I What Is the Frauchiger-Renner Theorem?

[A. Neumaier]

Any good sources for this?

Born discusses the issue in the introduction to

M. Born, Das Adiabatenprinzip in der Quantenmechanik, Z. Phys. 40 (1927), 167-192.

where he argues against Schroedinger's continuum view. Bohr's paper at the Solvay conference still says the same.

I haven't seen my claim explicitly researched on from a comparative historical point of view. But I am doing a historical study myself, and have plenty of detailed evidence, that will be the content of a paper to be finished later this year. Once one realizes what I wrote, many otherwise difficult to understand things get a straightforward sense.

(Unguru 1975).

Do you mean the following?

Unguru, S. (1975). On the need to rewrite the history of Greek mathematics. Archive for history of exact sciences, 15(1), 67-114.

 

[Auto-Didact]

Born discusses the issue in the introduction to

M. Born, Das Adiabatenprinzip in der Quantenmechanik, Z. Phys. 40 (1927), 167-192.

where he argues against Schroedinger's continuum view. Bohr's paper at the Solvay conference still says the same.

Thanks.

I haven't seen my claim explicitly researched on from a comparative historical point of view. But I am doing a historical study myself, and have plenty of detailed evidence, that will be the content of a paper to be finished later this year. Once one realizes what I wrote, many otherwise difficult to understand things get a straightforward sense.

Nice, can't wait to read it!

Do you mean the following?

Unguru, S. (1975). On the need to rewrite the history of Greek mathematics. Archive for history of exact sciences, 15(1), 67-114.

Yes. Stenlund's work is also pretty illuminating. I just noticed that I severly misjudged his age

 

[A. Neumaier]

Do you mean the following?
Unguru, S. (1975). On the need to rewrite the history of Greek mathematics. Archive for history of exact sciences, 15(1), 67-114.

Yes.

This is a critque on van der Waerden's (and others) way of writing about Greek mathematics. At the end is an editorial comment saying:
''A defense of his views will be published by Professor van der Waerden in a succeeding issue.''
Do you have the precise reference?

 

[Auto-Didact]

I think its:
B.L. Van der Waerden, “Defense of a ‘Shocking’ point of View”, A.H.E.S., 15, 1975, p.205.

There seems to be some controversy between mathematicians on this subject going back all the way to Hertz. Stenlund writes about this viewpoint and its counter viewpoint at length in his piece I linked above.

Prof. Van der Waerden's view is probably the more popular view among most mathematicians, practitioners of mathematics and teachers; it is difficult to imagine we could all be mistaken.

However, recalling the words of Feynman, there is sufficient reason to be careful to distinguish ones expertise in a subject from ones expertise on the history of that subject:

What I have just outlined is what I call a ‘physicist’s history of physics’, which is never correct… a sort of conventionalized myth-story that the physicist tell to their students, and those students tell to their students, and it is not necessarily related to actual historical development, which I do not really know!

Stenlund rejoins in this view, stating:

The normal interest in history of mathematics (among mathematicians who write history of mathematics) is interest in our mathematical heritage. This interest therefore tends to be conditioned by the contemporary situation and is not always an interest in what actually happened in mathematics of the past regardless of the contemporary situation. Only history in the latter sense deserves to be called history.$^1$ But history and heritage are often confused and one consequence of this kind of confusion is that the transformation of mathematics at the beginning of modern times is concealed. Features of modern mathematics are projected upon mathematics of the past, and the deep contrasts between ancient and modern mathematics are concealed. As a consequence, the nature of modern mathematics as symbolic mathematics is not understood as the new beginning of mathematics that it was.

1. Grattan-Guiness, I., 2004, The mathematics of the past: distinguishing its history from our heritage. Historia Mathematica, vol. 31, pp. 163-185.

 

[A. Neumaier]

B.L. Van der Waerden, “Defense of a ‘Shocking’ point of View”, A.H.E.S., 15, 1975, p.205.

I found instead:

Van der Waerden, Bartel L. "Defence of a “shocking” point of view." Archive for History of Exact Sciences 15.3 (1976): 199-210.

Prof. Van der Waerden's view is probably the more popular view among most mathematicians, practitioners of mathematics and teachers; it is difficult to imagine we could all be mistaken.

