Undergrad A new insight from the Frauchiger and Renner paper affecting MWI

[Quanundrum]

While the now infamous Frauchiger and Renner publication generated a lot of buzz, it was largely concluded that they drew way too premature conclusions with a too wide brush. Especially the topic of its implication that "Single Universe" interpretations were mostly ruled out garnered quite a lot of controversy. Now it appears that it may in fact do the opposite. Jeffrey Bub has weighed in with a seeming contradiction within MWI. Given how popular this topic was in the last months combined with Jeffrey Bub's distinct contributions to the field I thought it would be of interest to readers here.

Abstract
About ten years ago, Itamar Pitowsky and I wrote a paper, 'Two dogmas about quantum mechanics,' in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Here I revisit the paper and, following Frauchiger and Renner, I show that the Everett interpretation leads to modal contradictions in 'Wigner's-Friend'-type scenarios that involve 'encapsulated' measurements, where a super-observer (which could be a quantum automaton), with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures the memory of an observer system (also possibly a quantum automaton) after that system measures the spin of a qubit. In this sense, the Everett interpretation is inconsistent.

https://arxiv.org/abs/1907.06240

 

[charters]

Reposting my comment on this yesterday from a separate thread:

On page 10 Bub says:

"Since the two Wigners measure commuting observables on separate systems, W[bar] can communicate the outcome‘ok’of her measurement to W, and her prediction that she is certain, given the outcome‘ok,’ that W will obtain ‘fail,’ without ‘collapsing’ the global entangled state. Then in a round in which W obtains the outcome ‘ok’ for his measurement and so is certain that the outcome is ‘ok,’ he is also certain that the outcome of his measurement is not ‘ok.’"

I think this is just wrong. He is letting W-bar know both her own |ok> and F-bar's |tails> at the same time, which is just a complementarity violation. You can see the same error when he just changes the subscript from F-bar to W-bar in the subscripts in (16) to (17). If you keep W-bar and F-bar distinct in the correct way, the whole argument against MWI/representational QT falls apart (and actually instead shows the flaw in his own informational view).

 

[Michael Price]

Since MWI is standard QM without the collapse postulate it is impossible for MWI to suffer from a defect not shared with standard QM.

 

[A. Neumaier]

Since MWI is standard QM without the collapse postulate it is impossible for MWI to suffer from a defect not shared with standard QM.

Your premise is not valid. MWI claims a lot about what the wave function means in the context of measurements, none of which is true in ''standard QM without the collapse postulate'' (which is silent about measurement).

 

[Michael Price]

Your premise is not valid. MWI claims a lot about what the wave function means in the context of measurements, none of which is true in ''standard QM without the collapse postulate'' (which is silent about measurement).

We shall have to agree to disagree, unless you list the assumptions.

 

[A. Neumaier]

We shall have to agree to disagree, unless you list the assumptions.

Well, ''standard QM without the collapse postulate'' is silent about measurement. Thus anything about measurement is neither true nor false without adding interpretational statements about what a measurement is or entails. MWI takes a stand on the latter, hence is not just the former.

 

[Michael Price]

Well, ''standard QM without the collapse postulate'' is silent about measurement. Thus anything about measurement is neither true nor false without adding interpretational statements about what a measurement is or entails. MWI takes a stand on the latter, hence is not just the former.

MWI is silent about measurements, at the axiomatic level, because it need make no assumptions about them. Measurements are just an ill-defined subset of interactions in general. The consequences of measurements are deduced from the basic theory.

 

[A. Neumaier]

MWI is silent about measurements, at the axiomatic level, because it need make no assumptions about them. Measurements are just an ill-defined subset of interactions in general. The consequences of measurements are deduced from the basic theory.

But to deduce anything one needs a precise definition of what a measurement is. This definition (whatever it is; please give some details or a clear reference where the details can be found) is not shared by ''standard QM without the collapse postulate'', hence any deduction from it is not part of the latter.

 

[Michael Price]

But to deduce anything one needs a precise definition of what a measurement is. This definition (whatever it is; please give some details or a clear reference where the details can be found) is not shared by ''standard QM without the collapse postulate'', hence any deduction from it is not part of the latter.

IIRC a good measurement is where: The subject system couples with an object system. The object system is a superposition of orthogonal eigenstates. After the coupling is complete the subject system has decomposed into relative states which are also orthogonal to each other. The object-subject composite is now correlated. The correlation interpretation was Everett's original designation for his work.

 

[Mentz114]

Since MWI is standard QM without the collapse postulate it is impossible for MWI to suffer from a defect not shared with standard QM.

MWI is not standard QT. It follows from the mistaken belief that the universe demands perfect unitary evolution. It is an unnecessary and experimentally indeterminate invention.

 

[A. Neumaier]

IIRC a good measurement is where: The subject system couples with an object system. The object system is a superposition of orthogonal eigenstates. After the coupling is complete the subject system has decomposed into relative states which are also orthogonal to each other. The object-subject composite is now correlated. The correlation interpretation was Everett's original designation for his work.

What do you mean by ''After the coupling is complete''? The coupling is determined by the Hamiltonian of the universe, which knows nothing about subject systems and object systems.

 

[Michael Price]

What do you mean by ''After the coupling is complete''? The coupling is determined by the Hamiltonian of the universe, which knows nothing about subject systems and object systems.

