The significance and implications of a recent extension of Wigner’s friend thought experiment has been discussed and debated. The main aim of this online workshop is to help settle the controversial issues related to the suggested experiment.
Workshop Date: Sunday, October 21, 2018 to Wednesday, October 31, 2018
Advisory Board: Lajos Diósi, Arthur Fine, Gordon N. Fleming, Olival Freire Jr., Sheldon Goldstein, Robert B. Griffiths, Hans Halvorson, Richard A. Healey, Basil J. Hiley, Don Howard, Peter J. Lewis, Roger Penrose, and Maximilian Schlosshauer.
Based on the successful previous workshops, this online workshop will be more self-organized. Every participant, after logging in, may create a topic in the workshop forum on his own, which gives a concise introduction to his ideas to be discussed. Then other participants can leave comments and participate in the discussions by text chat in the forum.
All IJQF members are welcome.
Is there an inconsistent friend?
October 22, 2018 at 8:17 am #5198
I think the answer may be negative.
First, Tony in his 2017 FoP paper (p.667), as well as Baumann, Hansen and Wolf in their 2016 arxiv paper, pointed out a loophole in Frauchiger and Renner’s argument; they used the collapse postulate in SQM inconsistently.
Next, Richard in his recent FoP paper further shows that if consistently applying QM without the collapse postulate, then there will be no contradiction, see Eq. (19) and relevant analysis there.
Then, how about Jeff’s argument in his forthcoming SHPMP paper (see his analysis below Eq. (4) in the paper)? I think this does not contradict Richard’s analysis. Jeff assumed that all relevant non-commutable observables have precise values simultaneously. Thus it is not unexpected that he could derive a contradiction, which is consistent with the KG theorem. But this does not mean that there is inconsistency from any single observer’s view, including Wigner’s view. Thus Jeff’s analysis does not support Frauchiger and Renner’s conclusion that there is an inconsistent friend (see also Matt’s paper in Nature Physics).
Finally, it seems to me that Richard’s result about the Limits of Objectivity is not valid. This result is derived from the third argument in his paper. I think the argument is based on the implicit assumption of locality, like Bell’s theorem, and one should drop this locality assumption, not the objectivity of outcomes.
Comments are welcome!October 24, 2018 at 10:49 am #5199Nikolay L. ChuprikovParticipant
I would make one comment regarding the following statement in Abstract of the article “Quantum theory cannot consistently describe the use of itself” by Daniela Frauchiger and Renato Renner, arXiv:1604.07422v2:
“Analyzing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty. The agents’ conclusions, although all derived within quantum theory, are thus inconsistent.”
However, in my opinion, the conclusions of these agents were derived contrary to quantum theory, since this theory does not allow any conclusions to be drawn on the basis of a single measurement result. Strictly speaking, one can speak about the properties of a quantum system only after measurements have been carried out in an infinite set of identical experiments – all the predictions of quantum theory concern quantum ensembles!
I hope that this comment is true and relevant here.
Nikolay ChuprikovOctober 24, 2018 at 3:41 pm #5201
Dear Editor: Should I start a new topic to address the measurement problem, which is what is being illustrated by the Wigner’s Friends scenario? In particular, we don’t encounter a Wigner’s Friend dilemma in the first place if we have a means of delineating, in physical terms, what constitutes ‘measurement’ (where that is described by von Neumann’s Process 1 non-unitary transition) One can do so in the transactional interpretation, as discussed in these publications in IJQF: https://www.ijqf.org/archives/4398 and https://www.ijqf.org/archives/4871
The above analysis shows that the measurement transition will occur with overwhelmingly high probability before the systems involved get to the fully macroscopic level of Geiger counters and cats.
The community has been widely skeptical of TI, primarily because of Maudlin’s claimed refutation of it in 1996. However, that objection is fully nullified at the relativistic level (see https://arxiv.org/abs/1610.04609). Another reason for skepticism has been the stigma attached to the ‘absorber’ theory since Wheeler and Feynman turned away from it in the mid-20th century. What is little known is that Wheeler was resurrecting the absorber theory in 2003 (Wesley, D. and Wheeler, J. A., “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)October 25, 2018 at 12:58 am #5204
Thanks for your comments, Nikolay.October 25, 2018 at 12:58 am #5205
Yes, Ruth. You may start a new topic to address the measurement problem.October 25, 2018 at 7:20 pm #5211
I would just comment here that Brukner’s formulation of the measurement problem presupposes an epistemic interpretation of the quantum state relative to a particular observer. So his analysis and conclusions do not apply to cases in which the quantum state ontologically refers. In particular, he concludes that facts are necessarily observer-dependent, but that appears to be an inevitable result of the starting assumption, and would not necessarily follow from an ontic interpretation of the quantum state.October 25, 2018 at 9:07 pm #5213
” it seems to me that Richard’s result about the Limits of Objectivity is not valid. This result is derived from the third argument in his paper. I think the argument is based on the implicit assumption of locality, like Bell’s theorem, and one should drop this locality assumption, not the objectivity of outcomes.”