However, recalling the words of Feynman, there is sufficient reason to be careful to distinguish ones expertise in a subject from ones expertise on the history of that subject:

I am wholly behind van der Waerden. In addition to being an influential mathematician, he had strong historical expertise (many books, articles, editions of original sources), and his arguments given are cogent. The controversy is about the meaning of a piece of mathematics, and that cannot be decided by a historian without a good knowledge of mathematical culture. Whatever is said today about mathematics must be said in today's language to be properly understood, and this language is mathematical and formal, symbolical. Insisting on not doing this is like insisting that any proper history of the Babylonians must be stated in the Babylonian language.

Feynman's words are of course also true. there is simplified history just amounting to attribution from the heritage point of view. This is done in textbooks. Van der Waerden's history is far from such a superficial textbook history.

 

[A. Neumaier]

Nice, can't wait to read it!

If you send me an email, I'll send you a draft version (which should be ready end of February, I hope) in advance.

 

[Auto-Didact]

I appreciate the offer but as things currently stand I already have a long back log of work and reading to do; seeing February is just around the corner I should probably just wait patiently and read the finished manuscript.

I am wholly behind van der Waerden. In addition to being an influential mathematician, he had strong historical expertise (many books, articles, editions of original sources), and his arguments given are cogent. The controversy is about the meaning of a piece of mathematics, and that cannot be decided by a historian without a good knowledge of mathematical culture. Whatever is said today about mathematics must be said in today's language to be properly understood, and this language is mathematical and formal, symbolical. Insisting on not doing this is like insisting that any proper history of the Babylonians must be stated in the Babylonian language.

Feynman's words are of course also true. there is simplified history just amounting to attribution from the heritage point of view. This is done in textbooks. Van der Waerden's history is far from such a superficial textbook history.

I see your point and I don't question van der Waerden's expertise at all (I'm a huge fan of his two-spinor formalism). There was a time when I was as ardent about such matters as you seem to be, but I don't have such strong views anymore. In fact, now I am quite impartial to the matter in its full generality.

I think we are all the better when historians and philosophers intercede and try to contribute to the history/philosophy of science; it keeps us from segregating too far into separate domains and also keeps both parties sharp. I try to keep an open point of view and have learned at the least to take pleasure in reading such literature from any of the sides, especially when the debate gets fierce; sometimes, I hope that such old texts will be able to reveal to me somethings which have become lost over time.

By the way, Stephen Wolfram has a long list of articles on related topics over at his site; this one in particular, on Mathematical Notation: Past and Future is quite interesting.

 

[A. Neumaier]

seeing February is just around the corner I should probably just wait patiently and read the finished manuscript.

I had meant: The draft is likely to be finished end of February; the final version more like end of the year...

 

[entropy2information]

Frauchinger and Renner make this assumption:

If you want to hold on to the assumption that quantum theory is universally applicable, and that measurements have only a single outcome, then you’ve got to let go of the remaining assumption, that of consistency: The predictions made by different agents using quantum theory will not be contradictory.

https://www.quantamagazine.org/frau...where-our-views-of-reality-go-wrong-20181203/

Why do they make this assumption?

 

[RUTA]

Frauchinger and Renner make this assumption:
https://www.quantamagazine.org/frau...where-our-views-of-reality-go-wrong-20181203/

Why do they make this assumption?

They are following the conventional approach to Wigner's friend. That conventional approach makes inconsistent assumptions which I point out in post #142.

 

[bhobba]

A slight correction regarding Bohr's attitude.

The problem with Bohr was that he was quite philosophical and a notorious mumbler. I am pretty sure he was understandable if you thought hard enough, and I think his good friend Einstein understood what he was getting at, although he mostly did not agree, but I find him quite obscure. That Bohr understood QM is not in doubt - in fact better than Heisenberg who he corrected in his mistaken views about the uncertainty principle.

Personally, for what its worth, IMHO the only early pioneers whose views stand up to modern scrutiny is Dirac and maybe Einstein. I tend to shy away from what those of that era thought and look at more modern views like those Murray Gell-Mann who I find quite lucid. Just me.

Added Later
As an example people that know my views know I think far too much is made of EPR. I find Murray's take on it much more lucid than the usual, IMHO overly sensationalist, takes on it like Henry Stapp:


Trouble is its the views of Stapp etc that the pop-sci press seem to concentrate on.

Thanks
Bill

 

[DarMM]

I think Bub's papers are sort of a lucid modern version of Bohr. For instance replacing the "Classical" side of the cut with the "Boolean algebra" side of the cut, since that is the crucial point. One doesn't require actual Classical Physics on the observer's side of the cut, just an event space to which true/false can be assigned consistently since that is what is required to even define an outcome.