I'm a physicist; I shall let the philosophers address such matters. (PS see footnote on page 85 of the DeWitt Graham princeton series publication.)

 

[A. Neumaier]

I'm a physicist; I shall let the philosophers address such matters.

So you need philosophy before being able to make deductions from your definition. Not a good procedure for a physicist.

 

[Michael Price]

So you need philosophy before being able to make deductions from your definition. Not a good procedure for a physicist.

No, I don't need philosophy.

 

[A. Neumaier]

No, I don't need philosophy.

But then your deductions depend on poorly defined terms and are unconvincing for others.

 

[akvadrako]

It’s just a matter of definitions. I would say measurements are not defined by MW itself. It’s after all a theory about objective reality, not our ability to predict experimental outcomes. Figuring out how to recognize experimenters and devices more precisely in the state is the program.

 

[Michael Price]

It’s just a matter of definitions. I would say measurements are not defined by MW itself. It’s after all a theory about objective reality, not our ability to predict experimental outcomes. Figuring out how to recognize experimenters and devices more precisely in the state is the program.

Yes, measurements in MWI are not needed to be defined precisely at the beginning, because they are not core. I gave Everett's definition about correlation inducing interactions, which is sufficient, but I am sure other definitions will work also.

 

[DarMM]

Well the biggest problem with MWI is still the lack of a non-circular proof of the Born rule. I've read every single one and none work.

 

[Michael Price]

Well the biggest problem with MWI is still the lack of a non-circular proof of the Born rule. I've read every single one and none work.

The problem is that many of the articles are not very clear and easy to read. I think Zurek (2007 - ref in the link) solved the problem. I try to explain it here:
https://www.quora.com/How-does-the-...ding-to-the-Born-rule/answer/Michael-Price-29The idea is to find a way of counting the relative numbers of orthonormal, or equally normed, branches. Zurek does this by using using the environment.

 

[DarMM]

I've read it and understood it. We can discuss on another thread, but it also has issues.

 

[Michael Price]

I've read it and understood it. We can discuss on another thread, but it also has issues.

Look forward to it.

 

[akvadrako]

Well the biggest problem with MWI is still the lack of a non-circular proof of the Born rule. I've read every single one and none work.

I don't want to get too off-topic, but just to respond to this: I think Vaidman's view is sufficient. You assume that Hilbert space represents a density of worlds and the only sensible (non-contextual) choice for a measure on Hilbert space is the amplitude squared . Then with some reasonable model of an observer, it's possible to show the observer will experience outcomes according to the Born rule.

Maybe you call that circular because it requires some assumption, but I don't see why that's a MW issue; it seems like most derivations of the Born rule apply to most interpretations. For example, The measurement postulates of quantum mechanics are operationally redundant (2019).

 

[A. Neumaier]

You assume that Hilbert space represents a density of worlds and the only sensible (non-contextual) choice for a measure on Hilbert space is the amplitude squared .

Thus you assume what is to be proved.

 

[DarMM]

The issue with the circularity is not the derivation itself, but the structures one requires to be in place to perform it. This applies to Vaidmann's proof as well. Though I agree his is one of the better ones. As I've said before the place to focus on is deriving those superstructures first.

 

[akvadrako]

Thus you assume what is to be proved.

Basically yes, some equivalent assumption is made. But unlike with Copenhagen where the Born rule and unitary evolution are in conflict, this form of a Born-like assumption is compatible with unitary evolution.

 

[Michael Price]

I don't want to get too off-topic, but just to respond to this: I think Vaidman's view is sufficient. You assume that Hilbert space represents a density of worlds and the only sensible (non-contextual) choice for a measure on Hilbert space is the amplitude squared . Then with some reasonable model of an observer, it's possible to show the observer will experience outcomes according to the Born rule.

Maybe you call that circular because it requires some assumption, but I don't see why that's a MW issue; it seems like most derivations of the Born rule apply to most interpretations. For example, The measurement postulates of quantum mechanics are operationally redundant (2019).

You're correct it is not just a MW problem - making the Born rule an assumption, as in Copenhagen, hardly seems to solve the issue.
Vaidman's solution seems very similar, or even identical, to Everett's?

 

[DarMM]

Basically yes, some equivalent assumption is made. But unlike with Copenhagen where the Born rule and unitary evolution are in conflict, this form of a Born-like assumption is compatible with unitary evolution.

That can be done in Copenhagen as well by showing the unitary evolution is compatible with the existence of a Boolean lattice or similar for macroscopic quantities.

The difference is in Copenhagen views this is considered to show compatibility as collapse is viewed as a kinematic relation. Where as in MWI collapse is shown to be an effective description of a dynamic process. Ironically work by Bub and Pitowsky is probably one of the better ones for showing the Born rule in MWI, it just doesn't have a solely MWI reading.

 

[akvadrako]

You're correct it is not just a MW problem - making the Born rule an assumption, as in Copenhagen, hardly seems to solve the issue.
Vaidman's solution seems very similar, or even identical, to Everett's?

Vaidman's preferred approach is to just postulate it. It's called the the Born-Vaidman rule (see Tappenden 2011): an observer should set his subjective probability of the outcome of a quantum experiment in proportion to the total measure of existence of all worlds with that outcome. See also Vaidman's summary of his view.