Quantum theory cannot consistently describe the use of itself

The result in the paper is "No theory satisfies the three assumptions (Q, C, S)."

The table in the paper says that MWI violates assumption S and is "?" on the other two assumptions.

Unsurprisingly, when I look at the assumptions they all seem wrong or incoherent, depending on how you make the fuzzy statements precise. I'd guess most LW-ers are in a similar place (as are most quantum computing people probably), so this wouldn't really change any minds around here.

(Also their discussion of many-worlds sounds a bit silly. Nowhere in their table of interpretations is the natural one, "the wavefunction is all there is.")

I think this was also recently brought up in the Open Thread [LW(p) · GW(p)].

Mitchell_Porter wrote this:

It's a minor new quantum thought experiment which, as often happens, is being used to promote dumb sensational views about the meaning or implications of quantum mechanics. There's a kind of two-observer entangled system (as in "Hardy's paradox"), and then they say, let's also quantum-erase or recohere one of the observers so that there is no trace of their measurement ever having occurred, and then they get some kind of contradictory expectations with respect to the measurements of the two observers.

Undoing a quantum measurement in the way they propose is akin to squirting perfume from a bottle, then smelling it, and then having all the molecules in the air happening to knock all the perfume molecules back into the bottle, and fluctuations in your brain erasing the memory of the smell. Classically that's possible but utterly unlikely, and exactly the same may be said of undoing a macroscopic quantum measurement, which requires the decohered branches of the wavefunction (corresponding to different measurement outcomes) to then separately evolve so as to converge on the same state and recohere.

Without even analyzing anything in detail, it is hardly surprising that if an observer is subjected to such a highly artificial process, designed to undo a physical event in its totality, then the observer's inferences are going to be skewed somehow. So, you do all this and the observers differ in their quantum predictions somehow. In their first interpretation (2016), Frauchiger and Renner said that this proves many worlds. Now (2018), they say it proves that quantum mechanics can't describe itself. Maybe if they try a third time, they'll hit on the idea that one of the observers is just wrong.

The Renner-Frauchiger paper has been refuted, but usually with a lot of math. So I tried to write the simplest possible explanation, here:

http://byrden.com/quantum/Renner-explained.html

This paper is wrong.

The error is simple. The overall quantum system is also simple, but obfuscated by the authors spelling out all the steps of the setup.

As some have pointed out here, it's not a system that we could practically implement with people in "labs", no more than we could implement Schrodinger's Cat. But we can implement this system using quantum equipment. In fact Hardy's Paradox refers to a mathematically equivalent system which has been built (and works just as QM predicts).

So it behooves us to identify the error in the author's reasoning. It is this;

At the very beginning of the setup, they have "agent /F" read a quantum "coin". This entangles her with the "coin" and puts her into a superposition of "tails /F" and "heads /F".

The agent "tails /F" then calculates the results of the experiment AS IF SHE WAS THE ONLY COPY OF HERSELF. She ignores the contribution of her twin, "heads /F". But from the point of view of an outside observer, they both contribute information to the qubit that they jointly emit.

The entire chain of reasoning in the paper is based on this faulty assumption and is therefore wrong.

I agree with Scott Aaronson' objections to the paper. I think an inconsistency can be shown with a simpler argument:

Suppose two agents, each of which can be in two states, are prepared like in the paper and Aaronson's post.

Using the reasoning of the paper, if agent A finds it's in the $|1⟩$ state, it can deduce that B is in the $|0⟩$ state, so it can deduce that B is certain that A is in the $|+⟩$ state, so it can be certain that it's in the $|+⟩$ state, so it's not actually in the $|1⟩$ state as it sees itself to be. Then, because A is certain that it's in the $|+⟩$ state, it can deduce that B is in a more complicated state. This can go on infinitely. The problem is that in the first step A assumes it's certain of something when it knows it's in a superposition, and in the paper the details of that superposition matter in the final measurement.

Feels like there has to be something wrong with the paper. I don't have the knowledge to analyze it myself, but I read through the paper until the methods section and they don't discuss much beyond the math. It's unclear to me how they're arriving at a conclusion where different things happened from different perspectives, and particularly what percent of the time that would happen.

If someone familiar with the math could explain what the probability of each step is I think it could be a lot simpler to follow.