Where do you think this assumption is made in the third argument discussed in my paper? In formulating the argument I was concerned to make no such assumption.
RichardOctober 26, 2018 at 3:28 am #5215
I think there are two concerns about your third argument. The first is that in order to derive the Bell inequality (31), one needs a locality assumption for the factorization, e.g. of the term corr(c,d), which is the same as that in the original Bell inequality. The second concern is that in your thought experiment, it seems that the two terms corr(b, c) and corr(a, d) in (31) do not exist. The reason is that the measurements of Alice and Bob undo the measurements of Carol and Dan, and thus when Alice and Bob have obtained the results a and b, the other two results c and d already disappeared. In other words, c and d do not exist in any device or the memories of Carol and Dan after the undo procedure; they are erased by the undo procedure.
Maybe my analysis is not right. I would like to know what you think about these two concerns. Thanks!
ShanOctober 26, 2018 at 4:10 pm #5217
As stated in the first sentence of the paragraph in which equation (31) appears, it is a central assumption of this third argument that every spin measurement performed by A,B,C and D has a definite, physical outcome. Consistent with that assumption, the measurements by A, B destroy all
of C’s and D’s definite, physical outcomes. So none of A,B,C,D can
what all these definite, physical outcomes were: they all objectively occur (at various spacetime locations), even though they are not all intersubjectively knowable by anyone. Objectivity should not to be equated with intersubjective knowability here—that would confuse metaphysics with epistemology.
As stated in the last sentence of the same paragraph, inequality (31) is not derived using any locality assumption. As Arthur Fine showed in the referenced publication, (31) is a consequence of the existence of a joint distribution of values of variables representing the (assumed) definite physical outcomes of the spin measurement performed by A,B,C and D. If all those values exist in each run of the experiment, then their statistical distribution in many runs of the experiment must conform to (31). This is true without assuming anything like Bell’s Local Causality, and independent of any causal hypotheses as to how these outcomes were produced.October 27, 2018 at 5:40 am #5218
This is an interesting situation: assessments of the bearing and validity of the FR proof greatly depend on what quantum theory itself is taken to be. For example, Editor has referred to two different forms of QT:
(1) QT with collapse postulate — call it “QTCP”
(2) QT without collapse postulate — call it “QTNCP”
…and has noted, based on arguments in the literature so far, that inferences about the force of the proof depend on whether one is invoking (1) or (2).
But should consideration of the issues in play be limited to these choices? Of course, historically, ‘collapse’ was only a postulate, but that does not mean that one is merely helping oneself to a desired postulate when one supposes that measurements actually do have single outcomes (independently of epistemic considerations). That is, Nature may indeed yield measurement outcomes. I think this is one of the points Richard has been making.
So I would respectfully add that an important third alternative form of QT is
(3) QTC — that is, quantum theory with real collapse, not just a postulate to that effect. (Such a possibility is generally dismissed, perhaps based on the ad hoc nature of the ‘spontaneous collapse’ theories, but of course there is another approach that does not make ad hoc changes to the theory but uses the direct-action theory of fields to explicitly derive non-unitary processes heralding measurement–that is the transactional picture, which remains perfectly viable. As I’ve noted in another thread here, under TI we cure the Schrodinger’s Cat paradox, so we never have to get to the point whether Wigner and his friend disagree about what is the case–however fun it might be to explore perplexing implications arising from that hypothetical scenario.)
Asher Peres famously said “Unperformed measurements have no results.” Under formulation (2), even performed measurements have no results. More precisely, in unitary-only quantum theory, there is no distinct class of interactions that constitute ‘measurement’–so there are neither measurements nor results of measurements. There are just unitary interactions. (And the outstanding problem under (2) is trying to explain why ‘observers’ like ourselves see definite results if the theory says there aren’t any. Decoherence arguments don’t succeed, as I and others have noted in the literature–refs on request).
