## Was The Many Words Interpretation Proven?

My friend Cristi Soica brought to my attention a provocative preprint by Daniela Frauchiger and Renato Renner: Single-world interpretations of quantum theory cannot be self-consistent which he discussed at his blog.

Here is the abstract:

"According to quantum theory, a measurement may have multiple possible outcomes. Single-world interpretations assert that, nevertheless, only one of them "really" occurs. Here we propose a gedankenexperiment where quantum theory is applied to model an experimenter who herself uses quantum theory. We find that, in such a scenario, no single-world interpretation can be logically consistent. This conclusion extends to deterministic hidden-variable theories, such as Bohmian mechanics, for they impose a single-world interpretation."

Now it is not everyday that someone makes a bold claim like this and since I do not know any of the authors, I first checked their credibility. In the Acknowledgement section they wrote:

"We would like to thank Alexia Auffeves, Serguei Beloussov, Hans Briegel, Lıdia del Rio, David Deutsch, Artur Ekert, Nicolas Gisin, Philippe Grangier, Thomas Muller, Sandu Popescu, Rudiger Schack, and Vlatko Vedral for discussing ideas that led to this work." which made me decide to spend the time to try to read and understand their argument.

The paper starts dry with pedantic abstractions which takes some effort to read and understand. On page 11 there is the first clue something is fishy:

"We note that the purpose of the experiment is to prove Theorem 1. We therefore do not have to worry about its technological feasibility at this point. We only need to ensure that none of the steps of the experiment are forbidden by the basic laws of physics."

The basis of the argument is an extended Wigner's friend experiment:

and in the box on page 12 at n=30 it states:

@ n:30 A measures F1 with respect to a basis {$$|ok\rangle_{F1}$$, $$|fail\rangle_{F1}$$} and records the outcome x ∈ {ok, fail}.

where for example

$$|ok\rangle_{F1} = \sqrt{1/2}|head\rangle_{F1} − \sqrt{1/2}|tail\rangle_{F1}$$

which is a superposition of macroscopic states!!!  You do not need read the preprint past this point.

This is the same as measuring Schrodinger's cat in a basis dead + alive.  So here is the million dollar question: is a dead + alive basis not feasible from a technology point of view, or is it forbidden by some basic law of physics?

A naive quantum purist would think that since everything is quantum, why deny a superposition of macroscopic states basis? The answer: superselection rules.

Here are the rules in the quantum game with superselection rules:
• every physical quantity is represented by a self-adjoint operator, but not every self-adjoint operator represents a physical quantity,
• every pure state is represented by a one dimensional subspace, but not every one-dimensional subspace represents a pure state.
For example nobody can prepare a nucleon in a superposition of proton and neutron states due to the conservation of the electric charge. But what is the root cause of the impossibility of quantum superposition for macroscopic states? Who cares? You cannot perform any experiment in which you measure in a basis of a superposition of macroscopic states.

Physics is an experimental science and the experiment used in the argument cannot be performed. As such the conclusion of the preprint is vacuous. It would be a completely different matter if such a superposition would be allowed by nature. Then we would be forced to accept the result of this paper.

Bohr was right in demanding the treatment of the measurement apparatus as a classical object. Still, how can superselection arise out of a pure quantum formalism. This means that there are distinct relevant Hilbert spaces which when embedded into a single Hilbert space exhibit superselection. Hmmm... Where have I seen this before? Welcome to the measurement problem solution proposal using Grothendieck group construction. The physical basis of this is quantum indeterminacy. Outcome randomness in quantum mechanics is not some undesirable feature which needs to be explained away, but an essential part of nature.

1. The {dead+alive, dead-alive} basis isn't strictly "forbidden". It just requires a vastly more accurate external measurement apparatus outside the cat that is sensitive to the very fine interference effects between the dead and alive states.

If the cat, an observer, chose the basis itself, as something she can collapse the wave vector to, it would mean that her reasoning is sloppy. Errors would occur but all of them could be blamed on the sloppy reasoning of the cat. Only the bases which decohere well enough etc. may be used for an accurate enough verification of the laws of QM.

At the end, these Swiss authors say that the "single world is inconsistent" because they think that the existence of many different observers' viewpoints is a contradiction. (The whole paper may be shortened to the previous sentence.) But it's not a cnotradiction, it's a defining feature of QM. QM has to be applied in a framework where one divides objects to observer+observed, effects to external events + observations. No accurate description is possible without that. Because the cut is clearly not given canonically and real-world observers will make cuts according to their observations, it's obvious that different inequivalent irreconcilable observers' perspective to describe the same Nature exist - but that's simply not a contradiction. Only a contradiction within a single fixed observer's viewpoint would be a real contradiction.