He does similarly for other concepts from Bohr.

 

[bhobba]

As far as the paper being discussed goes I find it exasperating when statements like the following are made - Quantum theory cannot consistently describe the use of itself. It may be true, but people are working on the issue of the classical/quantum cut when of course everything is quantum. Progress has been made and I think it could eventually be completely resolvable. Certainly statements like that confuse beginners and even some at the intermediate level no end and should, again IMHO, be more judiciously expressed - it really is quite sensationalist the way its worded.

I personally have no issue with QM can't satisfy the three claimed assumptions simultaneously and do not see what the fuss is about. Just me.

Thanks
Bill

 

[Auto-Didact]

Certainly statements like that confuse beginners and even some at the intermediate level no end and should, again IMHO, be more judiciously expressed

This argument tends to get made, often by professors, but just out of curiosity: how many actual beginners or intermediaries are chased away by things like this? I would presume very few if any.

 

[bhobba]

This argument tends to get made, often by professors, but just out of curiosity: how many actual beginners or intermediaries are chased away by things like this? I would presume very few if any.

I do not think any get chased away but rather myths about QM are reinforced:
https://arxiv.org/abs/quant-ph/0609163

It isn't until you read an advanced book like Ballentine that they are 'corrected', by which time making that shift is harder than it should be. It even happened with me. I shudder when I think about some of my early posts of many years ago where I actually believed particles are literally everywhere at once etc - and I had read Ballentine by then. Getting things straight in QM seems particularly hard - it took me quite a while to develop my current views.

Thanks
Bill

 

[A. Neumaier]

replacing the "Classical" side of the cut with the "Boolean algebra" side of the cut, since that is the crucial point.

Let me just observe that 99.99% of all quantum mechanics done in practice and theory uses classical logic. Everything in quantum mechanics is Boolean in spite of the non-Boolean talk in some of the foundational work

 

[RUTA]

I think Bub's papers are sort of a lucid modern version of Bohr. For instance replacing the "Classical" side of the cut with the "Boolean algebra" side of the cut, since that is the crucial point. One doesn't require actual Classical Physics on the observer's side of the cut, just an event space to which true/false can be assigned consistently since that is what is required to even define an outcome.

He does similarly for other concepts from Bohr.

My language about Boolean vs non-Boolean is from Bub — I must have referenced his forthcoming paper Two Dogmas Redux somewhere in this thread. Hardy’s axiomatizations also emphasize the difference between classical probability theory and quantum probability theory. Garg and Mermin’s paper (ref 10 in my Insight Why the Quantum) make a similar point.

 

[Auto-Didact]

I do not think any get chased away but rather myths about QM are reinforced:
https://arxiv.org/abs/quant-ph/0609163

If no one is getting chased away, then this isn't a real issue. People - laymen, specialists outside QT and non-orthodox believers alike - are frustrated with QM and they should be; no other canonical physical or mathematical theory, contemporary or historical, suffers from the incoherent picture presented.

The fact that there are alternative ontological formulations like BM and the TSVF are clear indications that QM need not be the final picture. A monograph that makes an excellent case for this is Dürr & Teufel, Bohmian Mechanics.

It isn't until you read an advanced book like Ballentine that they are 'corrected', by which time making that shift is harder than it should be. It even happened with me.

Apart from Ballentine's introduction of BM halfway in the book, his remarks on the superiority of the many body SE over the Hartree-Fock scheme and his review of Bell's theorem, I honestly don't see what is so great about this book.

As an introductory textbook it's definitely not the best and as a monograph on QM written for a postgraduate audience it's nice but nothing to write home about. When others first recommended it to me, I was expecting a 'MTW for QM'; one should be able to imagine the disappointment I had when I finished it.

 

[Auto-Didact]

Let me just observe that 99.99% of all quantum mechanics done in practice and theory uses classical logic. Everything in quantum mechanics is Boolean in spite of the non-Boolean talk in some of the foundational work

As an undergrad I flirted awhile with Birkhoff-von Neumann (BvN) quantum logic, espousing essentially the same points as Hilary Putnam made of its fundamental nature.

This was until I came to realize that BvN quantum logic wasn't actually a proper non-standard logic and that a 'real' quantum logic doesn't differ as much from standard logic as to make a big deal out of it.

 

[atyy]

The fact that there are alternative ontological formulations like BM and the TSVF are clear indications that QM need not be the final picture. A monograph that makes an excellent case for this is Dürr & Teufel, Bohmian Mechanics.

