I Quantum theory - Nature Paper 18 Sept

[StevieTNZ]

Earlier this morning I came across this article -- https://phys.org/news/2018-09-errors-quantum-world.html -- which is about an open for all article in Nature Communications -- https://www.nature.com/articles/s41467-018-05739-8

Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here, we propose a Gedankenexperiment to investigate the question whether quantum theory can, in principle, have universal validity. The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory. Analysing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty. The agents’ conclusions, although all derived within quantum theory, are thus inconsistent. This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner.

I've yet to fully work through the paper, but if this thread is appropriate I would love to read other people's views on it.

 

[PeterDonis]

These authors have a number of previous papers on this general topic; here is a typical one from 2016:

https://arxiv.org/abs/1604.07422

What appears to me to be new about this latest paper is that the claimed inconsistency is not limited to single-world interpretations, as it was in previous papers like the one linked to above. The difference now is only that different interpretations have the inconsistency show up in different places (depending on which assumptions they make).

 

[akvadrako]

the claimed inconsistency is not limited to single-world interpretations, as it was in previous papers like the one linked to above. The difference now is only that different interpretations have the inconsistency show up in different places (depending on which assumptions they make).

Where do you see that? In the Nature article the main result seems to be "Theorem 1. Any theory that satisfies assumptions (Q), (C), and (S) yields contradictory statements when applied to the Gedankenexperiment of Box 1."

(S) is the single-world assumption

 

[DarMM]

It seems to be their 2016 paper tidied up and with a discussion about the various interpretations modified to have some responses from the proponents of those interpretations taken into account. I'll have a more careful look later. I think most see it as an inconsistency in uninterpreted QM, i.e. you have to reject Q, C or S or else you have a inconsistent framework.

 

[Demystifier]

The paper does not claim that QM is inconsistent. It claims that what is inconsistent is any interpretation of QM in which all 3 assumptions Q, C and S are satisfied. And then it explains that most known interpretations are consistent by violating at least one of those assumptions. The question that seems unanswered is the following: Is there any known interpretation of QM that satisfies all 3 assumptions and is therefore inconsistent? As far as I can see, the paper does not identify any such inconsistent interpretation.

 

[DarMM]

The question that seems unanswered is the following: Is there any known interpretation of QM that satisfies all 3 assumptions and is therefore inconsistent? As far as I can see, the paper does not identify any such inconsistent interpretation.

There was some discussion about certain orthodox versions of Copenhagen (as opposed to unorthodox like QBism) trying to hold all three conditions. See Matt Leifer's talk here:

39:44

Earlier in the same lecture he breaks down the "types" of Copenhagen into Objective and Perspectival.

However see the paper by Bub that argues that Orthodox (Objective) Copenhagen is fine with this result:
https://arxiv.org/abs/1804.03267

 

[DarMM]

Okay, I've read it and compared it to the previous paper. Small differences:

1. They simplify the experiment (less steps), but this is a trivial detail
   
2. The discussion on interpretations is longer with more references to how the interpretation responds to the theorem
3. They include a nice discussion of the original Wigner's friend
   
4. The point out how their set up reduces to Wigner's friend and Deustch's modification of it
5. (Biggest difference) The original paper derived the result within a framework they called "The story framework", how physical theories define narratives about results. This Nature paper simply presents it from the perspective of normal quantum mechanics. This was the hardest part of the original paper in my opinion. The assumptions Q, C, S now have a shorter forms stated purely in terms of textbook QM.

Overall one should just read this version.

 

[stevendaryl]

The axiom that mainstream interpretations (variants of Copenhagen) must reject (even though they don't explicitly reject it) is C, which I would paraphrase as follows:

If Alice is 100% certain that Bob is 100% certain that X is true, then Alice should also be 100% certain that X is true.

where being 100% certain of something means that the Born probability for something is 1, or that it's derived from other 100% certain facts using the various assumptions.

I couldn't completely follow the argument of the thought experiment, but my rough impression is that under certain circumstances, you can have a situation where Alice, treating Bob as a quantum mechanical system, calculates that there is a 100% certainty that Bob is in a state of being 100% certain that X is true, although Alice knows that X is false.

 

[Demystifier]

If Alice is 100% certain that Bob is 100% certain that X is true, then Alice should also be 100% certain that X is true.

It reminds me of the blue-eyes paradox: https://www.physicsforums.com/threads/blue-eye-paradox.875870/

 

[vanhees71]

The axiom that mainstream interpretations (variants of Copenhagen) must reject (even though they don't explicitly reject it) is C, which I would paraphrase as follows:

If Alice is 100% certain that Bob is 100% certain that X is true, then Alice should also be 100% certain that X is true.

This is not logically sound at all. If Alice knows that Bob is certain about X this doesn't imply that she can be certain about X too. That's often forgotten in discussions about the foundations.

Put it in physical terms. Say, we have our beloved two-photon Bell state again in the beginning, i.e., there are two photons in the polarization state
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle - |VH \rangle).$$
If now Bob measures the polarization of his photon and tells Alice that he measured it, Alice still describes her photon's state as
$$\hat{\rho}_{A}=\frac{1}{2} \hat{1}$$
She cannot be certain about Bob's outcome, before Bob has told her.

where being 100% certain of something means that the Born probability for something is 1, or that it's derived from other 100% certain facts using the various assumptions.