1. Only a contradiction within a single fixed observer's viewpoint would be a real contradiction. - agree

the {dead+alive, dead-alive} basis isn't strictly "forbidden". It just requires a vastly more accurate external measurement apparatus outside the cat that is sensitive to the very fine interference effects between the dead and alive states. - disagree

If QM is only about information (e.g QBism), there are no fine interference effects between macroscopic states. If QM has an ontic basis, then again there are no fine interference effects between macroscopic states. Anything in between, same thing. Either way, Bohr was right.

There are proposals on the table on how superselection rules emerge either as FAPP (for all practical purposes) like Zurek, or exact like mine. But in either case the preprint fails on page 12. Sure, it fails later too because "Only a contradiction within a single fixed observer's viewpoint would be a real contradiction.".

2. Lubos,

I am surprised by your take on the preprint. Let me quote some of your prior statements:

"Garrett Lisi's statement that the Coleman-Mandula theorem no longer holds because the cosmological constant is nonzero while Coleman and Mandula assumed the Poincaré symmetry instead of SO(4,1) is utterly naive. The cosmological constant is a tiny correction to the flat space, comparable to 10^{-120} in natural units, and the laws associated with the flat space must thus hold with the same accuracy"

"My point is that all these "crazy histories" are actually totally generic. Most of the histories that are "possible" or that occur with "at least slightly nonzero" probabilities are insane."

Are you talking out of both sides of your mouth, or did you have a change of heart on your prior points of view?

Are there crazy possibilities (which include superposition of macroscopic states)? Mathematically yes, physically no. I clearly state I am taking the physical point of view: "Physics is an experimental science and the experiment used in the argument cannot be performed."

Arguing from the physics point of view like you did against Lisi or MWI, or like I am arguing above ends the preprint validity on page 12. Arguing from the mathematical point of view like you did in your comment makes you read past page 12 to find the issue with the claim. However the paper make a very bold claim about the nature of reality and the standard which should be applied here is the physical one.

3. Sorry, Florin, but "If QM has an ontic basis, then again there are no fine interference effects between macroscopic states" is just bullšit.

There is no qualitative difference between large and small objects. All of them are quantum mechanical bound states of particles and all of them are subject to the laws of quantum mechanics. In particular, when studied accurately enough, all objects, large and small, imply quantum interference effects that may be measured in principle (although in practice, the largest objects where those may be verified are limited).

QM says that one has to pick an observer who treats himself classically. But that does *not* mean that the observed objects obeying the laws of QM can't contain macroscopic objects.

There can't be any strict "superselection rules" just because macroscopic objects arise. All such concepts of classical physics are always just approximations. They "heavily" fail for small and coherent enough physical systems but in principle, they always fail.

Your analogy with the cosmological constant is extremely sloppy and lame. But I am surely treating both cases in qualitatively the same case. In both cases, the tiny terms matter in principle, but they may also be neglected in an approximate theory, and a simplified approximate theory has to exist.

In the case of the C.C., it's the theory with the C.C. set to zero. In the case of the interference of macroscopic objects, the simplified theory is classical physics. Any viable theory - in both cases and all other cases - must also explain the simplified behavior in various limits where various effects are observed to be negligible. But that never means that the limit may "supersede" the full theory.

What's so hard about these basic issues?

2. Dear Florin,

It is impossible to isolate an object from the rest of the world. A box that could shield the gravitational or electric field of a particle would lead to violations of mass/energy or, respectively, charge conservation. If those fields cannot be shielded their effect will be perceived by any external observer even if he doesn't notice or care. For this reason "the Moon is not there if nobody looks at it" point of view is meaningless.

It is also interesting to notice that both MWI and Qbism deny the existence of well-defined experimental results. Instead of trying to explain the experiments they explain them away by inventing fantastic stories. MWI invents parallel universes so that a textbook example of logical contradiction (the electron did emit a photon in a magnetic field AND the electron did not emit a photon a magnetic field) is fine after all. Qbism is worse. All experimental results are a sort of qualia, an illusion in some observer's mind. No explanation is given for the reason that an observer has this sort of qualia, etc. It is unfortunate that such stories can be accepted as science.