TVSF is basically a reformulation of Copenhagen, and does not attempt to solve the measurement problem.

 

[kurt101]

As an example people that know my views know I think far too much is made of EPR. I find Murray's take on it much more lucid than the usual, IMHO overly sensationalist, takes on it like Henry Stapp:

I am not sure I understood your comment about Gell-Mann being lucid, but in the video Gell-Mann sounds to me like an evangelist for his particular interpretation. It sounds like he is certain his is the right one.

In the video Murray Gell-Mann says the following about the EPR experiment:

People say loosely, crudely, wrongly that when you measure one of the photons, it does something to the other one. It doesn't. All it happens is that you measure the property of one and you learn the corresponding property of the other one. Now what these people who try to confuse us will say is yes but you choose which property and there by you choose what state the other one will be in. The point is that the different measurements say of linear polarization of one revealing the linear polarization of the other or circular polarity of one revealing the circular polarization of the other, those measurements are made on different branches of history, decoherent with each other, only one of which occurs. So its simply not true. And Einstein's point of view which was if some variable could ever be measured with certainty it should have some sort of physical reality and a definite value. That’s just wrong, that’s just in contradiction to Quantum Mechanics. When two variables at the same time don't commute any measurement of both of them would have to be carried out with one measurement on one branch of history and the other measurement on another branch of history and that's all there is to it. I presented that in my book, and of course Jim and I have argued for that and some other people, but it doesn't seem to get across. People are still mesmerized by this confusing language of non-locality.

In Gell-Mann's EPR interpretation, how are the branches of history selected? When are the two branches of history selected?

Whatever selects the two branches of history will have to know what angles the polarizers will be at when the entangled photons interact with them. This would have to be communicated/known instantly and acted on at the time of measurement or predicted and acted on by something that had complete knowledge of the future (i.e. knows the entire state of the universe and knows how the future will unfold). So I don't see how Gell-Mann is avoiding action at a distance. Although Gell-Mann does not use the phrasing of "selecting a history", I don't see how he avoids it and selecting a history seems like "action".

 

[atyy]

I am not sure I understood your comment about Gell-Mann being lucid, but in the video Gell-Mann sounds to me like an evangelist for his particular interpretation. It sounds like he is certain his is the right one.

That shows complete unity and lucidty on interpretations across the physics community - everyone agrees "quantum theory needs no interpretation - except mine" :)

My apologies to Fuchs and Peres for misappropriating their idea :) http://www.phy.pku.edu.cn/~qhcao/resources/class/QM/PTO000070.pdf

 

[bhobba]

In Gell-Mann's EPR interpretation, how are the branches of history selected? When are the two branches of history selected?

Probabilistically. Probability theory is silent on questions like that. You may not like it, but it is a legit position to take. In order for you to say whatever selects it you must show something does - which of course does not have to be the case - nature may simply be like that.

Thanks
Bill

 

[bhobba]

I honestly don't see what is so great about this book.

Well many have a different view. He develops QM from just 2 axioms - the dynamics comes from symmetry. I know of no other book that does that.

Thanks
Bill

 

[DarMM]

Let me just observe that 99.99% of all quantum mechanics done in practice and theory uses classical logic. Everything in quantum mechanics is Boolean in spite of the non-Boolean talk in some of the foundational work

True, what's the relation to Bub's point or are you just pointing that out? Or are you saying that demonstrates what Bohr and Bub are talking about?

To me Bub is speaking of the event algebra being Boolean at the macrolevel to permit a truth function having a clean definition and that's the real property of the non-Quantum side of the cut, i.e. you can assign true/false to macroevents even if they result from interaction with the microscopic.

I would have thought this is a separate issue as to whether you can use classical logic to reason about the mathematics of QM, unless I'm missing the point.

 

[DarMM]

I personally have no issue with QM can't satisfy the three claimed assumptions simultaneously and do not see what the fuss is about. Just me.

The original FR paper is quite odd the more I think about it. It has the superobservers model the observers as being in an entangled state, but has them reason about their outcomes in a way that ignores the implications of entanglement (i.e. ignores intervention sensitivity as Healey calls it).

 

[DarMM]

In Gell-Mann's EPR interpretation, how are the branches of history selected?

Gell-Mann's views are very similar to those in Omnés's book "The Interpretation of Quantum Mechanics", not surprising as they are both formulators of the decoherent histories approach. Omnés says that which actual branch occurs lies outside mathematical or scientific comprehension, i.e. it is a part of reality that seems like it cannot be captured mathematically.

