The error in the Frauchiger and Renner paper "Quantum theory cannot consistently describe the use of itself"

UPDATE  June 17, 2019: We corrected the spelling in the headline of this page and made a new blog page.

Note that the paper of Frauchiger and Renner is also logically inconsistent. If the various observers in the experiment do correct quantum mechanical reasoning, then they all will inevitably draw the same conclusions as an external observer. Frauchiger and Renner let the observers do incorrect reasoning and then derive a contradiction - which is no surprise.

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https://arxiv.org/abs/1604.07422

https://www.nature.com/articles/s41467-018-05739-8

Daniela Frauchiger and Renato Renner claim that quantum theory cannot "consistently describe the use of itself". The paper has appeared in Nature Communications and it was a cover story in New Scientist in March 2019.

In short, the error in the paper is that the authors fail to recognize that a measurement changes the state of a quantum system.

The experiment

      W  external observer does
      weak measurements M1 and M2
  _____________________________
 |  F1   r = heads or r = tails
 |                                          
 |  F2   z = -1/2 or z = +1/2  
 |_____________________________|
      isolated laboratory

Observers F1 and F2 are in a perfectly isolated laboratory. F1 uses a quantum system to generate a random variable r in a pure state where the probability of r = heads is 1/3 and r = tails is 2/3.

Then she measures the variable. If she got r = heads, she prepares an electron spin z = -1/2. If she got r = tails she prepares the electron in a pure state where the probability of z = +1/2 and z = -1/2 is 1/2 each.

F2 then measures the electron spin.

We assume one external observer W(igner). W makes a weak measurement M1 on the macroscopic observer F1 on the basis

       "r = heads"  -  "r = tails".

The quotes mean that W scans the memory of F1. Her memory stored the result of her measurement. By the "weak" measurement we mean that W does not measure the value of "r =..." straight away but only measures something which gives a little hint on the value.

If that measurement yields a non-zero result, we say W got "ok" from M1.

W makes another weak measurement M2 on the other macroscopic observer F2 on the basis

       "z = +1/2"  -  "z = -1/2".

One can calculate that W will 1/12 of the times get "ok" from both M1 and M2.

Try to derive a contradiction

Let us now try to derive a contradiction.

Assume that W got "ok" in M1.

Then if W would measure precisely the macroscopic observer F2, we know that W would get "z = +1/2". That is very simple to calculate. If W would after that measure F1 precisely, he would trivially get "r = tails".

If F1 measured r = tails, then she prepared the spin in a way that W cannot get "ok" from M2, that is trivial. We have an apparent contradiction, because F1 "can deduce" that "ok" from M1 implies not "ok" from M2. But we showed that sometimes M1 and M2 both yield "ok". A contradiction.

The error in the reasoning is that W never measured F2 and got "z = +1/2". A measurement changes the state of the system. Indeed, if W would measure F1 without measuring F2 first, he would sometimes get "r = heads".

In quantum mechanics, if we know that after a measurement M the system will be in the state S, that does not imply that it is in the state S before the measurement. In classical physics this is different.

Another aspect is if the incarnation of F1 who measures r = tails can assume that she is the only incarnation. In our previous blog post we stressed that no one can assume that he personally is able to collapse the wave function and cut off branches of Many Worlds. The incarnation of F1 who measures r = tails in a branch cannot assume that the other branch does not exist.

Scott Aaronson made a similar analysis in his blog:

https://www.scottaaronson.com/blog/?p=3975

Aaronson quotes Asher Peres:
"Unperformed measurements have no results."