I couldn't completely follow the argument of the thought experiment, but my rough impression is that under certain circumstances, you can have a situation where Alice, treating Bob as a quantum mechanical system, calculates that there is a 100% certainty that Bob is in a state of being 100% certain that X is true, although Alice knows that X is false.

I've still to read the Nature Communications paper, though. Since it has been discussed in the community for a while, I'm sure, it's not as simple a (unfortunately quite) common misunderstanding of QT as suggested in #8.

 

[Andy Resnick]

The paper does not claim that QM is inconsistent. It claims that what is inconsistent is any interpretation of QM in which all 3 assumptions Q, C and S are satisfied. And then it explains that most known interpretations are consistent by violating at least one of those assumptions. The question that seems unanswered is the following: Is there any known interpretation of QM that satisfies all 3 assumptions and is therefore inconsistent? As far as I can see, the paper does not identify any such inconsistent interpretation.

I admit that I don't fully understand the paper- the quantitative details of the gedankenexperiment are (IMO) cryptic and hard to parse. Tables 1 and 2 gave me a headache, for example...

However, the main point of their argument seems to concern a situation where multiple independent observers each have (partially overlapping) incomplete information about a pure state; when the observers compare their predictions about what the pure state is, they have irreconcilable differences. Is that a reasonable summary?

If that's a correct summary, then I'm not sure there's any paradox: Gibbs' paradox is a related problem with a well-understood solution: whether or not we agree that 2 populations of objects mix depends on if we agree that the groups of objects are the same or different.

That said, I appreciate their Table 4 and related discussion.

 

[stevendaryl]

Put it in physical terms. Say, we have our beloved two-photon Bell state again in the beginning, i.e., there are two photons in the polarization state $$|\Psi \rangle=\frac{1}{\sqrt{2}} (|HV \rangle - |VH \rangle).$$ If now Bob measures the polarization of his photon and tells Alice that he measured it, Alice still describes her photon's state as $$\hat{\rho}_{A}=\frac{1}{2} \hat{1}$$

She cannot be certain about Bob's outcome, before Bob has told her.

I'm talking about the case in which Alice knows what it is that Bob is 100% certain of.

What the paper means by rejecting C is the possibility of the following sort of situation:

Alice says: "I'm 100% certain that Bob is 100% certain that his photon is vertically polarized. But his photon is actually horizontally polarized."

 

[vanhees71]

I still have to read the paper...

 

[stevendaryl]

Okay, so I think I finally understand the argument. It's not presented in the clearest way, in my opinion.

So there are two different systems that are being treated as quantum-mechanical systems.

1. System $\overline{F}$, has states $|\overline{h}\rangle$ and $|\overline{t}\rangle$. For the thought experiment, we consider a few special superpositions:
   • $|\overline{ok}\rangle = \frac{1}{\sqrt{2}} (|\overline{h}\rangle - |\overline{t}\rangle)$
   • $|\overline{fail}\rangle = \frac{1}{\sqrt{2}} (|\overline{h}\rangle + |\overline{t}\rangle)$
     
   • $|init\rangle = \frac{1}{\sqrt{3}} (|\overline{h}\rangle + \sqrt{2} |\overline{t}\rangle)$
2. System $F$, which has states $|\frac{+1}{2}\rangle$ and $|\frac{-1}{2}\rangle$. For the thought experiment, we consider the alternative basis:
   • $|ok\rangle = \frac{1}{\sqrt{2}} (|\frac{+1}{2}\rangle - |\frac{-1}{2} \rangle)$
     
   • $|fail\rangle = \frac{1}{\sqrt{2}} (|\frac{+1}{2}\rangle + |\frac{-1}{2} \rangle)$

The interaction between systems is such that:

• If System $\overline{F}$ is in state $|\overline{h}\rangle$, then it puts System $F$ into the state $|\frac{-1}{2}\rangle$
• If System $\overline{F}$ is in state $|\overline{t}\rangle$, then it puts System $F$ into the state $|fail\rangle$

We set up $\overline{F}$ so that it is initially in state $|init\rangle$.

The system evolves according to the interaction rule above, and the linearity of the evolution equations into the state:

$|final\rangle = \frac{1}{\sqrt{3}} |\overline{h}\rangle |\frac{-1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |\frac{+1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |\frac{-1}{2}\rangle$

For the sake of the reasoning that follows, I'm going to write this in three different ways:

1. $|final\rangle = \sqrt{\frac{1}{3}} |\overline{h}\rangle |\frac{-1}{2}\rangle + \sqrt{\frac{2}{3}} |\overline{t}\rangle |fail\rangle$
2. $|final\rangle = \sqrt{\frac{2}{3}} |\overline{fail}\rangle |\frac{-1}{2}\rangle + \sqrt{\frac{1}{3}} |\overline{t}\rangle |\frac{+1}{2}\rangle$
3. $|final\rangle = \sqrt{\frac{3}{4}} |\overline{fail}\rangle |fail\rangle - \sqrt{\frac{1}{12}} |\overline{fail}\rangle |ok\rangle - \sqrt{\frac{1}{12}} |\overline{ok}\rangle |fail\rangle - \sqrt{\frac{1}{12}} |\overline{ok}\rangle |ok\rangle$

The twist in this thought experiment is that systems $\overline{F}$ and $F$ contain observers who can also reason using quantum-mechanics. So we have four observers: $\overline{W}, \overline{F}, W, F$ (I hope it's not confusing to use the same name for system $F$ and observer $F$ and the same name for system $\overline{F}$ and observer $\overline{F}$). They are measuring different things:

