To inaugurate this blog I want to talk about Daniela Frauchiger and Renato Renner’s polemical new paper, Single-world interpretations of quantum theory cannot be self-consistent. Since lots of people want to understand what the paper is saying, but do not want to go through its rather formal language, I thought it would be useful to present the argument here in a more friendly way.
To put the paper in context, it is better to first go through a bit of history.
Understanding unitary quantum mechanics is tough. The first serious attempt to do it only came in 1957, when Everett proposed the Many-Worlds interpretation. The mainstream position within the physics community was not to try to understand unitary quantum mechanics, but to modify it, through some ill-defined collapse rule, and some ill-defined prohibition against describing humans with quantum mechanics. But this solution has fallen out of favour nowadays, as experiments show that larger and larger physical systems do obey quantum mechanics, and very few people believe that collapse is a physical process. The most widely accepted interpretations nowadays postulate that the dynamics are fundamentally unitary, and that collapse only happens in the mind of the observer.
But this seems a weird position to be in, to assume the same dynamics as Many-Worlds, but to postulate that there is anyway a single world. You are bound to get into trouble. What sort of trouble is that? This is the question that the paper explores.
That you do get into trouble was first shown by Deutsch in his 1985 paper Quantum theory as a universal physical theory, where he presents a much improved version of Wigner’s friend gedankenexperiment (if you want to read something truly insane, take a look at Wigner’s original version). It goes like this:
Wigner is outside a perfectly isolated laboratory, and inside it there is a friend who is going to make a measurement on a qubit. Their initial state is
\[ \ket{\text{Wigner}}\ket{\text{friend}}\frac{\ket{0}+\ket{1}}{\sqrt2} \]
After the friend does his measurement, their state becomes
\[ \ket{\text{Wigner}}\frac{\ket{\text{friend}_0}\ket{0} + \ket{\text{friend}_1}\ket{1}}{\sqrt2} \]
At this point, the friend writes a note certifying that he has indeed done the measurement, but without revealing which outcome he has seen. The state becomes
\[ \ket{\text{Wigner}}\frac{\ket{\text{friend}_0}\ket{0} + \ket{\text{friend}_1}\ket{1}}{\sqrt2}\ket{\text{I did the measurement}} \]
Now Wigner undoes his friend’s measurement and applies a Hadamard on the qubit (i.e., rotates them to the Bell basis), mapping the state to
\[ \ket{\text{Wigner}}\ket{\text{friend}}\ket{0}\ket{\text{I did the measurement}} \]
Finally, Wigner and his friend can meet and discuss what they will get if they measure the qubit in the computational basis. Believing in Many-Worlds, Wigner says that they will see the result 0 with certainty. The friend is confused. His memory was erased by Wigner, and the only thing he has is this note in his own handwriting saying that he has definitely done the measurement. Believing in a single world, he deduces he was either in the state $\ket{\text{friend}_0}\ket{0}$ or $\ket{\text{friend}_1}\ket{1}$, and therefore that the qubit, after Wigner’s manipulations, is either in the state $\frac{\ket{0}+\ket{1}}{\sqrt2}$ or $\frac{\ket{0}-\ket{1}}{\sqrt2}$, and that the result of the measurement will be either 0 or 1 with equal probability.
So we have a contradiction, but not a very satisfactory one, as there isn’t an outcome that, if obtained, falsifies the single world theory (Many-Worlds, on the other hand, is falsified if the outcome is 1). The best one can do is repeat the experiment many times and say something like: I obtained N zeroes in a row, which means that the probability that Many-Worlds is correct is $1/(1+2^{-N})$, and the probability that the single world theory is correct is $1/(1+2^{N})$.
Can we strengthen this contradiction? This is one of the things Frauchiger and Renner want to do. Luckily, this strengthening can be done without going through their full argument, as a simpler scenario suffices.
Consider now two experimenters, Alice and Bob, that are perfectly isolated from each other but for a single qubit that both can access. The state of everyone starts as
\[ \ket{\text{Alice}}\frac{\ket{0}+\ket{1}}{\sqrt2}\ket{\text{Bob}} \]
and Alice makes a first measurement on the qubit, mapping the state to
\[ \frac{\ket{\text{Alice}_0}\ket{0}+\ket{\text{Alice}_1}\ket{1}}{\sqrt2}\ket{\text{Bob}} \]
Now focus on one of Alice’s copies, say Alice$_0$. If she believes in a single world, she believes that Bob will definitely see outcome 0 as well. But from Bob’s point of view both outcomes are still possible. If he goes on to do the experiment and sees outcome 1 it is over, the single world theory is falsified.