The reason superposition cannot be observed is simple. They do not exist. They are a useful calculation tool, nothing else. Couder's oil-drop experiments provide prima-facie evidence that superpositions are not actualy required. If an oil drop can "interfere with itself" in a pure classical setup an electron should be able to do the same.

Andrei

1. Dear Andrei,

I am not clear: do you agree or not with the preprint?

2. I do not agree. As I have argued it is impossible to isolate objects from one another so the conditions required for the experiment cannot be achieved. You cannot have a perfectly isolated laboratory.

Andrei

3. Hi Florin,
Superselection rules about charge, baryon number etc are easy to understand. But can you elaborate on the superselection rules you are talking about?

1. Hi Kashyap,

In Zure's case superselection is an emergent phenomena, but in my proposal they are exact. Let's start at the meaning of superselection: you have a Hilbert space where some linear combination does not correspond to a physical system.

A Hilbert space has only one characteristics: its dimension. The physics is captured by the operator algebras. In my case I have different Hilbert spaces, each of them arising out of distinct GNS constructions. If you embed all those Hilbert spaces Hilbert space you get superselection. All those Hilbert spaces are linked by an equivalence relationship and the physical meaning of this equivalence is the random nature of QM. If QM is not inherently random, then you are in the realm of hidden variables and you have only one allowed GNS construction and one Hilbert space. Measurement means breaking the equivalence relationship.

Long story short, in my proposal I have many Hilbert spaces corresponding to GNS representations of the operator algebras right after measurement. Combine all those Hilbert spaces into a single one and you get QM with superselection rules.

2. Hi Kashyap,

Let me clarify one more thing. Exact or emergent FAPP (due to quantum darwinism and massive information copying), we o not need to split hairs on it to reject the preprint at page 12. In the text I stated: "Who cares?"

Why? Because the preprint claim is extremely strong and you need back it up with extremely solid evidence as well. In other words you need to adopt the physical point of view. Even if their contradiction would be valid, it would not matter if you cannot experimentally confirm the critical steps of the argument.

4. I am not entirely sure about your assessment of this paper. I would for instance take some issue with your superposition of a proton and neutron. The old nuclear gauge theory, going back to the original work of Yang and Mills, had the proton and neutron in a two state system.

If you have a large cavity and a nucleon is introduced you have no way of knowing if it is a proton or a neutron until you apply an electric field. This QED interaction splits the degeneracy of the nucleon state into proton or neutron. This was the basis of the old nuclear gauge theory, around 1950 or so, that was an SU(2) theory of mesons with nucleons in a two state system analogous to spin up or down, or proton-neutron.

It is of course the case you can't have a superposition of electric charge q = 0 or 1, but you can have a superposition of states for two particles with these charges if there is no electric field applied to split the degeneracy. Also protons and neutrons are not macroscopic states.

The superposition of macroscopic states is only impossible depending upon where you place the "cut off" between quantum and classical mechanics. Bohr insisted on the existence of a classical world in which classical information is communicated about quantum measurements. Heisenberg pointed out a problem with where in scale this cut happens, and the Schrodinger cat or Wigner's friend problem also illustrates this. We do have to provide a cut off, even if it is just a definition. To not do that puts observed and observer on the same footing and this is a sort of Godel loop; ultimately a quantum system is measuring itself or encoding quantum numbers with quantum numbers. From a pragmatic perspective that is too difficult a thicket to cut through. Further, if there is a Godel loop involved maybe the self-referential outcome is that you have to provide a cut off --- something we already knew.

LC

1. Dear Lawrence,

The example with proton/neutron is the textbook example for superselection precisely due to Y-M. See for example Chapter 5 on page 45 of Beltrametti and Casinelli.

The problem of the cut is genuine and the paper assumes there is no cut and everything is quantum all the way down. Here the opinions are split. My take on this is that nature is quantum all the way down but there are distinct Hilbert spaces which give rise to superselection. However my position is not universally accepted. My criticism of the paper is not based on it but on the fact that I need strong evidence for a strong claim.

At the root of the argument is the ability to have superposition between macroscopic states. A grandiose conclusion follows from an experimental impossible to be verified statement.

2. Feynman's original idea was that a particle zig-zagged everywhere. Feynman thought that an electron here was the same as an electron there and a positron over there and … . This was never realized in its full. However, suppose that in the early universe this was the state of affairs. Inflation sets in and isolates paths within O-regions bounded by the horizon, which with reheating and the expansion of the horizon defines the particles we see. These paths are “frozen out” from each other so we observe a great number of electrons, as well as each quark flavor with a color charge, photon and W or Z, gluon and so forth. This sounds a bit like a grand degeneracy breaking or superselection rule.