• $F$ is measuring whether his system is in state $|\frac{+1}{2}\rangle$ or $|\frac{-1}{2}\rangle$
• $\overline{F}$ is measuring whether his system is in state $|\overline{h}\rangle$ or $|\overline{t}\rangle$
  
• $W$ is measuring whether system $F$ is in state $|ok\rangle$ or $|fail\rangle$
• $\overline{W}$ is measuring whether system $\overline{F}$ is in state $|\overline{ok}\rangle$ or $|\overline{fail}\rangle$

Let's write down what each observer can reason about the others, based on their observations:

1. If $F$ measures +1/2, then it means that it is impossible that $\overline{F}$ got result $\overline{h}$. That's because there is no overlap between the final state and $|\overline{h}\rangle |\frac{+1}{2}\rangle$. So $F$ concludes that if he got +1/2, $\overline{F}$ must have gotten $\overline{t}$
2. If $\overline{W}$ measures $\overline{ok}$, then it means that is impossible that $F$ got -1/2. That's because there is no overlap between the final state and $|\overline{ok}\rangle |\frac{-1}{2}\rangle$. So $\overline{W}$ concludes that if he got $\overline{ok}$ then $F$ must have gotten +1/2.
3. If $\overline{F}$ gets $\overline{t}$, then it is impossible that $W$ got $ok$. That's because there is no overlap between the final state and $|\overline{t}\rangle |ok\rangle$. So $\overline{F}$ concludes that if he got $\overline{t}$, then $W$ got $fail$.

Now, what happens if $\overline{W}$ gets $\overline{ok}$?

From 2 above, $\overline{W}$ concludes that $F$ got +1/2.
From 1 above, it follows that $F$ concludes that $\overline{F}$ got $\overline{t}$
From 3 above, it follows that $\overline{F}$ concludes that $W$ got $fail$

So in this case, $\overline{W}$ is certain that $F$ is certain that $\overline{F}$ is certain that $W$ got $fail$. So if we adopt the inference rule:

Rule C: If agent A is certain (according to the Rules of Quantum Mechanics) that agent B is certain (according to the Rules of Quantum Mechanics) that fact X is true, then agent A should be certain that X is true

then it follows:

If $\overline{W}$ gets $\overline{ok}$, then he should be certain that $W$ gets $fail$.

But actually, there is a 1/12 chance that $\overline{W}$ gets $\overline{ok}$ and that $W$ gets $ok$. This just follows from the fact that the overlap between $|final\rangle$ and $|\overline{ok}\rangle |ok\rangle$ is $- \frac{1}{\sqrt{12}}$ leading to a probability of 1/12.

 

[atyy]

There was some discussion about certain orthodox versions of Copenhagen (as opposed to unorthodox like QBism) trying to hold all three conditions. See Matt Leifer's talk here:

It's an interesting to talk, but it has not much to do with most "orthodox" Copenhagen-type interpretations, since he defines the "objective" Copenhagen interpretation not to be instrumentalism (ie. does not regard measurement as fundamental), and also to assume that hidden variables don't exist. In contrast, the Copenhagen-type interpretation in Landau and Lifshitz clearly treats measurement as fundamental, and Messiah goes with Copenhagen while not ruling out hidden variables. Also, one just has to say in his words that "Alice's outcomes exist for Alice (but not for Bob), and Bob's outcomes exist for Bob (but not for Alice)", which is already part of the orthodox Copenhagen-type interpretation, eg. Wiseman's and Cavalcanti say 'strict operationalists do indeed operate "by denying independent real situations as such", as Einstein subsequently allowed.'

 

[atyy]

Is the Frauchiger and Renner result related to an earlier result by Hays and Peres about conditions needed for quantum and classical descriptions of a measuring apparatus to agree?

https://arxiv.org/abs/quant-ph/9712044
Quantum and classical descriptions of a measuring apparatus
Ori Hay, Asher Peres
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality. Alternatively, the apparatus may always be treated by quantum mechanics, and be measured by a second apparatus which has such a dual description. This article examines whether these two different descriptions are mutually consistent. It is shown that if the dynamical variable used in the first apparatus is represented by an operator of the Weyl-Wigner type (for example, if it is a linear coordinate), then the conversion from quantum to classical terminology does not affect the final result. However, if the first apparatus encodes the measurement in a different type of operator (e.g., the phase operator), the two methods of calculation may give different results.

 

[DarMM]

It's an interesting to talk, but it has not much to do with most "orthodox" Copenhagen-type interpretations, since he defines the "objective" Copenhagen interpretation not to be instrumentalism (ie. does not regard measurement as fundamental), and also to assume that hidden variables don't exist.

I think it's very hard to know what Copenhagen is at this point. Many interpretations call themselves Copenhagen despite being quite unlike Bohr's views. He's using the classification given by Adán Cabello in his paper here:
https://arxiv.org/abs/1509.04711

It seems to be the typical view in Quantum Foundations currently.

From my own understanding, I thought Bohr didn't viewed measurements as fundamental ontologically, just that they must necessarily be treated classically due to human nature, Heisenberg was similar.

Bohr thought that the "stuff" under QM did exist but was ineffable/indescribable and thus there were no hidden variables, as there was no mathematical description. Again, this is my reading of his papers on the subject.

 

[stevendaryl]

There is one part of quantum orthodoxy that I think is actually wrong, although it doesn't usually get anyone into trouble. The "soft" contradiction described in this paper exploits this part of the orthodoxy, and I think that the argument falls through without it.