This argument has the obvious disadvantage of not being testable, as Alice$_0$ and Bob$_1$ will never meet, and therefore nobody will see the contradiction. Still, I find it an uncomfortable contradiction to have, even if hidden from view. And as far as I understand, this is all that Frauchiger and Renner have to say against Bohmian mechanics.
The full version of their argument is necessary to argue against a deeply personalistic single-world interpretation, where one would only demand a single world to exist for themselves, and allow everyone else to be in Many-Worlds. This would correspond to taking the point of view of Wigner in the first gedankenexperiment, or the point of view of Alice$_0$ in the second. As far as I’m aware nobody actually defends such an interpretation, but it does look similar to QBism to me.
To the argument, then. Their scenario is a double Wigner’s friend where we have two friends, F1 and F2, and two wigners, A and W. The gedankenexperiment starts with a quantum coin in a biased superposition of heads and tails:
\[ \frac1{\sqrt3}\ket{h} + \sqrt{\frac23}\ket{t} \]
At time t=0:10 F1 measures the coin in the computational basis, mapping the state to
\[ \frac1{\sqrt3}\ket{h}\ket{F1_h} + \sqrt{\frac23}\ket{t}\ket{F1_t} \]
To avoid clutter, I will redefine the degrees of freedom of this coin to be part of F1’s degrees of freedom, and write simply
\[ \frac1{\sqrt3}\ket{F1_h} + \sqrt{\frac23}\ket{F1_t} \]
Now, F1 prepares a qubit in the state $\ket{0}$ if she saw heads, or the state $\ket{+}$ if she saw tails, mapping the state to
\[ \frac1{\sqrt3}\ket{F1_h}\ket{0} + \sqrt{\frac23}\ket{F1_t}\ket{+} \]
F1 sends this qubit to F2, who measures it in the computational basis at time t=0:20, mapping the state to (I’m writing the state of the qubit inside F2’s state to avoid clutter, as before)
\[ \frac1{\sqrt3}\ket{F1_h}\ket{F2_0} + \frac1{\sqrt3}\ket{F1_t}\ket{F2_0} + \frac1{\sqrt3}\ket{F1_t}\ket{F2_1}\]
Note that the term in the superposition that has $\ket{F2_1}$ has also $\ket{F1_t}$, and no other term in the superposition has $\ket{F2_1}$. Based on that, F2 reasons: If there is a copy of F2 that sees 1 at t=0:20, there must be a copy of F1 that saw tail at t=0:10.
F1, on her side, knows that this is happening, and furthermore she knows that W will at time t=0:40 measure F2 in the basis \[\{\ket{F2_+},\ket{F2_-}\} = \left\{\frac{\ket{F2_0} + \ket{F2_1}}{\sqrt2},\frac{\ket{F2_0} – \ket{F2_1}}{\sqrt2}\right\}\]
On that basis, the current state reads
\[ \frac1{\sqrt6}\ket{F1_h}\ket{F2_+} + \frac1{\sqrt6}\ket{F1_h}\ket{F2_-} + \sqrt{\frac23}\ket{F1_t}\ket{F2_+} \]
Based on this, F1 reasons: If there is a copy of F1 that sees tail at t=0:10, there must be a copy of W that sees $\color{red} F2_+$ at t=0:40.
Now it is A’s turn to act. She measures at time t=0:30 the state of F1 in the basis
\[\{\ket{F1_+},\ket{F1_-}\} = \left\{\frac{\ket{F1_h} + \ket{F1_t}}{\sqrt2},\frac{\ket{F1_h} – \ket{F1_t}}{\sqrt2}\right\}\]
In this basis (and the computational basis for F2) the state of F1 and F2 is
\[ \frac2{\sqrt6}\ket{F1_+}\ket{F2_0} + \frac1{\sqrt6}\ket{F1_+}\ket{F2_1} – \frac1{\sqrt6}\ket{F1_-}\ket{F2_1} \]
Based on this state, A reasons: If there is a copy of A that sees – at t=0:30, there must be a copy of F2 that saw 1 at t=0:20.