Under (1), one has to to help oneself to the idea that measurements have results, with no theoretical basis for that, since ‘measurement’ is not defined therein either. That was the original form of quantum theory and it is what drove von Neumann to appeal to the consciousness of an ‘external’ observer, where ‘external’ can never be defined (that is the Heisenberg Cut of course).
Only under a form of (3) which defines physically what is meant by ‘measurement’ can one meaningfully say that performed measurements have results–because one can say what ‘measurement’ is and why they produce results.
So once again, the basic problem is that ‘measurement’ remains ill-defined in conventional ways of talking about and formulating quantum theory (those that only recognize (1) and (2)). Only in a physics that defines what ‘measurement’ is and provides a physical reason for non-unitarity (rather than just postulating it) can one meaningfully assert that measurements have results. Perhaps this conundrum over the implications of the Wigner’s Friend Paradox (which need not arise at all in option (3)) is a good time to step back and take a critical look at convention?October 27, 2018 at 8:37 am #5223
Thanks for your kind explanation!
I understand that the inequality (31) is derived from the hidden variable assumption in Fine’s paper. But the statistical correlations between pairs of *actual experimental outcomes* does not necessarily satisfy the inequality. It is the assumption that these outcomes directly reflect the values of the *measured observables* (i.e. the hidden variable assumption) that leads to the inequality, which is violated by QM and the experimental observations.
Moreover, I think the thought experiment discussed in your third argument is essentially the same as the original Bell experiment. In the thought experiment, the EPR pair of spin-1/2 particles is measured two times in the same state. It seems to me that this is equivalent to measuring two EPR pair of spin-1/2 particles in the same state.
I understand that you tried to use the extended Wigner’s friend thought experiment to extend the Bell-KG theorem for hidden variables to prove the non-existence of the experimental outcomes of different observables. I also had the same idea after FR’s paper appeared. But I think it may not go through. For actual experimental outcomes of observables are different from the values of these observables, and these outcomes are only different values of the same pointer observable.
ShanOctober 27, 2018 at 6:21 pm #5224
The third argument makes no assumption of hidden variables. In particular, it makes no assumption concerning the actual spin values of the measured particles, either before or after the spin measurements. It assumes only that each measurement has a definite physical outcome, which may correspond to a light flashing red rather than green (for example), considered as registering the actual outcome of the spin measurement. Of course, in the case of Carol’s and Dan’s measurements all evidence of that registration must be completely erased by Alice and Bob prior to their own spin measurements.
We don’t need to appeal to Fine’s result to prove inequality (31). This is a straightforward consequence of Boolean algebra, applied to the assumed physical outcomes of A,B,C,D’s measurements in multiple repetitions of the entire sequence of measurements. Just draw the 4-set Venn diagram and consider the relative frequency measures of the 16 elements of the partition.
In the thought experiment, the EPR pair of spin-1/2 particles is measured two times in the same state. It seems to me that this is equivalent to measuring two EPR pair of spin-1/2 particles in the same state.
In the thought experiment the EPR pair is effectively measured four times in the same state: by CD,AD,BC and AB. But there are only four actual outcomes, unlike in measuring four EPR pairs, for which there would be eight actual outcomes—two distinct outcomes for each measured spin-component, one in each of two separate experiments. That is why the set-ups are not equivalent, even though QM predicts the same probabilities in both set-ups.
Ruth wants to consider what she calls QTC. In my paper I considered only what she calls QTNCP. That is indeed how I think of quantum theory—as a theory that involves no physical collapse. Many believe there can be no definite physical outcomes of quantum measurements if there is no physical collapse. I think this belief is connected to the view that a state vector represents the physical condition of the system to which it is assigned, so that condition cannot be definite if the vector is an “uncollapsed” superposition. I maintain that the role of the quantum state is not to represent the condition of the system to which it is assigned, but to prescribe rational credences regarding the (
) definite condition of that or some other system following a suitable interaction. QM cannot explain definite outcomes since it must take them for granted. That’s why it is so important that it can consistently do so!October 27, 2018 at 7:23 pm #5225
Thanks, Richard for this clarification.
Of course, I think your analysis can also perfectly well apply to an ontic role for the quantum state.
Under an epistemic view of the quantum state, then it seems to me that if one posits that measurements really do have definite outcomes, then an implicit hidden variable view must be lurking in the background–or at least, there a significant lacuna in what is going on in the transition from rational credence to the ontic existence of an outcome. (There is of course also the PBR theorem which precludes a hidden ontic property dictating the outcome in an epistemic approach to the quantum state; I realize there are loopholes to that of course. Taking all measurement outcomes for granted, up to the end of time, is one of them. Under that approach, measurement outcomes function as a form of hidden variable, since they are unavoidably, ontologically destined for the system but unknown to us.)