The orthodox interpretation of the Born rules is that any Hermitian operator corresponds to an observable, and measuring any observable results in an eigenvalue of the corresponding operator. In practical terms, though, many Hermitian operators are not actually measurable.

I can illustrate the absurdity of "any operator is measurable" using Schrodinger's dead cat. Suppose you have a dead cat, and you want to bring it back to life. Then let me define two cat states: $|A\rangle = \frac{1}{\sqrt{2}} |Dead\rangle + \frac{1}{\sqrt{2}} |Alive\rangle$ and $|B\rangle = \frac{1}{\sqrt{2}} |Dead\rangle - \frac{1}{\sqrt{2}} |Alive\rangle$. Let the AB-ness operator be some operator $AB$ such that $AB |A\rangle = +|A\rangle$ and $AB |B\rangle = - |B\rangle$. If I perform a measurement of the AB-ness of a dead cat, I'll either get +1 or -1 with 50/50 probability. Afterward, the cat will be in the state $|A\rangle$ or $|B\rangle$ depending on whether I got $\pm 1$. Regardless of what I got, I can now check whether the cat is alive or dead, and I'll find it alive (the state $|Alive\rangle$) with 50% probability. If I do this procedure enough time, I will eventually get a live cat.

What's wrong with this story (well, there are many things wrong with it, but...) is that you can't actually measure the AB-ness of a cat.

 

[Demystifier]

There is one part of quantum orthodoxy that I think is actually wrong, although it doesn't usually get anyone into trouble. The "soft" contradiction described in this paper exploits this part of the orthodoxy, and I think that the argument falls through without it.

The orthodox interpretation of the Born rules is that any Hermitian operator corresponds to an observable, and measuring any observable results in an eigenvalue of the corresponding operator. In practical terms, though, many Hermitian operators are not actually measurable.

I can illustrate the absurdity of "any operator is measurable" using Schrodinger's dead cat. Suppose you have a dead cat, and you want to bring it back to life. Then let me define two cat states: $|A\rangle = \frac{1}{\sqrt{2}} |Dead\rangle + \frac{1}{\sqrt{2}} |Alive\rangle$ and $|B\rangle = \frac{1}{\sqrt{2}} |Dead\rangle - \frac{1}{\sqrt{2}} |Alive\rangle$. Let the AB-ness operator be some operator $AB$ such that $AB |A\rangle = +|A\rangle$ and $AB |B\rangle = - |B\rangle$. If I perform a measurement of the AB-ness of a dead cat, I'll either get +1 or -1 with 50/50 probability. Afterward, the cat will be in the state $|A\rangle$ or $|B\rangle$ depending on whether I got $\pm 1$. Regardless of what I got, I can now check whether the cat is alive or dead, and I'll find it alive (the state $|Alive\rangle$) with 50% probability. If I do this procedure enough time, I will eventually get a live cat.

What's wrong with this story (well, there are many things wrong with it, but...) is that you can't actually measure the AB-ness of a cat.

Would there be anything wrong with that if "dead" and "alive" were replaced by "spin up" and "spin down"? I guess not. So one could still say that any Hermitian operator of a microscopic system corresponds to an observable. But then there is no precise border between microscopic and macroscopic, so one should conclude that your example is, in principle, possible even with the macroscopic cat. And it should not be any more strange than the fact that physical laws do not, in principle, forbid to transform a dead cat into an alive one. Of course, it's impossible in practice due to the statistical 2nd law of thermodynamics, but in principle it's possible.

 

[stevendaryl]

Would there be anything wrong with that if "dead" and "alive" were replaced by "spin up" and "spin down"?

I actually think that spin isn't measurable, either. The way that you measure spin is that you set things up so that a particle with spin-up will go to the left, and a particle with spin-down will go to the right. You still haven't measured the spin. But now, you crash the electron into a photographic plate, and it makes a dark spot. Now, you either see a dark spot on the left, or on the right, and you deduce that the particle must have been spin-up or spin-down. But what you're actually measuring isn't spin, but the presence/absence of dark spots.

So it's not really Hermitian operators that are measurable. It's macroscopic facts about the world. You can try to be clever and set up an interaction between systems so that this or that value of the operator leads to this or that macroscopic fact about your measurement device. But there is no guarantee that you'll be able to do that for all possible operators.

I guess not. So one could still say that any Hermitian operator of a microscopic system corresponds to an observable. But then there is no precise border between microscopic and macroscopic, so one should conclude that your example is, in principle, possible even with the macroscopic cat. And it should not be any more strange than the fact that physical laws do not, in principle, forbid to transform a dead cat into an alive one. Of course, it's impossible in practice due to the statistical 2nd law of thermodynamics, but in principle it's possible.

I sort of agree. It's a FAPP (for all practical purposes) impossibility. So that's what makes the contradiction described in this paper a "soft" contradiction. You can't actually perform an experiment to resolve the contradiction.

Some paradoxes in physics suggest experiments to resolve them. If two different lines of reasoning lead to two different predicted outcomes, then you can set up an experiment to see which one is right. But if the contradiction would require a FAPP impossible experiment, then it stays in the realm of philosophy, rather than physics.

 

[akvadrako]

I sort of agree. It's a FAPP (for all practical purposes) impossibility. So that's what makes the contradiction described in this paper a "soft" contradiction. You can't actually perform an experiment to resolve the contradiction.