 

[DarMM]

Okay a basic sketch of how Copenhagen seems to avoid Masanes's theorem in light of Bub's paper and what @atyy has been saying.

So basically the whole proof relies on Carol and Dan make measurements on an entangled pair. Then the hyperobservers Alice and Bob reversing everything the observers Carol and Dan do with the entangled pair and then perform the measurement themselves. This allows two things to happen:

1. A single run of this experiment has four outcomes, $a,b,c,d$, meaning there is a probability of a specific set of outcomes $P(a,b,c,d)$.
2. However any single pair of outcomes is a complete measurement of entangled pairs and thus obey the Bell inequality violating statistics.

The contradiction as such is that (1.) means each pair of measurements has probabilities that can be derived as marginals of $P(a,b,c,d)$, however being marginals means they can't have the correlations Quantum theory says they must from (2.). Hence a contradiction.

Or even briefer, the set up uses reversal to make a Bell experiment a marginal of a larger experiment. However the statistics of Bell experiments preclude the fact that they could be marginals.

So the rational thing to say here in the Copenhagen view is that it shows reversals are impossible. If Bell experiments cannot be marginals from their statistical properties and reversal allows you to make them marginals, what this really shows is that reversing measurements is indeed impossible, not anything about quantum theory being perspectival or there not being a single world. That is exactly what @atyy and Bub say. I'll discuss this in more detail now.

So how does Copenhagen get out of this?

Really as @atyy and Bub say, there is a quantum-classical cut. From Asher and Peres, this can be shifted a bit but not indefinitely. There are "sections" of the world that are Boolean in their logical properties as an objective fact, which is just a formalization of Bohr's idea of the classical side of the cut. If Carol and Dan are on the Boolean/Classical side then they have outcomes and you can model them Classically by putting them on the Classical side of the cut with yourself. If you decided to model them Quantum Mechanically anyway decoherence would grant them effective Boolean status (to the point of errors terms so small, it's questionable as to whether they have a physical meaning) and following Asher-Peres you could lower the cut, although due to decoherence it won't really matter for your predictions if you do or not.

So if they are on the classical side, in the original FR paper this means they'd have a chance of $\frac{1}{4}$ for the following superobserver measurements, either from being Boolean or via decoherence. In Masanes paper this means their outcomes cannot be reversed, so the superobservers cannot go on to obtain their $c,d$ outcomes and so there is no $P(a,b,c,d)$.

If they're on the Quantum side, they don't have any outcomes and so superposition is valid to use. In the FR paper this means the superobservers should assign a $\frac{1}{12}$ chance to their superobservable outcomes. In the Masanes version it means there are no $a,b$ outcomes from which to form $P(a,b,c,d)$.

In short, if they are classical there are no $c,d$ outcomes, if they are quantum there are no $a,b$ outcomes. So $P(a,b,c,d)$ doesn't exist in either scenario and thus there is no contradiction.

Bub has a paper here:
https://www.mdpi.com/1099-4300/17/11/7374 (PDF is freely accesible)

It contains other examples of errors you'll obtain if you attempt to view experiments as reversible. Bub essentially describes reverisble experiments being incompatible with the "intrinsic randomness" of QM, the fact that information loss must occur when you make a measurement. The only special thing about the Masanes scenario then is that it shows this line of reasoning extends to superobservers as well.

Another point might be the general unreasonableness of the concept of a superobserver, it might be like taking an arbitrarily large observer in General Relativity and ignoring the fact that as they get larger they'd distort the spacetime. However I haven't thought enough about that.

 

[A. Neumaier]

True, what's the relation to Bub's point or are you just pointing that out? Or are you saying that demonstrates what Bohr and Bub are talking about?

To me Bub is speaking of the event algebra being Boolean at the macrolevel to permit a truth function having a clean definition and that's the real property of the non-Quantum side of the cut, i.e. you can assign true/false to macroevents even if they result from interaction with the microscopic.

I would have thought this is a separate issue as to whether you can use classical logic to reason about the mathematics of QM, unless I'm missing the point.

Mathematically, one can of course assume whatever one wants, including Boolean or non-Boolean projectors, calling them events. But I think the correct way of thinking about these is as commutative and noncommutative, not as different kinds of logic. In quantum logic, one does not even have a reasonable ''implication'' operation, and almost nothing of logical interest can be done with noncommuting ''events'' in the quantum sense.