Finally, Wigner acts. He measures at time t=0:40 the state of A and the state of F2, both in the superposition basis. The full state is, before the measurement (with F1 included within A)
\[ \frac3{\sqrt{12}}\ket{A_+}\ket{F2_+} + \frac1{\sqrt{12}}\ket{A_-}\ket{F2_+} + \frac1{\sqrt{12}}\ket{A_+}\ket{F2_-} – \frac1{\sqrt{12}}\ket{A_-}\ket{F2_-} \]
so Wigner obtains the result $A_-,F2_-$ with probability $1/12$. Let us assume he did so (otherwise we just repeat the experiment a few times, and this result will happen with exponentially high probability). Furthermore, we assume that Wigner is the superobserver for whom there is a single world, so there is only one copy of him. Collecting this statement together with the statements in red, we have:
- The only copy of Wigner sees $A_-,F2_-$ at t=0:40.
- If there is a copy of A that sees – at t=0:30, there must be a copy of F2 that saw 1 at t=0:20.
- If there is a copy of F2 that sees 1 at t=0:20, there must be a copy of F1 that saw tail at t=0:10.
- If there is a copy of F1 that sees tail at t=0:10, there must be a copy of W that sees $F2_+$ at t=0:40.
Following the chain of implications, we have
The only copy of Wigner sees $A_-,F2_-$ at t=0:40.
There is a copy of A that saw – at t=0:30.
There is a copy of F2 that saw 1 at t=0:20.
There is a copy of F1 that saw tail at t=0:10.
There is a copy of W that sees $F2_+$ at t=0:40.
Contradiction.
What should we conclude from this? Is this kind of reasoning valid? The discussions about this paper that I have witnessed have focussed on two questions: Are the red statements even valid, in isolation? Assuming that they are valid, is it legitimate to combine them in this way?
Instead of giving my own opinion, I’d like to state what different interpretations make of this argument.
Collapse models: I told you so.
Copenhagen (old style): Results of measurements must be described classically. If you try to describe them with quantum states you get nonsense.
Copenhagen (new style): There exist no facts of the world per se, there exist facts only relative to observers. It is meaningless to compare facts relative to different observers.
QBism: A measurement result is a personal experience of the agent who made the measurement. An agent can not use quantum mechanics to talk about another agent’s personal experience.
Bohmian mechanics: I don’t actually know what Bohmians make of this. But since Bohmians know about the surrealism of their trajectories, know that “empty” waves have an effect on the “real” waves, know that their solution to the measurement problem is no better than Many-Worlds’, and still find Bohmian mechanics compelling, I guess they will keep finding it compelling no matter what. In this point, I agree with Deutsch: pilot-wave theories are parallel-universes theories in a state of chronic denial.
What do you think?
Update: Rewrote the history paragraph, as it was just wrong. Thanks for Harvey Brown for pointing that out.
Update 2: Changed QBist statement to more accurately reflect the QBist’s point of view.
Congratulations on your first post! I hope that more will follow.
The red statements are indeed the more debatable parts of the arguments; it’s nice of you to highlight them :). Each of them, taken in isolation, seem like a perfectly fine statement about the global state of the system consisting of all observers. However, these statements apply at three different times, and I find it strange to combine them. If measurement is a physical process, why should we be allowed to conclude that there is a contradiction, when we are combining instantaneous facts about the (evolving) state of the system at three different times? It seems that no reasonable interpretation would actually follow this line of reasoning, although I am quite ignorant about Bohmian mechanics.
Thanks for the comment!
Strictly speaking you are correct, but I think one can perfectly well combine statements about the system at different times if one checks that they remain true under the specified time evolution (as trivially there will always be a time evolution that makes them false). And Frauchiger and Renner didn’t actually check that they remain true, so this is something they should do, at least in the Many-Worlds interpretation.
But more generally I think that Copenhagen’s blanket ban on combining statements is just obscurantism. About Bohmian mechanics, I just don’t know. I wish I could find a Bohmian to tell me what they think about this, I’m genuinely curious.
As an author of the paper, let me clarify that the statements we make in the paper *do* include the time when the values are observed.