The question is whether this has something to do with the Gribov ambiguity. The large number of each type of elementary particle might reflect a large gauge redundancy on moduli. More parochially this might have some bearing on a superselection rule that gives rise to what we call classical mechanics or the macroscopic world. The einselection concept has a type of diagonal basis for the classical outcome, and maybe something of this sort is at work. There are potentially a lot of questions to ponder here.

I wrote this once and it disappeared. Trying again. LC

3. Lawrence,

I am not familiar with the subtleties of Feynman's path integrals. I know there are not well defined mathematically, but given their success there must be some solid math foundation waiting to be discovered.

Indeed, the question raised by superselection are open and I only have a starting point on the issue. The paradigm for my approach comes from Zurek, but I am improving on it.

On the paper itself, I don't want to turn into Lubos, but I cannot agree with its big claim based on an experimentally undecidable argument.

5. Dear Florin,
I agree the paper we are discussing is wrong.But I am still trying to understand problems with Macroscopic superposition.If all the world is quantum, in agreement with what Lubos says, then it can be only a matter of technology and experimental accuracy (and not a matter of principle) how large quantum systems you can superpose. With the super selection rules, are you drawing some line between classical and quantum domains? I hope I have not misunderstood the basic issue.

"If QM is only about information (e.g QBism), there are no fine interference effects between macroscopic states. If QM has an ontic basis, then again there are no fine interference effects between macroscopic states. Anything in between, same thing. Either way, Bohr was right."
This sounds as if belief in macro superposition depends on which QM interpretation you believe in.In that case the authors can say that they believe in MWI and hence macro superposition is justified!! That will be funny!

2. There are people like Gisin who think it is only a matter of time and money to perform interference experiments with trucks. I disagree with this. All is quantum does not mean all is one Hilbert space where everything is allowed. There are clear physical cases of superselection which represent a counterexample to this view.

This is why I stated: "A naive quantum purist..."

3. Hi Florin,
Thanks for the reply. I do not know enough about mathematics of Hilbert spaces to keep arguing. It seems that the whole field about interpretations of QM and Hilbert spaces has continued to be muddled for some 90 years!! However, I would like to see your opinion about the following.
(1) Penrose's suggestion that soon it may be possible to study superpositions of micro grams(or was it even more massive?) of objects.
(2) Wilczek's blog on quanta magazine where he seems to be arguing in favor of MWI.

4. Hi Kashyap,

Sorry for the delay, it is only now that I got a chance to reply.

On Penrose, I am not sure which proposal you are talking about. I know Penrose has some old proposal with mirrors in outer space. Is this the same thing? I did not look closely at this particular proposal and I cannot comment on it cogently.

On Wilczek, I do not follow his blog, do you have a link for his MWI arguments so I can take a look?

5. Hi Florin,
I just want to know how large is very large in your proposal to make Hilbert spaces different?
(1) Penrose proposal is in his old book on road to reality. His idea, if I remember right, is that the two superposed masses would be in different space locations, different gravity and thus when their wave function collapses you can tell!He was perhaps talking about micrograms or nanograms.
(2) Wilczek wrote a popular article recently in quanta magazine blog where he is hinting strongly that MWI may be consistent or at least may be verifiable by some experiments. I asked him what expts? But he has not replied! https://www.quantamagazine.org/20160428-entanglement-made-simple/

6. Hi Kashyap,

Thank you for the link. On Penrose I did not read his book, so I cannot comment. On Wilczek, I understand his subtle references in the text, but this is because I know what he is hinting about. To a non-expert his piece is not clear at all and you leave more confused than you started. Worse, you may draw the wrong conclusion.

His article looks more like his personal journey log in his quest to understand quantum mechanics than a well thought out exposition on the topic.

7. Hi Florin,
I found a more recent paper mentioned in an article by Penrose and Hameroff on consciousness! It mentions mirrors so it must be the same that you saw before. I suppose the experiment is not done yet otherwise it would have been in NY times!
Towards Quantum Superpositions of a Mirror

William Marshall, Christoph Simon, Roger Penrose, and Dik Bouwmeester
Phys. Rev. Lett. 91, 130401 – Published 23 September 2003; Erratum Phys. Rev. Lett. 91, 159903 (2003)

ABSTRACT
We propose an experiment for creating quantum superposition states involving of the order of 1014 atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.