 

[DarMM]

Mathematically, one can of course assume whatever one wants, including Boolean or non-Boolean projectors, calling them events. But I think the correct way of thinking about these is as commutative and noncommutative, not as different kinds of logic. In quantum logic, one does not even have a reasonable ''implication'' operation, and almost nothing of logical interest can be done with noncommuting ''events'' in the quantum sense.

Okay I see what you mean. I think in a way this is Bub's point, that only when one has a commuting subalgebra do you have a Boolean structure that permits a truth function (as a two-valued homomorphism on the algebra) and hence that you have the concepts of outcomes and events that you can reason about logically. When looking at algebras that aren't Boolean you can't really view them as outcomes/events.

I think this is more a problem with my paraphrasing of him, in the sense that he means non-Boolean more as "not Boolean and thus not supporting the notion of events" rather than as a valid alternative logic, or such is what I took from his papers.

So I think the two of you might be saying basically the same thing, as he rejects there being non-Boolean events. This being part of the fact that he views quantum mechanics non-representationally.

He's not taking a Quantum Logic view if I have given that impression.

 

[DarMM]

I find Murray's take on it much more lucid than the usual, IMHO overly sensationalist, takes on it like Henry Stapp:

This has nothing to do with physics as such, but I love in those videos how Gell-Mann attempts a native like pronunciation at everybody's names, rather than just saying them in English phonetics. You can see he really loves languages.

 

[atyy]

Really as @atyy and Bub say, there is a quantum-classical cut. From Asher and Peres, this can be shifted a bit but not indefinitely.

The theory of indirect measurement, measurement ancilla etc is also about being able to shift the cut. But when the cut is shifted, what is real is also shifted.

One can see the different ideas of reality on each side of the cut in figure 1 of https://arxiv.org/abs/0706.1232 where the measurement outcomes are treated as real invariant events in the sense of classical special relativity, but the quantum state has no reality in that sense, eg. collapse is in a different plane of simultaneity in every Lorentz frame.

There is also a little bit of implicit (not explicit) discussion of the issue in https://arxiv.org/abs/quant-ph/0509061, where Einstein mentions the option to make Alice not real in an EPR experiment, to deny the nonlocality of quantum mechanics.

Another point might be the general unreasonableness of the concept of a superobserver, it might be like taking an arbitrarily large observer in General Relativity and ignoring the fact that as they get larger they'd distort the spacetime. However I haven't thought enough about that.

Interesting thought. So the relationship between BM (a full description of reality, where superobservers that can unitarily reverse measurements are allowed) and Copenhagen (measurements must be irreversible) is analogous to the relationship between full GR and the approximation with geodesics? There has been some speculation that the measurement problem has to be solved for quantum gravity to be solved (my very, very free reading of standard comments in string theory). Because Copenhagen QM needs an observer, and the observer needs a stable place to stand, that explains why quantum gravity has so far only been defined in AdS space, which provides a boundary for the observer to stand.

 

[DarMM]

@DarMM there is one additional question that I would like to discuss with you. Do we really need the undoing of measurement in the FR-Masanes-Leifer theorem? Or can we achieve the same just by preparing another copy of the system?

Let me explain. The basic common scheme in all these thought experiments is the following:
1. First prepare the system in the state $|\Psi\rangle$.
2. Then perform a measurement described by a unitary operation $U|\Psi\rangle$.
3. After that undo the measurement by acting with $V=U^{-1}$, which gives $VU|\Psi\rangle=|\Psi\rangle$.
4. Finally perform a new measurement $U'|\Psi\rangle$.

But for the sake of proving the theorem, it seems to me that we don't really need the step 3. Instead, we can perform:

3'. Prepare a new copy of the state $|\Psi\rangle$.

After that, 4. refers to this new copy. Note that $|\Psi\rangle$ is a known state, so the no-cloning theorem is not an obstacle for preparing a new copy in the same state.

The only problem I see with this is the following. The state $|\Psi\rangle$ is really something of the form
$$|\Psi\rangle=|\psi\rangle |{\rm detector \;\; ready}\rangle$$
which involves not only a simple state $|\psi\rangle$ of the measured system, but also a complex state $|{\rm detector \;\; ready}\rangle$ of the macroscopic detector. In practice it is very very hard to have a control under all microscopic details of the macroscopic detector, meaning that it is very very hard to prepare two identical copies of $|\Psi\rangle$. Nevertheless, it is not harder than performing the operation $V$, which also requires a control under all microscopic details of the macroscopic detector to ensure that $V$ is exactly the inverse of $U$. So for practical purposes, 3.' is as hard as 3. Yet the advantage of 3.' over 3. is that it is more intuitive conceptually.