In contrast, an ontic state really undergoes collapse to the recorded outcome.
So, of course I again respectfully differ with the view that QM cannot explain definite outcomes/takes them for granted. Even taking for granted measurement results, in QTNCP (or simply QTNC, quantum theory no-collapse) there can be no definition of ‘measurement,’ and we arrive squarely in the Schrodinger’s Cat/Wigner’s Friend situation that can give no reason for an interaction counting as a ‘measurement’ that yields an outcome.
And of course, the idea that QM must take measurement outcomes for granted is contradicted under QTC (see my publications in this journal for technical specifics).October 28, 2018 at 12:10 pm #5228
Thanks a lot for your further explanation! I now understand your third argument more clearly. I think the potential issue is that you used results from two different frames in the same inequality (32). Concretely speaking, I think in Alice’s frame corr(b, c) is not equal to E(b, c) = −cos(b − c). It seems that QM does not require this relation in Alice’s frame (we need a more careful analysis here). In other words, the predictions of QM should be complete in each inertial frame. And we should be able to derive corr(b, c) in Alice’s frame if QM permits. This can be seen from the non-SR cases. If we assume the Galileo transformations as in QM, then we cannot derive corr(b, c) in Bob’s frame as you did in your paper. I would like to know what you think about this. Thanks!
ShanOctober 29, 2018 at 4:53 am #5229
PS. Moreover, when Bob and Carol are in different frames, it seems that the relation E(b, c) = −cos(b − c) cannot be consistently defined in QM, since the measured states for them, which extends to two spacelike-separated regions, are not the same.October 29, 2018 at 4:29 pm #5231
You focus on an important part of the third argument.
In my paper I first considered the use of QM to predict the probabilistic correlation E(a,d) in equation (29), and then appealed to Lorentz symmetry to justify the analogous equation for E(b,c). So let’s consider the argument for equation (29).
If Carol had performed no measurement (C and 1 had never interacted) then QM may be legitimately applied to calculate E(a,d) (equation (28). It is true that Alice and Dan perform their measurements in different inertial frames, but that does not invalidate this application of QM in Alice’s frame (or, if we so chose, in Dan’s frame). The two measurements are timelike separated, as in a standard timelike-separated Bell test. The relative motion of the two frames does not rule out application of QM here (see my reference (17) for details on how to handle such cases of relative motion of frames). But it does require careful analysis of what spin-components are actually measured, since Dan’s representation of the directions a and d will differ from Alice’s because of the Wigner rotation associated with their relative velocities. But once this has been taken care of, there is no problem applying QM to calculate E(a,d) as in equation (28).
In my paper I attributed the following reasoning to Alice to justify equation (29).
In the present case, C and 1 interacted twice between t^1 and t^4, but these interactions had no overall effect on the state of the joint system 12D at the time when Alice performed her measurement of a-spin: its state was the same at t^3 as it had been at t^1.
Do you think there is something wrong with Alice’s reasoning here? It seems valid to me, but I recognize that this is a crucial part of the argument. Alice and Dan may assign different (since Lorentz boosted) states to 12D, but they must still agree on the probabilistic correlations E(a,d) predicted by QM.October 29, 2018 at 6:57 pm #5232
Richard, do I understand correctly that in your proposed approach, measurement outcomes have no relation to values of observables for the system? My question arises from your statement:
In particular, it makes no assumption concerning the actual spin values of the measured particles, either before or after the spin measurements. It assumes only that each measurement has a definite physical outcome, which may correspond to a light flashing red rather than green (for example), considered as registering the actual outcome of the spin measurement.
Also, do I understand correctly that the ontology you have in mind is a block-world type picture (i.e. B-time-series) in which there is a set of events constituting measurement outcomes? If so, is the quantum system also part of this block world?
Thanks for any clarification you can provide.