In the paper what they propose is to run the experiment on a quantum computer, with the experimenters implemented as agents that are simple enough to simulate. If you have a large enough quantum computer then the experiment should be practical, so it's only FAPP impossible if we never build large quantum computers.

 

[Demystifier]

But if the contradiction would require a FAPP impossible experiment, then it stays in the realm of philosophy, rather than physics.

I disagree. Even if you cannot do the experiment with true cats, you can do experiments with larger and larger objects. For instance, interference experiments have been performed not only with electrons and photons, but even with large molecules containing several hundreds of atoms. And there are even serious proposals that it could be done with viruses. So, if you cannot resolve a contradiction by doing experiment with cats, you can do an analogous experiment with something smaller. Whatever results of such experiments might be, it is scientifically justified to extrapolate conclusions and argue that essentially the same can be said about cats.

For an example of that kind of reasoning, see my https://lanl.arxiv.org/abs/1406.3221

 

[mfb]

Only if you keep the objects coherent. Anything that would remotely resemble an intelligent system will lead to decoherence.

 

[Demystifier]

Only if you keep the objects coherent. Anything that would remotely resemble an intelligent system will lead to decoherence.

How about quantum computers? Would you say that they can remotely resemble an intelligent system? Would you say that we shall ever have sufficient control over decoherence to build a quantum computer that for some tasks works better than the classical one?

 

[mfb]

Would you say that they can remotely resemble an intelligent system?

Parts of the computing, if you keep them in coherent states? No. The overall computer? Yes.

Would you say that we shall ever have sufficient control over decoherence to build a quantum computer that for some tasks works better than the classical one?

I expect so but I don't see the relevance of this.

 

[stevendaryl]

I disagree. Even if you cannot do the experiment with true cats, you can do experiments with larger and larger objects. For instance, interference experiments have been performed not only with electrons and photons, but even with large molecules containing several hundreds of atoms.

Going back to the "soft contradiction" of the paper under discussion, I think it's pretty close to being a "quantum resurrection" type of thing.

In the Schrodinger's cat thought experiment, Schrodinger flips a coin and if it's heads, he kills the cat, and if it's tails, he let's the cat live. Later, you ask the live cat whether his evil master got heads or tails, and the cat would presumably say "tails", since he's alive. But if quantum resurrection is possible, then the cat doesn't know---he may have died and been brought back to life.

A lot (or maybe all) of common-sense reasoning about cause and effect---if this then that---only works if you disregard certain outlandish possibilities, such as quantum resurrection or Maxwell's demon or reversing the momentum of every molecule of air so that all the air in a room concentrates into one corner.

In the paper, it's assumed that the participants in the thought experiment can reason common-sensically along the lines of: "If I get heads, then I send a spin-down particle to the other participant. I see heads. Therefore, the other participant got spin-down." Not necessarily. You may have gotten tails and sent a spin-up particle, and then later someone placed you in the state of seeing heads by performing a series of noncommuting measurements (in the same way that quantum resurrection works).

 

[Stephen Tashi]

Not necessarily. You may have gotten tails and sent a spin-up particle, and then later someone placed you in the state of seeing heads by performing a series of noncommuting measurements (in the same way that quantum resurrection works).

What prevents this possibility from casting doubt on the validity of any real experiment where the experimenters think they have prepared a system in a certain way?

 

[stevendaryl]

What prevents this possibility from casting doubt on the validity of any real experiment where the experimenters think they have prepared a system in a certain way?

That's my point. Common-sense reasoning really depends on discounting certain possibilities as infeasible or extremely unlikely. If you propose a situation where those skeptical possibilities come into play, then you can no longer trust common-sense reasoning along the lines of "If I see X, I will do Y. I remember seeing X, so Y must have been done."

 

[vanhees71]

I disagree. Even if you cannot do the experiment with true cats, you can do experiments with larger and larger objects. For instance, interference experiments have been performed not only with electrons and photons, but even with large molecules containing several hundreds of atoms. And there are even serious proposals that it could be done with viruses. So, if you cannot resolve a contradiction by doing experiment with cats, you can do an analogous experiment with something smaller. Whatever results of such experiments might be, it is scientifically justified to extrapolate conclusions and argue that essentially the same can be said about cats.

For an example of that kind of reasoning, see my https://lanl.arxiv.org/abs/1406.3221

Well, I also don't think that this is so easily refuted, although of course, I don't think the description in the paper is very clear. In my opinion one should describe all steps using the complete state, which is in a tensor-product space of four (I hope, I got at least this right) 2D Hilbert-space systems (why some are coined spin some are coined heads-tail is incomprehensible to me, but the math should be clear). I guess, one can then do all the steps in a quite straight-forward way, and I think the authors assume only PV measurements, i.e., what I'd call von Neumann filter preparations. I can't believe that there is a real contradiction since the math is pretty save for such a simple system. I rather believe it's a complication of interpretations putting more meaning to the formalism than there is within the minimal probabilistic interpretation, but I have to do carefully this calculation for myself, before I can definitely confirm this.