For example, the first highlighted statement is actually, in its full version:
“If there is a copy of F2 that sees 1 at time t=0:20, there must be a copy of F1 that saw tail at time t=0:10.”
Similarly, the complete version of the second one starts with: “If there is a copy of F1 that sees tail at time t=0:10, …”
I guess that Mateus just shortened them to simplify the presentation. But indeed, without the timing information there would be some ambiguity.
Thanks for chiming in, Renato. I had replaced the exact time with the verbal tenses “saw” and “sees” as only the ordering is important, not the exact times. But that was clearly a bad idea, since people are getting confused by it, so I updated the post to include the time information.
But my point was that you did not mention the time evolution when making the statements. Since the evolution is trivial in statements 1,2, and 3, this needs to be done only for statement 4, that is, one needs to check that the unitary that is applied to F1 at time t=0:30 does not affect his prediction about what W will observe. It clearly doesn’t, at least in the Many-Worlds interpretation, but some crazy interpretations might say it does, I don’t know.
Thanks for the clarifying reply.
I have one other comment, which concerns your analysis of the Deutsch version of the Wigner’s friend gedankenexperiment. As you are writing, the contradiction one obtains from it is not a very satisfactory one, because it is only probabilistic. I would like to point to another important reason why this gedankenexperiment is not sufficient to rule out single-world theories in general.
The reason is that the analysis you are describing relies on “self-referencing”, i.e., it assumes that the friend can reason about his own quantum state. Such self-referencing (also known as “self-measurement”, see Section 4 of http://plato.stanford.edu/entries/qm-relational/) is explicitly forbidden by many interpretations of quantum mechanics (notably interpretations according to which a system’s state is defined only relative to an observer, e.g., QBism or Rovellis’ “Relational Quantum Mechanics”). Other interpretations (e.g., “new style Copenhagen”) do not forbid it explicitly, but are ambiguous about how one should deal with it.
These considerations forced us to “extend” Wigner’s Friend experiment to two friends (in the way described in our preprint). As one can easily verify, its analysis does not involve any self-referencing (i.e., each experimenter can make their predictions without reasoning about the quantum state of theirself).
I’m aware that they forbid it, but I don’t think this prohibition is defensible: it is just obscurantism.
But I get your point: by avoiding it you make your argument hit even people who take this prohibition seriously, so in this sense it does strengthen Deutsch’s argument.
Dear Mateus: thanks for the very clear and nice blog. I am a SUAC type of scientist (and a chemist by background) so I probably miss some subtleties. But in the first experiment I would guess that the paradox is solved de facto by making impossible to perform a Hadamard gate in the state of the friend without touching at the same time the state of the note. If I am not mistaken, following decoherence, it is not possible to perform coherent manipulations on a macro state that moreover has left some imprints on the environment, like writing a note. Even if I do not write what I saw, it is really a different me that emerges depending on the outcome of the first experiment.
Thanks =)
Performing a Hadamard in the state of the friend without touching the note is no more difficult than doing the Hadamard in the state of the friend in the first place. Both require an absurd level of control over extremely complex quantum systems (and the note can be replaced by a qubit).
This argument does require the assumption that it is in principle possible to such an experiment, or some analogous one (for example with a quantum computer taking the place of the friend). Denying this assumption is believing that the proper description is some sort of collapse model, and this is a very unpopular choice.
Mateus: Thank you for the reply.
As I see it, accepting that one can erase the memory of an observer (which basically implies there was no increase of entropy and no psychological time and lots of confusion) makes the whole idea of a contradiction no really that powerful or surprising. There is no contradiction for the external observer and the internal observer did not really work as a reliable observable – his brain was manipulated from the outside and he is in a state of total confusion.
But on the other hand, if “collapse” theories are not considered appropriate (or popular), how would one explain the final result if no Hadamard is performed and Wigner measures a single outcome that a priori had 50% of probabilities?
(I apologize if I reach the “dull” or annoying level. I understand we all have to do other stuff.)
If you wish the friend can make his prediction before Wigner erases his memory: regardless of the outcome he observed, he will predict that both final outcomes will happen with the same probability, and he will be proven wrong. He can also write down this prediction on the piece of paper, that will not be erased.