RuthOctober 30, 2018 at 12:45 am #5233
In my view quantum theory may be applied to predict probabilities for certain magnitude claims, each restricting a dynamical variable to a Borel subset of real numbers. When quantum theory is targeted on a quantum system, a quantum state is assigned to that system in order to apply the Born rule to yield these probabilities. The magnitude claims assigned probabilities may be about that system, or they may be about some other system with which it will interact. I give an example of the former kind of application in my paper “Quantum decoherence in a pragmatist view: Dispelling Feynman’s mystery”. Foundations of Physics 42 (2012), 1534–55. Applications of quantum field theory never yield probabilities for magnitude claims about the quantum fields on which they are targeted, and only sometimes about particles such as photons that are their associated quanta. Even applications of non-relativistic quantum mechanics typically issue in probabilities of magnitude claims about systems other than those assigned quantum states in the application. But the Born rule always explicitly yields probabilities for magnitude claims, whether or not these may be glossed as measurement outcomes. If they can, the measurement outcomes supervene on values of “observables” (i.e. dynamical variables)–but not necessarily observables of the system assigned a quantum state when applying the Born rule. Only significant magnitude claims may be assigned probabilities: which these are depends on what interactions are involved. Models of decoherence are a guide to the significance of a magnitude claim. In a spin-component measurement what get assigned probabilities will typically not be magnitude claims about that spin-component but about a magnitude on some other “detector” system with which the spinning system interacts. That is why the spin-component itself need not have a definite value before or after its measurement. My book The Quantum Revolution in Philosophy offers an introduction to this way of thinking about quantum theory. It is based on several other published papers.
I do assume an “eternalist” spacetime within which measurement events and (the histories of) all systems are represented (if not located—I don’t think I’m committed to spacetime substantivalism), though I dislike the “blockworld” metaphor.October 30, 2018 at 4:02 am #5234
I think Alice’s reasoning is right. My worry is still that the inequality (32) should be defined (and can also be calculated) in one frame such as Alice’s frame. But in this frame it seems that QM does not require the relation E(b, c) = −cos(b − c), since the result of Carol has been erased by Alice and replaced by Alice’s result before Bob’s measurement, and thus E(b, c) = −cos(b − c) cannot be derived by using QM in Alice’s frame.
In Alice’s frame, we have the quantum links c —> d —> a —>b, but no the required quantum link b —> c or c —> b for directly deriving the relation E(b, c) = −cos(b − c). For example, suppose the four directions have the relations: c=b and a=d but c is not equal to a. Then when the result c=+1, your relation E(b, c) = −cos(b − c) requires that the result b must be -1. But QM only restricts the correlations E(c, d), E(a, d) and E(a, b) in Alice’s frame, while these correlations do not require that b must be -1. In fact, when c=b and a=d, it can be derived that E(b,c)=4sin^2[(a-b)/2]cos^2[(a-b)/2]-1, and there is no violation of the inequality (32).
In your paper, you derived the relation E(b, c) = −cos(b − c) in another frame (i.e. Bob’s frame) by using the Lorentz transformations (where exchanging the time orders of events seems to be a trick). But one should be able to derive this relation in Alice’s frame (if the relation is true), and moreover, one should be able to derive this relation by using the Galileo transformations (in this case your derivation in Bob’s frame will not go through). After all, these correlation functions in QM should not depend on SR.
I think this is a potential issue, and maybe if this issue is solved, then there will be no contradiction.
PS. I would like to know how you can derive the relation E(b, c) = −cos(b − c) in Alice’s frame. Could you tell me more details? Thanks a lot!October 30, 2018 at 4:08 am #5235
Thanks very much, Richard.
Regarding the interpretation of probability, it seems that this is still an open question. I don’t think the Born probability is restricted to being about semantic objects such as claims. It can be directly about a system’s actualized properties (at least it certainly can in TI).
But in any case: I recognize that you’ve written about these issues at length in the refs you mention, but would it be possible (just for the purposes of this workshop) to give a simple example/illustration of a system, such as an electron or atom, in which the spin component has no definite value before or after a measurement that yields an outcome for the spin observable? This does seem somewhat counter-intuitive, and I think an example might help convey the intent of the relevant physics and its interpretation. Thanks again!October 31, 2018 at 12:44 am #5240
A modern version of the Stern-Gerlach experiment uses a hot-wire detector (see, for example, http://web.mit.edu/8.13/www/JLExperiments/JLExp18.pdf ).
In this case, potassium atoms pass through an S-G magnet, thereby entangling their spin and translational quantum states (not collapsing the spin state)! Interaction with the hot wire likely ionizes the atom, and the charged ion is then collected on a plate, thus producing a current in a circuit including the wire and plate. So what is directly measured is the current in the circuit, which varies as the wire is tracked across what one tends to think of as the beam of potassium atoms emerging from the S-G magnet. But the QM representation is not of two separate beams, but as an entangled superposition of spin+translational states of the emerging atoms. Ionization of an atom on the hot wire certainly involves interaction with its spin state and induces further entanglement, this time with the state of the wire constituents. So you might think of this as a measurement of the atom’s position, rather than of its spin-component. In my view, its is only when an interaction in this whole sequence corresponds to stable decoherence in the state of some system or other that one is entitled to make a meaningful claim about the value of a magnitude on that system. Like most actual quantum measurements, this is a very complicated situation, and it is pretty clearly false that the spin of the atom is itself decohered as a result of these interactions. So there is no reason to believe it is meaningful (let alone true) that the atom has a definite spin-component at any time after it emerges from the S-G magnet. But before passing through that magnet its quantum spin state was a superposition, so there is even less reason to assign it a definite spin-component prior to the measurement.