 

[Lord Jestocost]

There is a recent comment by Scott Aaronson on Frauchiger's and Renner's paper: https://www.scottaaronson.com/blog/?p=3975

 

[stevendaryl]

To what extent does the argument shed light on any of the actual interpretations of QM? It seems to me that it doesn't actually cause problems for a "collapse" interpretation. To quote the basic inferences again:

Let's write down what each observer can reason about the others, based on their observations:

1. If $F$ measures +1/2, then it means that it is impossible that $\overline{F}$ got result $\overline{h}$. That's because there is no overlap between the final state and $|\overline{h}\rangle |\frac{+1}{2}\rangle$. So $F$ concludes that if he got +1/2, $\overline{F}$ must have gotten $\overline{t}$
2. If $\overline{W}$ measures $\overline{ok}$, then it means that is impossible that $F$ got -1/2. That's because there is no overlap between the final state and $|\overline{ok}\rangle |\frac{-1}{2}\rangle$. So $W$ concludes that if he got $\overline{ok}$ then $F$ must have gotten +1/2.
3. If $\overline{F}$ gets $\overline{t}$, then it is impossible that $W$ got $ok$. That's because there is no overlap between the final state and $|\overline{t}\rangle |ok\rangle$. So $\overline{F}$ concludes that if he got $\overline{t}$, then $W$ got $fail$.

These inferences are true of the initial state of the system. If you allow for measurements to affect the thing that is being measured (collapse), then the inferences no longer hold:

If $\overline{W}$ measures $\overline{ok}$, then that places the composite system into the state $\langle \overline{ok}, \frac{+1}{2}\rangle$. $F$ measures +1/2, and the composite system is in the same state. If then $\overline{F}$ measures his system's state, he can get $\overline{h}$ or $\overline{t}$, with equal probability. So that means that 1. above is wrong: $F$ can't conclude that $\overline{F}$ will get $\overline{t}$. He could have concluded that in the initial state, but not after $\overline{W}$ messed with it.

Many-Worlds is a little more complicated. If you try to analyze it using Many-Worlds, what you would find is that different observers may disagree about what's true in "the real world". After $\overline{W}$ measures $\overline{ok}$ and $F$ measures $\frac{+1}{2}$, they disagree about whether $\overline{F}$ is in a definite state or not. $\overline{W}$ thinks he's in a superposition of $|\overline{h}\rangle$ and $|\overline{t}\rangle$, while $F$ thinks he's definitely in state $|\overline{t}\rangle$. So this thought experiment shows that the counting of "possible worlds" is a little problematic, because you can't consider a possible world to be one where everyone agrees on all macroscopic facts.

The only interpretation that to me seems inconsistent with this thought experiment is the combination of:

1. There is only one world.
2. There is no collapse.
3. There is nothing special about observers/measurements.
4. The Born rule gives the probabilities of all measurement outcomes.

 

[atyy]

There is a recent comment by Scott Aaronson on Frauchiger's and Renner's paper: https://www.scottaaronson.com/blog/?p=3975

I haven't read Frauchiger and Renner's work closely enough, but my knee jerk reaction was similar to what Scott Aronson is saying.

 

[DarMM]

My reading:

1. When the observer $\overline{F}$ obtains the $\overline{t}$ result, he can then infer that the $F$ observer's lab is in the $|fail\rangle$ state and thus the $W$ observer will not get the $okay$ result, as the $|fail\rangle$ state is orthogonal to $|okay\rangle$
2. Via application of the Born Rule in the $P(E) = 1$ (i.e. certain) case and the assumption of recursive conclusions based on other agents' reasoning, $\overline{F}$'s conclusion that $W$ must obtain $fail$ can be transferred to $W$ themselves, who will then predict they must measure $fail$.
   To obtain this conclusion they must pass through the reasoning of $\overline{W}$.
   This results in the paradox as in the original state $W$ can get $okay$. So from reasoning from the initial quantum state, $W$ deduces they can obtain $okay$, but from reasoning via $\overline{W}$ (and thereby obtaining $\overline{F}$'s conclusion) they conclude they cannot.
3. The reasoning $W$ and $\overline{W}$ use ultimately involves considering $F$ and $\overline{F}$ to be in the Hardy paradox state:
   $$\frac{1}{\sqrt{3}}\left(|\overline{h}\downarrow\rangle + |\overline{t}\downarrow\rangle + |\overline{t}\uparrow\rangle\right)$$

At this point there are a few possible objections, two of which:

1. What Scott Aaronson said. $\overline{F}$'s conclusion in typical QM can be considered to have the appended proviso:
   "provided $\overline{W}$ doesn't measure me".
   Since $\overline{F}$ is entangled with $F$, any observations by $\overline{W}$ should update conclusions about $F$.
   $W$ can only obtain $\overline{F}$'s conclusions after hearing the result of a $\overline{W}$ measurement, the exact scenario that would invalidate $\overline{F}$'s reasoning
2. Can you actually consider $F$ and $\overline{F}$ to be in the Hardy paradox state? This is Bub's point I believe.
   If they actually cause measurement/macro outcomes they are not in such an entangled state, thus you cannot use:
   $$\frac{1}{\sqrt{3}}\left(|\overline{h}\downarrow\rangle + |\overline{t}\downarrow\rangle + |\overline{t}\uparrow\rangle\right)$$
   but only something like:
   $$|\overline{h}\downarrow\rangle$$
   And then there is no inconsistent conclusions.
   If the Hardy state is valid to use on them, then there isn't macroscopic events associated with them, thus no "if $\overline{F}$ got $\overline{t}$".

 

[Michael Price]

Where do you see that? In the Nature article the main result seems to be "Theorem 1. Any theory that satisfies assumptions (Q), (C), and (S) yields contradictory statements when applied to the Gedankenexperiment of Box 1."