Well, your second question is exactly what this whole discussion is about: if you assume that there is no collapse, can you explain the gedankenexperiment with anything other than Many-Worlds?
It is unfortunate that the direct-action (transactional) theory has thus far been ignored by the mainstream, since it does provide real physical collapse that does not depend on the ill-defined concept of ‘the consciousness of an external observer”. See, for example: http://www.cambridge.org/9781108407212; and https://arxiv.org/abs/1709.09367; and for the general reader: http://www.worldscientific.com/worldscibooks/10.1142/p993. For why the unitary-only approach does not work as advertised, see, e.g.: https://arxiv.org/abs/1603.04845. Perhaps you might include reference to this in your post, for a complete picture of the relevant published literature on quantum interpretations? Best wishes, R. E. Kastner
To be on-topic, could you say what the transactional interpretation makes of the Frauchiger-Renner argument?
The transactional interpretation has collapse, so evades the inconsistency aspect of their argument. I’m just pointing out that collapse does not have to be a subjective thing, or something dependent on an external observing consciousness, which appears to be the usual assumption when considering collapse in this context.
I thought this was well-known no? At least with the more usual collapse models like GRW or CSL.
I was really responding to this statement: ” The mainstream position within the physics community was not to try to understand unitary quantum mechanics, but to modify it, through some ill-defined collapse rule, and some ill-defined prohibition against describing humans with quantum mechanics. But this solution has fallen out of favour nowadays, as experiments show that larger and larger physical systems do obey quantum mechanics, and very few people believe that collapse is a physical process.”
My point is that collapse in the transactional interpretation is neither ill-defined nor based on an ill-defined prohibition against describing humans with QM. So collapse can indeed be physical, well-defined, and not ad hoc (as in GRW-type approaches). This is pointed out in the references I provided in the first post. Here’s another way to understand the need for a new paradigm involving genuine physical collapse: https://www.sciencenews.org/blog/context/quantum-mysteries-dissolve-if-possibilities-are-realities
In this paragraph I was talking about the past, so the ill-defined collapse I was criticizing was Copenhagen’s. The ones from GRW and probably yours are well-defined, I have no problem with them.
But still, it is empirically true that “very few people believe that collapse is a physical process.”
Yes, but when one says that ‘very few people believe’ something, it’s usually taken for granted that such beliefs (or non-beliefs) are based on having taken into account the relevant information. That is not the case regarding the transactional picture, which is part of the peer-reviewed literature and yet continues to be disregarded by the ‘mainstream.’ This may be a holdover from a general skepticism about direct-action theories, which is also not valid, especially in view of Wheeler’s 2003 paper (with Wesley) Wesley, D. and Wheeler, J. A. (2003). “Towards an action-at-a-distance concept of spacetime,” In A. Ashtekar et al, eds. (2003). Revisiting the Foundations of Relativistic Physics: Festschrift in Honor of John Stachel, Boston Studies in the Philosophy and History of Science (Book 234), pp. 421-436. Kluwer Academic Publishers.
Since the argument about the thought experiment talks so extensively about facts at different moments in time, it would have been natural to also include the “Consistent Histories” reformulation (by Griffith, Gell-Mann, Hartle, Omnes, and others) of the Copenhagen rules of quantum mechanics in the description of what different interpretations make of this argument. This would have been interesting for two reasons: 1) it would have clarified whether the facts in the thought experiment even constitute a consistent history at all 2) if yes, then it should give the same conclusions as the normal Copenhagen rules. (This is at least what the literature on consistent histories claims. Would be nice to see this in practice.)
I didn’t add a Consistent Histories analysis of the gedankenexperiment because I’m mostly ignorant about it. As far as I understand it is just the Many-Worlds interpretation together with a baroque formalism for constructing the eponymous histories.
Thanks for answering me, and many more thanks for writing this blog. From what I read so far, I got the impression that I really like your way to present the material.
The “Consistent Histories” approach (or reformulation) is so consistent with the ideas behind the Copenhagen interpretation that it probably shouldn’t be regarded as a separate interpretation. The basis is still that you (have to) describe the experiment in everyday words which can be communicated (which meant using classical mechanics for Copenhagen). And you still have an explicit (generalisation of the Born) rule to assign probabilities to the possible outcomes of the experiments. Hence it is different from the Many-Worlds interpretation, which claims that probabilities would emerge by themselves from unitary evolution alone. And it basically inherits also most of the (really) fundamental problems of the Copenhagen interpretation. But at least its authors are honest with respect to this point.