Probabilities may be assigned to events (e.g. a coin landing heads) or to propositions asserting their occurrence. Born probabilities are assigned either to events of magnitudes taking on values, or to magnitude claims about what those values are. I use the language of claims rather than propositions, since claims are what people actually make, while propositions are rather dubious abstract objects. But I’m happy saying Born probabilities are assigned to events, if you prefer.October 31, 2018 at 4:38 pm #5244
1. It is important to notice that a quantum state assignment on a fixed spacelike hyperplane (like the hyperplane t*^3) may itself be made with respect to different inertial frames (say, Alice’s and Bob’s). Quantum states on different spacelike hyperplanes (like t^3 and t*^3) are not related by a boost transformation. So a derivation of E(b,c)= -cos(b-c) in Alice’s frame would still proceed from an assignment of a quantum state on t*^3 even though that is not a simultaneity slice in Alice’s frame. To derive the relation E(b,c)= -cos(b-c) in Alice’s frame you would first have to transform both the state on t*^3 as well as the angles b,c from Bob’s frame (in which the derivation is easiest) to Alice’s frame. This cannot affect the result of the calculation, since E(b,c) is invariant under changes of frame. But the calculation would be unnecessarily complicated.
2. The boosts (and rotations) must be Lorentz transformations, not Galilean boosts here. This is important because the whole discussion must be set in Minkowski spacetime, not Galilean spacetime: if it were not, then there could be no switching of time order of spacelike separated events between frames. Such Lorentz transformations are standard in discussions like that of my reference (17).
3. I don’t understand how you have derived your alternative value for E(b,c) in the special case c=b, a=d. Can you explain?November 1, 2018 at 9:00 am #5245
Many thanks for your further clarification! Here is my responses:
> 3. I don’t understand how you have derived your alternative value for E(b,c) in the special case c=b, a=d. Can you explain?
In Alice’s frame, we have the quantum links $c —> d —> a —>b$. We can then derive $E(b, c)$ from the correlation functions $E(c, d) = −cos(c − d)$, $E(d, a) = −cos(d − a)$, and $E(a, b) = −cos(a − b)$, which have been derived correctly in your paper.
Consider the simple case where $c=b$ and $a=d$. When the result of Carol is $c=+1$, the conditional probability of $d=+1$ is $sin^2[(c-d)/2]$, the conditional probability of $a=-1$ when $d=+1$ is 1, and the conditional probability of $b=+1$ when $a=-1$ is $cos^2[(a-b)/2]$. When the result of Carol is $c=+1$, the conditional probability of $d=-1$ is $cos^2[(c-d)/2]$, the conditional probability of $a=+1$ when $d=-1$ is 1, and the conditional probability of $b=+1$ when $a=+1$ is $sin^2[(a-b)/2]$. Then, when the result of Carol is $c=+1$, the total probability of $b=+1$ is $2sin^2[(a-b)/2]cos^2[(a-b)/2]$.
Similarly, when the result of Carol is $c=+1$, the total probability of $b=-1$ is $1-2sin^2[(a-b)/2]cos^2[(a-b)/2]$, which is not equal to $1$ in general. This already shows that the relation $E(b, c) = −cos(b − c)$ does not hold in Alice’s frame or in the rest frame where the particles and labs of the experimenters in the Gedankenexperiment are at relative rest.
On the other hand, when the result of Carol is $c=-1$, the total probability of $b=-1$ is $2sin^2[(a-b)/2]cos^2[(a-b)/2]$, and the total probability of $b=+1$ is $1-2sin^2[(a-b)/2]cos^2[(a-b)/2]$. Then we can calculate the correlation function $E(b,c)$, which turns out to be $E(b,c)=4sin^2[(a-b)/2]cos^2[(a-b)/2]-1$. It can be readily checked that the inequality (32) is not violated when using this correlation function $E(b,c)$.