(S) is the single-world assumption

You've hit the nail on the head, and there is little more that need be said. Only many worlds survives the triple-condition-test, because MW does not assume (S) and hence can retain (Q) and (C), both of which seem essential. Why the paper never mentions many worlds is strange and clearly intentional. Weird.

 

[stevendaryl]

You've hit the nail on the head, and there is little more that need be said. Only many worlds survives the triple-condition-test, because MW does not assume (S) and hence can retain (Q) and (C), both of which seem essential. Why the paper never mentions many worlds is strange and clearly intentional. Weird.

It does:

Theories that violate Assumption (S)
Although intuitive, (S) is not implied by the bare mathematical formalism of quantum mechanics. Among the theories that abandon the assumption are the “relative state formulation” and “many-worlds interpretations”6,45,46,47,48. According to the latter, any quantum measurement results in a branching into different “worlds”, in each of which one of the possible measurement outcomes occurs. Further developments and variations include the “many-minds interpretation”49,50 and the “parallel lives theory”51.

 

[Michael Price]

It does:

Theories that violate Assumption (S)
Although intuitive, (S) is not implied by the bare mathematical formalism of quantum mechanics. Among the theories that abandon the assumption are the “relative state formulation” and “many-worlds interpretations”6,45,46,47,48. According to the latter, any quantum measurement results in a branching into different “worlds”, in each of which one of the possible measurement outcomes occurs. Further developments and variations include the “many-minds interpretation”49,50 and the “parallel lives theory”51.

.
Thanks for the correction. Obviously I didn't pay as close attention as I thought.

 

[DarMM]

Only many worlds survives the triple-condition-test,

Not so, several other interpretations survive it, as the section on interpretations states. Also dropping inter-agent consistency or absolute holding to the Born rule doesn't seem any more essential to me than a single world.

For example Bohmian Mechanics, according to the paper, violates the Born rule in this situation. However it's a very extreme situation.

 

[Michael Price]

Not so, several other interpretations survive it, as the section on interpretations states. Also dropping inter-agent consistency or absolute holding to the Born rule doesn't seem any more essential to me than a single world.

For example Bohmian Mechanics, according to the paper, violates the Born rule in this situation. However it's a very extreme situation.

I don't quite get your example. I thought Louville's theorem holds in a classical phase space for Bohmian Mechanics, which implies standard probability theory? But then I have always have problems with BM as a 'proper' interpretation since it contains the Universal Wavefunction and hence MW.

 

[PeterDonis]

I have always have problems with BM as a 'proper' interpretation since it contains the Universal Wavefunction and hence MW.

I don't see the implication here. BM has the wave function, but it does not claim that the wave function is the complete state of the system. MW requires the latter.

 

[DarMM]

I don't quite get your example. I thought Louville's theorem holds in a classical phase space for Bohmian Mechanics, which implies standard probability theory?

Bohmian mechanics reproduces the Born rule via a Louville type theorem called quantum equilibrium. Others here are more knowledgeable on Bohmian Mechanics and can give more details, but it does reproduce the Born rule.

 

[eloheim]

Let's write down what each observer can reason about the others, based on their observations:

1. If $F$ measures +1/2, then it means that it is impossible that $\overline{F}$ got result $\overline{h}$. That's because there is no overlap between the final state and $|\overline{h}\rangle |\frac{+1}{2}\rangle$. So $F$ concludes that if he got +1/2, $\overline{F}$ must have gotten $\overline{t}$
2. If $\overline{W}$ measures $\overline{ok}$, then it means that is impossible that $F$ got -1/2. That's because there is no overlap between the final state and $|\overline{ok}\rangle |\frac{-1}{2}\rangle$. So $W$ concludes that if he got $\overline{ok}$ then $F$ must have gotten +1/2.

Hey on post #14 in this thread, I'm assuming that the $W$, in the last sentence of bullet point number 2, should be $\overline{W}$, right? I only point it out because the post is detailed and amazing, and I'm too dull at this stuff to know immediately that that's the case. Anyway great job!

 

[stevendaryl]

Hey on post #14 in this thread, I'm assuming that the $W$, in the last sentence of bullet point number 2, should be $\overline{W}$, right? I only point it out because the post is detailed and amazing, and I'm too dull at this stuff to know immediately that that's the case. Anyway great job!

Yes, you're right.

 

[Demystifier]

So it's not really Hermitian operators that are measurable. It's macroscopic facts about the world. You can try to be clever and set up an interaction between systems so that this or that value of the operator leads to this or that macroscopic fact about your measurement device. But there is no guarantee that you'll be able to do that for all possible operators.

I agree with this. But there is no any general principle that forbids to do that for all possible operators (except the superselection rules, which would require a separate discussion). In the absence of such a general principle, we say that any hermitian operator is measurable in principle.

 

[Strilanc]

Scott Aaronson did a good blog post explaining what he thinks (and what I think) is the hole in the argument: https://www.scottaaronson.com/blog/?p=3975

In order to perform the compound measurement described in the experiment, you have to uncompute Alice and Bob's thoughts, do the measurement on a single qubit, then recompute the thoughts. During the recomputation, when Alice or Bob is thinking "My state is X therefore the other state is Y", the reasoning is not valid because they no longer started in the 00+01+10 state. This breaks the "if I'm correctly certain they're correctly certain of X, then I'm certain of X" chain, because "they" are no longer correctly certain of X.

 

[DarMM]

In order to perform the compound measurement described in the experiment, you have to uncompute Alice and Bob's thoughts, do the measurement on a single qubit, then recompute the thoughts.