So is there any reason why would theorem lose its power if we used 3'. instead of 3.?

Sorry for the late reply only got around to this now.

I would view that set up as a set of four measurements on the four particle state $|\Psi,\Psi\rangle$, a product state of two Bell pairs.

In that situation $E(a,d)$ and $E(b,c)$ would vanish and there is no contradiction with Fine's theorem.

Or so it seems to me.

 

[Demystifier]

Sorry for the late reply only got around to this now.

I would view that set up as a set of four measurements on the four particle state $|\Psi,\Psi\rangle$, a product state of two Bell pairs.

In that situation $E(a,d)$ and $E(b,c)$ would vanish and there is no contradiction with Fine's theorem.

Or so it seems to me.

Interesting argument, but I disagree because I wouldn't say that $E(a,d)$ and $E(b,c)$ would vanish. For definiteness, let me concentrate on $E(a,d)$. Clearly, it does not vanish if $a$ and $d$ are measured on the same copy of $|\Psi\rangle$. In the original version of the thought experiment, the non-vanishing $E(a,d)$ corresponds to an experimental procedure in which $a$ and $d$ are measured without undoing any of the measurements. It is only $corr(a,d)$ (which is different from $E(a,d)$) that involves undoing of measurements.

 

[DarMM]

Interesting argument, but I disagree because I wouldn't say that $E(a,d)$ and $E(b,c)$ would vanish. For definiteness, let me concentrate on $E(a,d)$. Clearly, it does not vanish if $a$ and $d$ are measured on the same copy of $|\Psi\rangle$. In the original version of the thought experiment, the non-vanishing $E(a,d)$ corresponds to an experimental procedure in which $a$ and $d$ are measured without undoing any of the measurements. It is only $corr(a,d)$ (which is different from $E(a,d)$) that involves undoing of measurements.

Sorry yes, I should say $corr(a,d)$.
$E(a,d)$ being the Bell correlations with those same angles $a$ and $d$, which would be $corr(a,d)$'s numerical value if you believe in a interpretation satisfying Masanes's conditions.

So let me be more clear.

$corr(a,d)$ in Masanes's set up would have the value $E(a,d)$ if you believe in an interpretation satisfying his conditions. It doesn't have to in all interpretations as we have already discussed, Bohmian Mechanics and Retrocausal theories could have $corr(a,d) \neq E(a,d)$. It is the fact that $corr(a,d) = E(a,d)$ that ultimately leads to the contradiction with Fine's theorem.

In the version you propose $a,d$ are measurements on separate Bell pairs, not a measurement on the same Bell pair after one has been measurement reversed. Thus $corr(a,d) = 0$ due to it being product state and hence there is no contradiction with Fine's theorem.

 

[Demystifier]

In the version you propose $a,d$ are measurements on separate Bell pairs, not a measurement on the same Bell pair after one has been measurement reversed. Thus $corr(a,d) = 0$ due to it being product state and hence there is no contradiction with Fine's theorem.

Fine, but then I think that $corr(a,d) = 0$ also in the Masanes's version. In particular, $corr(a,d) = 0$ is compatible with Eq. (31). Is there anything in the paper that contradicts my claim that $corr(a,d) = 0$ in the Masanes's setup?

 

[DarMM]

Fine, but then I think that $corr(a,d) = 0$ also in the Masanes's version. In particular, $corr(a,d) = 0$ is compatible with Eq. (31). Is there anything in the paper that contradicts my claim that $corr(a,d) = 0$ in the Masanes's setup?

Once Alice has reversed Carol's measurement, then the entanglement between the two photons is restored and thus Alice's measurement on the first photon and Dan's measurement on the second photon proceed as if Carol hadn't done anything, thus it is a typical Bell measurement and $corr(a,d) = E(a,d) = -cos(a - d)$.

This is unlike your case where Alice is performing a measurement on the first photon of a separate pair to Dan rather than the first photon of the same pair and thus you'd expect no correlation.

 

[Demystifier]

Once Alice has reversed Carol's measurement, then the entanglement between the two photons is restored and thus Alice's measurement on the first photon and Dan's measurement on the second photon proceed as if Carol hadn't done anything, thus it is a typical Bell measurement and $corr(a,d) = E(a,d) = -cos(a - d)$.