A short summary of the consistent histories approach and a feeling for the clarity and honesty of it authors can be found in the 5 page Review of R. Omnes, THE INTERPRETATION OF QUANTUM MECHANICS by Robert B. Griffiths.
Let me be honest myself how much I really understand the consistent histories approach. In 1998, I had to endure a QM 1 course at university, and I didn’t manage to connect at all to QM. (I did get those spherical harmonics and Laguerre polynomials, operators acting on functions, commutativity, Hermitian vs. self-adjoint, and other mathematical techniques, but I couldn’t create a picture or film in my head of how to use this to describe nature. My favourite defence was to ask others to explain the Compton effect to me in terms of that stuff – or any other simple interaction between electrons and light which can be observed.) Occasional attempts to read material discussing interpretation of QM failed quite early, I couldn’t penetrate into the material and words at all. Around 2005, I read (or rather browsed) “Understanding Quantum Mechanics” by Roland Omnès, and it was the first time that I felt that the material was presented in a way that I would understand it, if I invested the time to work through it. It felt like “let me calculate and explain” as opposed to “don’t ask questions, nobody understands QM anyway”. Today, years later (and with experience in statistical optics as a basis for forming pictures and films or at least analogies in my head), I actually learned QM from various normal text books (which probably got significantly better, because of the recent interest in quantum computers, or at least I got better at finding good books), and I also read and understood Heisenberg’s, von Neumann’s and Schrödinger’s original explanations. Yesterday, I returned “Quantum Philosophy” by Roland Omnès to the library, which was nicely written as a philosophical text (with historical context and all that), but didn’t contain any calculations at all. If you really wanted to know technical details from me, I would have trouble to even write down the consistency conditions.
“Consistent histories” also evades the basic interpretational question of ‘what counts as a measurement?” For why “Complementarity” and the “Copenhagen Interpretation” fail as a realist interpretation of the formalism (i.e., just become instrumentalist accounts in which the formalism just tells us what phenomena to expect), see https://arxiv.org/abs/1601.07545. The same criticisms apply to so-called “QBism”, which could be called ‘QBism-Solipsism’ or QBS. (The latter applies because it prohibits you from asking questions about results of other observers’ measurements. Such prohibitions on what questions can be asked about what might be going on outside of our own experiences are hallmarks of the antirealist aspect of instrumentalism. And claims that QM ‘forces’ us into that position are completely without basis, since there is at least one realist alternative that is not at all ad hoc or pseudo-classical.)
Dear Ruth E. Kastner,
I see that you have done research concerning Griffiths approach in the past, and also argued against the claim that Many-Worlds interpretation would be able to proof that probabilities emerge by themselves. I also read about the transactional interpretation now. I started to read arxiv-1601.07545 “Beyond Complementarity” (which you recommended above), but got the impression that it is more concerned with Bohr’s position than with “Consistent Histories” or instrumentalist accounts more generally, so I stopped reading it. (I still have trouble penetrating into Bohr’s writing, Heisenberg, von Neumann and Schrödinger feel much clearer to me, and I doubt that your article would help me.)
There is nothing wrong with instrumentalistic accounts of quantum mechanics. Heisenberg justifies both the instrumentalistic position and completeness of his interpretation by explicitly allowing the possibility that a realistic theory could be possible beyond the Planck scale (which he frames in terms of energy) that might violate causality and time direction if required. He argues that completeness is independent of this, just like Newton’s mechanics is complete in its domain of application. With respect to the transactional interpretation, I have the impression that it tries indeed to be a realistic theory, but that the cost of it is that it can not say anything anymore about informal accounts in words from everyday language like the thought experiments with Wigner’s friends described above. (This is simply not the stuff that it talks about…) On the other hand, it probably could say something about my old defence “to ask others to explain the Compton effect to me in terms of that stuff”.
