I Can ambiguity in the word "measurement" allow contradictions in QM?

[msumm21]

Take 2 people P1 and P2. P1 claims that a Stern-Gerlach device collapsed an electron’s spin to + or - (mixed state if P1 doesn’t know which) while P2 may say it did not collapse, but instead remains in a pure, entangled state. If we continue this sort of thinking (2 people applying different criteria for measurement) in a more complicated situation (maybe requiring interference), could P1 and P2 end up with “disjoint” probabilities for future outcomes. By disjoint here I mean the set of possible (non zero probability) outcomes are disjoint? I.e. the actual outcome will prove at least one of them “wrong.” Presumably this can’t happen, but has it been proven? Reference?

 

[Heikki Tuuri]

https://www.physicsforums.com/threa...an-enhanced-theory-or-just-philosophy.973442/

The question is connected to the paper of Frauchiger and Renner. The authors claimed that various observers can draw different conclusions with "correct" quantum mechanical reasoning.

I think there is a logical contradiction in the very claim of the paper: if people do correct reasoning, then they draw the same conclusions.

In your example case, if P1 calculates that the probability of an outcome X is zero, but P1 anyway observes that X happened, then P1 made a calculation error.

 

[charters]

Take 2 people P1 and P2. P1 claims that a Stern-Gerlach device collapsed an electron’s spin to + or - (mixed state if P1 doesn’t know which) while P2 may say it did not collapse, but instead remains in a pure, entangled state. If we continue this sort of thinking (2 people applying different criteria for measurement) in a more complicated situation (maybe requiring interference), could P1 and P2 end up with “disjoint” probabilities for future outcomes. By disjoint here I mean the set of possible (non zero probability) outcomes are disjoint? I.e. the actual outcome will prove at least one of them “wrong.” Presumably this can’t happen, but has it been proven? Reference?

Yes, they will disagree about the outcome statistics if they attempt to unitarily reverse the SG measurement and then measure the qubit on the original preparation basis. This is basically the difference between the predictions of quantum versus GRW theory.

I think there is a logical contradiction in the very claim of the paper: if people do correct reasoning, then they draw the same conclusions.

In your example case, if P1 calculates that the probability of an outcome X is zero, but P1 anyway observes that X happened, then P1 made a calculation error.

Of course if the experiment is actually done, whoever is wrong changes their opinion. The issue is we can't do this experiment, it has way too many degrees of freedom to control, so we can't empirically determine whose reasoning is correct. We can only ask if anyone's logical consistency falls apart when extrapolating their beliefs to thought experiments.

 

[PeterDonis]

P1 claims that a Stern-Gerlach device collapsed an electron’s spin to + or - (mixed state if P1 doesn’t know which) while P2 may say it did not collapse, but instead remains in a pure, entangled state.

You're leaving out an important part of this: P2 has to say the electron is entangled with the measuring apparatus. And P2 also has to say that the two branches of the entangled wave function of electron + apparatus are decohered, meaning they can't interfere with each other, because otherwise he would predict interference effects that obviously do not occur.

Also, P1 says that the electron's state collapsed, but so did that of the measuring apparatus (otherwise the apparatus would be entangled with the electron and the electron wouldn't be collapsed, which is what P2 is saying). And P1 says that this explains why no interference effects are observed with other possible measurement results.

So both P1 and P2 still agree on the actual observable: that no interference effects are ever observed between different possible results of the same measurement. Hence, they can never resolve their disagreement by experiment.

 

[msumm21]

Thanks, here are some followups:

I think there is a logical contradiction in the very claim of the paper: if people do correct reasoning, then they draw the same conclusions.

I'd looked over that paper a few months ago but also thought there were some mistakes in the analysis. It maybe what got me wondering if this proof exists.

You're leaving out an important part of this: P2 has to say the electron is entangled with the measuring apparatus. And P2 also has to say that the two branches of the entangled wave function of electron + apparatus are decohered, meaning they can't interfere with each other, because otherwise he would predict interference effects that obviously do not occur.

If P2 concludes it's a pure, entangled state couldn't there still be interference taking the whole system into account? I realize this entanglement makes it very complicated including all the entangled entities, but nevertheless theoretically possible, right?

 

[PeterDonis]

If P2 concludes it's a pure, entangled state couldn't there still be interference taking the whole system into account?

The entangled state is a state of the whole system--the electron and the measuring apparatus. The different entangled branches of the state can't interfere with each other because they are decohered.