become mixed according to Wigner (I mean the external observer), not pure. So I think that when these things are done correctly, it's not possible to find this kind of a "contradiction" in practice.

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