Maybe I found some better links for summaries of the “consistent histories” approach now:
http://quantum.phys.cmu.edu/CHS/histories.html
https://en.wikiquote.org/wiki/Consistent_histories
In the end, R. Omnès implicitly admits that the histories approach is instrumentalistic. At least that is how I interpret the following paragraph on page 233:
The only comment we wish to add concerns the choice of the properties entering into the practical use of histories. This choice was criticized because of its arbitrariness, but it can be very easily justified: a physicist needs to describe what he is doing in simple words. She needs to draw conclusions from observations with the help of logic. She wishes to put some of the steps in a form that can be directly investigated using the theory’s mathematical techniques. Which properties to choose? Only those most convenient for the purpose at hand. Many other descriptions may do as well, all different because of complementarity. Some of them will lead to the same conclusions and they are just as good. Others will be useless, not necessarily wrong but only idle talk of no consequence. Why bother? Asking questions about the existence of useless histories amounts to performing calculations that are of no help in solving a problem. They belong in the waste-paper basket.
And R. Omnès is also pretty clear that he is convinced that there is only a single world, even if the “consistent histories” doesn’t explain it, and cannot even disprove Many-Worlds. His defence is to admit that there is still a disagreement left between Reality and quantum theory, but that it would be hubris to expect otherwise. At least that is how I interpret the words on page 214:
… have reproached quantum physics for not explaining the existence of a unique state of events. It is true that quantum theory does not offer any mechanism or suggestion in that respect. This is, they say, the indelible sign of a flaw in the theory, … Those critics wish at all costs to see the universe conform to a mathematical law, down to the minutest details, and they certainly have reason to be frustrated.
…
I embrace, almost with prostration, the opposite thesis, the one proclaiming how marvelous, how wonderful it is to see the efforts of human beings to understand reality produce a theory fitting it so closely that they only disagree at the extreme confines. They must eventually diverge, though; otherwise Reality would lose its nature proper and identify itself with the timeless forms of the kingdom of signs, frozen in its own interpretation. No, science’s inability to account for the uniqueness of facts is not a flaw of some provisional theory; it is, on the contrary, the glaring mark of an unprecedented triumph. Never before has humanity gone so far in the conquest of principles reaching into the heart and the essence of things, but that are not the things themselves.
Since I have already comment excessively anyway, let me also add my thoughts about Frauchiger and Renner’s thought experiment. (So that I can stop commenting…) One of my troubles with the way Many-World tries to explain collapse (or world-splitting) is that the Schmidt decompostion only works for the tensor product of two spaces. If we have three or more factors (spaces) in the tensor product, then the decomposition is just not unique anymore. You might say it depends on the order in which you take the binary products if you want, but how do you decide which order to use? So I like the fact that the thought experiment works with sufficiently many different spaces to highlight the trouble this might create.
One point about which I am unsure in this thought experiment is: “Now, F1 prepares a qubit in the state |0⟩ if she saw heads, or the state |+⟩ if she saw tails, mapping the state to …” That could be a quite non-linear mapping, and it is unclear how one could implement this on a quantum computer. With respect to thinking about quantum computations, I find Craig Gidney’s approach to distinguish between “before-hand experience” description vs. “in-the-moment experience” descriptions enlightening:
https://chat.stackexchange.com/transcript/message/41324513#41324513
The thought experiment above was described as “in-the-moment experience”, but any real experiment should also allow a “before-hand experience” description. It would be interesting to see that description for the above thought experiment.
Dear gentzen,
You are quite right that using the Schmidt decomposition to derive the “worlds” in the Many-Worlds interpretation is unworkable. That is why this approach has been abandoned, and the way that worlds are derived in the contemporary literature is by using the decoherence basis (i.e. the worlds are the wavefunctions which are stable under decoherence). See e.g. arXiv:1111.2189.
As for the mapping you mentioned in the Frauchiger-Renner gendakenexperiment, it is actually linear, give by the unitary $U = \ket{h}\bra{h}\otimes I + \ket{t}\bra{t}\otimes H$
Of course there is nothing wrong with instrumentalism as a ‘shut up and calculate’ tactic for evading the conceptual and physical puzzles presented by QM. What is wrong is
elevating that evasion to a dogmatic prescription about how to ‘interpret’ QM–which is what we see from many instrumentalists. That’s the only thing I’ve been contesting.