> 2. The boosts (and rotations) must be Lorentz transformations, not Galilean boosts here. This is important because the whole discussion must be set in Minkowski spacetime, not Galilean spacetime: if it were not, then there could be no switching of time order of spacelike separated events between frames. Such Lorentz transformations are standard in discussions like that of my reference (17).
Yes, I agree. My point is that one should be able to derive the correlation function $E(b,c)$ by using the Galileo transformations. After all, these correlation functions in *non-relativistic* QM should not depend on SR (Special Relativity). But, in this non-SR case, your derivation in Bob’s frame (by the switching of time order of spacelike separated events) will not go through.
> 1. It is important to notice that a quantum state assignment on a fixed spacelike hyperplane (like the hyperplane t*^3) may itself be made with respect to different inertial frames (say, Alice’s and Bob’s). Quantum states on different spacelike hyperplanes (like t^3 and t*^3) are not related by a boost transformation. So a derivation of E(b,c)= -cos(b-c) in Alice’s frame would still proceed from an assignment of a quantum state on t*^3 even though that is not a simultaneity slice in Alice’s frame. To derive the relation E(b,c)= -cos(b-c) in Alice’s frame you would first have to transform both the state on t*^3 as well as the angles b,c from Bob’s frame (in which the derivation is easiest) to Alice’s frame. This cannot affect the result of the calculation, since E(b,c) is invariant under changes of frame. But the calculation would be unnecessarily complicated.
Yes, I agree. But I think you ignored the important influence of each measurement process on the entangled wave function (I just realized this). The influence is nonlocal, as clearly manifested in collapse theories or Bohm’s theory. If there were no such influences, then the relation $E(b,c)= -cos(b-c)$ would indeed hold also in Alice’s frame as you have derived. Then it would be not surprised that the Bell inequality (31) is violated by QM. This is consistent with the Bell theorem.
On the other hand, when considering the underlying nonlocal processes, the relation $E(b,c)= -cos(b-c)$ will not hold in Bob’s frame, as well as in Alice’s frame, and we will again have the above relation $E(b,c)=4sin^2[(a-b)/2]cos^2[(a-b)/2]-1$ in Alice’s frame. As noted above, this does not lead to the violation of the inequality (32).
ShanNovember 1, 2018 at 9:15 pm #5246
Thanks very much Richard.
Of course, in the transactional picture, once photons are detected/actualized (as is necessary to yield a current), collapse has occurred, and conserved quantities (such as angular momentum, spin, etc) have been transferred. (Photons are the mediator of em processes such as the creation of electron current; for details, see https://arxiv.org/abs/1610.04609). So in that approach, such a procedure would count as a robust spin measurement. The entanglement does not proceed beyond that point, so no traditional ‘decoherence’ arguments are necessary (or, I argue here https://arxiv.org/abs/1406.4126, are they sufficient anyway). Publication reference: Studies in History and Philosophy of Modern Physics, Volume 48, p. 56-58 (2014)November 2, 2018 at 4:55 pm #5247
No one in the topic on Frauchiger and Renner (FR) “Quantum theory cannot consistently describe the use of itself” (2018) answered this question, so I’ll post it here.
FR talk about a measurement of |h> – |t> by Wbar on the isolated lab Lbar. What does this measurement mean? If Lbar is a quantum system for Wbar, then all possible Hilbert space bases obtained via rotation from the basis |h>,|t> correspond to some physical measurement and the eigenvalues correspond to the physical measurement outcomes. I understand what such rotated bases and outcomes for spin measurements mean in terms of up-down results for relatively rotated SG magnets. Would someone please describe the measurement process and outcomes corresponding to the Wbar measurement of |h> – |t> on Lbar? Clearly, it’s not merely “opening the door and peaking inside,” as that would simply be a measurement in the original |h>,|t> basis. Right?
Thnx in advance for the answer,
Mark StuckeyNovember 4, 2018 at 5:04 pm #5249
Re 3. I think your derivation of $E(b,c)=4sin^2[(a-b)/2]cos^2[(a-b)/2]-1$ is incorrect. The derivation proceeds by separately considering two possible outcomes of Carol’s measurement and then summing over the associated probabilities, treated as exclusive and exhaustive. In effect, this is to treat Carol’s measurement as inducing a physical collapse in the state of 12D, in violation of the condition of unitary evolution of this state. But the calculation of $E(d, a) = −cos(d − a)$ (correctly) assumed there was no such collapse.