But we agreed that $corr(i,j) \neq E(i,j)$ for some $i,j$. So if $corr(a,d) = E(a,d)$, then for which $i,j$ do we have $corr(i,j) \neq E(i,j)$?

 

[DarMM]

But we agreed that $corr(i,j) \neq E(i,j)$ for some $i,j$. So if $corr(a,d) = E(a,d)$, then for which $i,j$ do we have $corr(i,j) \neq E(i,j)$?

$corr(i,j) \neq E(i,j)$ for some $i,j$ only for interpretations breaking one of Masanes's assumptions.

 

[Demystifier]

$corr(i,j) \neq E(i,j)$ for some $i,j$ only for interpretations breaking one of Masanes's assumptions.

Fine, so let us consider one such interpretation. For definiteness, let it be Bohmian mechanics. Then for which $i,j$ do we have $corr(i,j) \neq E(i,j)$?

 

[DarMM]

Fine, so let us consider one such interpretation. For definiteness, let it be Bohmian mechanics. Then for which $i,j$ do we have $corr(i,j) \neq E(i,j)$?

I don't know, I don't know Bohmian Mechanics well enough to carry out the computation. This paper here: https://arxiv.org/abs/1809.08070, shows how it avoids the original Frauchiger-Renner argument. Probably a similar calculation will show what occurs in Masanes's version, an empty wave comes along and causes $corr(i,j) \neq E(i,j)$ for some $i,j$.

However I don't think it matters because Bohmian Mechanics doesn't obey the assumptions of the theorem and thus isn't susceptible to it. It's not a theorem that shows anything about Bohmian Mechanics.

What it does counter are views like those of Healey himself (which is why Healey is concerned with it), Cutless Objective Copenhagen views, i.e. views that want QM to be an objective generalized probability calculus and no more.

 

[DarMM]

Hold the phone!

I was just reading this paper here:
https://arxiv.org/pdf/1901.10331.pdf

Which agrees with you that $corr(b,c) = 0$ for Alice's frame (and similar at least one vanishes for every frame) and that no real contradiction is reached even for views like Healey's (which would mean Healey is wrong about his own incorrectness!)

I'd be interested to hear your thoughts.

If that paper is valid, then my original post could be modified to
"Summary of Frauchiger-Renner: Don't bother!"

EDIT:
From a proper read of their paper they basically say once Carol obtains a result, the $b$ result will be correlated with it via the normal predictions for a Bell pair $E(c,b) = -cos(c - b)$.

However once you reverse the measurement, you restore the first particle back to its original state and could result in any value upon Alice's $a$ measurement. This reversal then decouples the value of $b$ from the value of $c$ and thus $E(c,b) = 0$, because for predicting $b$ it is as if $c$ never occurred.

Similarly for $E(a,d)$. Thus there is no contradiction with Fine's theorem.

This seems pretty valid to me and would render Masanes's result fairly powerless.

Open to correction though.

 

[Demystifier]

@DarMM It seems interesting, but I need some time to study it in detail.

 

[DarMM]

No worries. In short I think it validates your example. If you totally reverse the measurement it is like preparing a new state because you've completely undone any effects. So the event $c$ becomes completely detached from the event $b$ and similarly $d$ from $a$. Hence $E(b,c) = E(a,d) = 0$

 

[Demystifier]

No worries. In short I think it validates your example. If you totally reverse the measurement it is like preparing a new state because you've completely undone any effects. So the event $c$ becomes completely detached from the event $b$ and similarly $d$ from $a$. Hence $E(b,c) = E(a,d) = 0$

Did you mean $corr(b,c) = corr(a,d) = 0$?

 

[DarMM]

Ha! Sorry, yes indeed $corr(b,c) = corr(a,d) = 0$.

The papers themselves aren't very careful in making that distinction in their notation just to warn you.

 

[Demystifier]

Ha! Sorry, yes indeed $corr(b,c) = corr(a,d) = 0$.

So, whatever the Masanes theorem proves, the same thing can also be proved without undoing measurements, by using two copies of the state. Do we agree now?

 

[DarMM]

Yes and I think that means Masanes proves very little.

 

[Demystifier]

Yes and I think that means Masanes proves very little.

Yes, I have concluded it already in #44, while my later arguments only served to refine that conclusion. Thank you very much for the discussion, without you I would never understood all that.

 

[Demystifier]

The final summary:

What do the Frauchiger-Renner-Masanes-Leifer-Healey (FRMLH) theorems actually prove?

They just prove contextuality, that is the already known fact that the process of measurement can change the properties of the system.