And of course there is no need to retreat to the metaphysical/epistemological (as opposed to scientific/empirically grounded) choice to forbid exploration into what QM says about the nature of physical reality, since we already have a perfectly viable *physical* interpretation of the formalism (which is simply being ignored or, when engaged, subjected to spurious ‘straw man’ dismissals). See, e.g., https://arxiv.org/abs/1709.09367 .
(The interesting thing is that the above approach also explains why we get real energy transferred from one thing to another despite the fact that the field itself only has units of the square root of energy. You need the square of the field, as a physically real entity, to transfer energy. Any interpretation which disregards the squaring procedure of the Born Rule as a real physical process must portray energy being conveyed by an entity that has the wrong units and therefore cannot really convey the required energy.)
Re ‘decoherence basis’: there is no ‘decoherence basis’ allowing for the ‘split’ to occur in what amounts to a classically coherent world unless classicality is put in by hand at the very beginning. This is what is pointed out in https://arxiv.org/abs/1406.4126 .
‘Decoherence,’ as derived in a unitary-only account, is neither necessary nor sufficient to explain the existence of measurement results and the emergence of a classical–looking world. On the other hand, the transactional interpretation does this, while defining ‘measurement’ in unambiguous physical terms. And it needs to be reminded that previous ‘refutations’ of TI were no such thing, as is pointed out in the recent (post-2012) literature.
Best wishes,
RK
I should add that the new trend of asserting a metaphysical/epistemological claim that interpretations of QM ‘must diverge’ (i.e., that there can be no correct physical interpretation of the formalism) arises from an implicit actualist assumption. If you allow for physical possibility, then understanding of QM is perfectly capable of converging to a very nice account of the interplay between possibility and actuality. See, e.g.: https://www.sciencenews.org/blog/context/quantum-mysteries-dissolve-if-possibilities-are-realities
And of course the post-2012 transactional interpretation provides the specifics of how QM expresses this interplay, for anyone who is interested in those specifics.
Dear Renato Renner;
You posted here that your experiment is designed to avoid “self referencing”.
I quote:
“self-referencing…. assumes that the friend can reason about his own quantum state. Such self-referencing (also known as “self-measurement”, see Section 4 of http://plato.stanford.edu/entries/qm-relational/) is explicitly forbidden by many interpretations”
I don’t understand the equivalence that you stated here, between “self referencing” and “self measurement”.
Reading the article that you linked, I can see that “self measurement” is not completely possible.
In your experiment, as an example, your agent “F” might observe the randomness generator reading “heads”. She might suspect herself to be in a superposition, with another copy of her seeing “tails”. Or, alternatively, the generator might be broken. She has no way of finding out. She cannot “self measure”.
But she doesn’t need to.
You stated that all of the agents are aware of the full experimental setup. Agent F therefore knows that she was given a quantum randomess generator, she knows the probabilities of “heads” and “tails”, and she can therefore assume that she is in a superposition.
She can reason about herself. In other words, she can “self reference”.
And, based on that assumption, she can reason about the entire experiment, and come to the conclusion that “ok ok” is a possible result, and there is no contradiction, and quantum mechanics is not broken.
I simply cannot understand why an inability to “measure” yourself could be equivalent to an inability to think about yourself. Can you clarify if I’m missing something, please?
I could explain the error in this paper in several ways. But the entanglement of the two “labs” adds needless confusion.
So I will apply the same faulty logic to Schrodinger’s Cat.
Imagine the standard Schrodinger setup. But add a survey form inside the box. Immediately before we open the box, the cat must fill out the form.
Question one; “Are you alive?”
The dead cat won’t write anything. The live cat will write “YES!”
Question two; “What are your chances of meeting Schrodinger again?”
The live cat will write “One hundred percent!”
Question three; “What are Schrodinger’s chances of meeting you again?”
And here is the error in the paper: Schrodinger’s Cat would write “Fifty percent”. But Renner’s Cat would write “One hundred per cent”.
Indeed, this is the mistake in the paper. Note that in my presentation above I corrected it.
I’ve now written a more readable analysis of the Renner Frauchiger experiment.
And in this article, I don’t focus on nit-picking their obscure mistake. This article aims to educate. I take you through their experiment and I explain how Quantum Mechanics consistently deals with “nested observers”.
I hope this will be helpful to somebody.
http://byrden.com/quantum/Renner-explained.html