I understand Aaronson's reasoning, but I don't quite grasp this, probably just missing something.

Alice and Bob are the superobservers corresponding to $\overline{W}$ and $W$ in Frauchiger-Renner's Nature paper. Where does performing their two measurements require uncomputing their thoughts and measuring a single qubit. I would have thought for each of them independently they are simply measuring an alternate outcome basis for the respective labs under their control. However they themselves are left alone.

If you are referring to $\overline{F}$ and $F$ instead, even there is one uncomputing their thoughts? I would have thought for example that $W$ measures some strange observable $Q$ that places the $L$ lab containing $F$ into the $\{|okay\rangle,|fail\rangle\}$ basis. However I'm not sure how that corresponds to uncomputing $F$'s thoughts measuring a qubit and recomputing them. Again most likely I am missing something.

 

[Demystifier]

Scott Aaronson did a good blog post explaining what he thinks (and what I think) is the hole in the argument: https://www.scottaaronson.com/blog/?p=3975

In order to perform the compound measurement described in the experiment, you have to uncompute Alice and Bob's thoughts, do the measurement on a single qubit, then recompute the thoughts. During the recomputation, when Alice or Bob is thinking "My state is X therefore the other state is Y", the reasoning is not valid because they no longer started in the 00+01+10 state. This breaks the "if I'm correctly certain they're correctly certain of X, then I'm certain of X" chain, because "they" are no longer correctly certain of X.

Yes, I had similar objections on the earlier paper by the same authors. See e.g.
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"

I've also noted the relation with the Hardy state here
"Single-world interpretations... cannot be self-consistent"

 

[Demystifier]

For example Bohmian Mechanics, according to the paper, violates the Born rule in this situation.

What is at stake here is the Born rule in the subsystem. Is probability of a subsystem given by $|\psi|^2$?

In standard QM the answer is no, simply because there is no such thing as $\psi$ for a subsystem. A subsystem is not in a pure state $|\psi\rangle$, but in a mixed state $\rho\neq|\psi\rangle\langle\psi|$.

Surprisingly, the paper talks a lot about subsystems, but, as far as I can see, it never mentions mixed states. It only talks about pure states in coherent superpositions.

What can Bohmian mechanics say about subsystems? For simplicity, suppose that the full system consists of two particles with positions $x_1$ and $x_2$. The full wave function is $\Psi(x_1,x_2,t)$. But in Bohmian mechanics there are also trajectories $X_1(t)$, $X_2(t)$, so one can define the wave function of the first subsystem as
$$\psi_1(x_1,t)=\Psi(x_1,X_2(t),t)$$
This is called conditional wave function and it does not have an analog in standard QM. In general, this conditional wave function does not satisfy Schrodinger equation, despite the fact that $\Psi(x_1,x_2,t)$ does. Indeed, according to Bohmian mechanics, it is this violation of Schrodinger equation that creates the illusion of wave function collapse in a subsystem.

Finally, what about the Born rule for conditional wave function? Well the probability is (up to a normalization factor) equal to $|\psi_1(x_1,t)|^2$. This looks like a Born rule, but this is not really the standard Born rule given by $|\Psi(x_1,x_2,t)|^2$. Particularly interesting case is when $\Psi$ is an energy-eigenstate, in which case $|\Psi(x_1,x_2,t)|^2=|\Psi(x_1,x_2)|^2$ is time-independent. Despite this time-independence in standard QM, the Bohmian $|\psi_1(x_1,t)|^2$ depends on time.

 

[stevendaryl]

I don't understand

Yes, I had similar objections on the earlier paper by the same authors. See e.g.
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"
"Single-world interpretations... cannot be self-consistent"

I've also noted the relation with the Hardy state here
"Single-world interpretations... cannot be self-consistent"

I'm not sure I understand the objections. The states $|\overline{h}\rangle, |\overline{t}\rangle, |\overline{ok}\rangle, |\overline{fail}, |\frac{+1}{2}\rangle, |\frac{-1}{2}\rangle, |ok\rangle, |fail\rangle$ are states of the entire labs, not just the particle and/or coin that determined them. What's being measured by $\overline{W}$ and $W$ are the states of the whole labs.

Realistically, there shouldn't just be a single state corresponding to $|\overline{h}\rangle$, etc. By definition of a macroscopic object, there are many, many states consistent with a macroscopic description such as "Observer $\overline{F}$ sees a heads". I'm not sure whether this complication affects the conclusions, or not.

 

[stevendaryl]

What is at stake hear is the Born rule in the subsystem. Is probability of a subsystem given by $|\psi|^2$?

In standard QM the answer is no, simply because there is no such thing as $\psi$ for a subsystem. A subsystem is not in a pure state $|\psi\rangle$, but in a mixed state $\rho\neq|\psi\rangle\langle\psi|$.

When people talk about a mixed state, they mean two different things: (1) The mixed state resulting from ignorance about what the actual pure state is, (2) the mixed state that results from starting with a pure state for a composite system and tracing over all subsystems except the one of interest.

I don't see why it's necessary to consider mixed states (as opposed to superpositions) in this thought experiment.

 

[Demystifier]

What's being measured by $\overline{W}$ and $W$ are the states of the whole labs.

This measurement necessarily changes the state (of the lab). The issue is the following. Once you measure it, can you later unmeasure it and turn back into the initial state before measurement? I would say no, while the authors seem to saying yes.