The reasoning of your derivation is analogous to the familiar fallacy of assuming passage of an x-spin up eigenstate through a z-oriented S-G magnet induces collapse into a z-spin eigenstate, implying that on subsequent passage of the “recombined beams” through a second x-oriented S-G magnet an atom would be equally likely to be recorded in the up and down emerging beams. In fact, of course, if the recombination has been performed properly, the atom will certainly be recorded as emerging from the x-oriented S-G magnet in the up beam.
In the third argument it is crucial that after Carol’s measurement Alice has completely erased its result—effectively “recombining the states” corresponding to the two possible outcomes of Carol’s measurement into a single superposed state. This is why it is wrong to analyse the $E(b,c)$ correlation as resulting from mutually exclusive possible processes, each corresponding to a distinct one of Carol’s possible measurement outcomes.
Re 2. You can easily derive $E(b,c)$ in Bob’s frame (after suitably representing the directions b,c in that frame) ) in the way I gave in my paper. If the relative velocities are small enough, the directions will be represented in essentially the same way in all the relevant frames, since Lorentz transformations reduce to Galilean transformations. So in the non-SR case Bob’s derivation will go through in his frame, just as Alice’s derivation of $E(a,d)$ goes through in her frame. But Alice will reject Bob’s derivation, and Bob will reject Alice’s derivation, since they will disagree about the objective time order of two pairs of events that are actually spacelike separated—a relativistic relation that makes no sense in Galilean spacetime.
Re 1. I don’t like to speak of influences on wave functions, because I don’t think wave functions are capable of bearing causal relations, even though they are objective. But certainly by performing a local measurement one may gain information that permits one to reassign the quantum state of a distant system (as happens in the EPR case). In my view this involves no “causal” influence or nonlocal processes.
Note that while (31) has the mathematical form of a Bell inequality, it is a simple consequence of Boolean algebra, given the assumption that it concerns objective events that can be described as definite outcomes of measurements: no Bell-type locality assumption is involved in deriving this inequality.November 4, 2018 at 5:22 pm #5250
Wbar measures an observable z on a quantum system composed of everything in Fbar’s lab (including the quantum coin, Fbar herself, her measurement apparatus and recording devices, …). z is a two-valued observable with orthonormal eigenstates okbar, failbar. No-one, including Frauchiger and Renner, has any idea of how to measure this observable. But under the assumptions of their argument, z uniquely corresponds to a self-adjoint operator on a Hilbert space that is the tensor product of a vast number of component Hilbert spaces in which are represented possible states of the coin, of Fbar, …. . The argument simply assumes that every self-adjoint operator corresponds to a measurable observable, including z. Given this assumption, it is not necessary further to specify any operational procedure for measuring z.November 5, 2018 at 2:16 am #5251
Thanks for your further clarification!
I think you did not understand my objection concerning the non-SR case. In the non-SR case, since the time order of spacelike separated events is invariant in different frames, you cannot derive the relation $E(b,c)=-cos(b-c)$ in Bob’s frame using your derivation in the SR case, since just like in Alice’s frame, when Bob obtains his result, Carol’s result has been erased. I think you should at least admit this point.
However, one should be able to derive the correlation function $E(b,c)$ in the non-SR case. After all, these correlation functions in non-relativistic QM should not depend on SR. This suggests that your derivation of the relation $E(b,c)=-cos(b-c)$ in the SR case is problematic.
Concerning my derivation of $E(b,c)$, I think it does not depend on any assumption about the measurement process such as the collapse of the wave function. We just analyze the joint probability distribution of the results (a,b,c,d) in a large number of trials. The distribution already shows that when $c=+1$, the probability of $d=+1$ is $sin^2[(c-d)/2]$, etc, and then we can use these probability relations to derive $E(b,c)$ as I have done in my last post.
I have just written a draft paper which tries to solve these issues from a new angle. Your comments are very welcome!
ShanNovember 5, 2018 at 5:40 pm #5256
Mark: of course, I’ve contended and continue to contend that the disease infecting conventional approaches to QM is that nobody can define ‘measurement’. This leaves adherents of these traditional approaches to simply help themselves to measurement results. In particular, I would have to respectfully differ with Richard’s comment:
The argument simply assumes that every self-adjoint operator corresponds to a measurable observable, including z. Given this assumption, it is not necessary further to specify any operational procedure for measuring z
But it doesn’t follow from the stated assumption that there is no necessity to give an account for ‘measuring z’. Only if one simply helps oneself to a measurement result can one bypass this requirement. IMHO this is not physics. It’s just inventing an ad hoc ontology that has what one requires, without any physical theory supporting it.
Re Shan’s concern: my understanding is that in the above approach for unitary-only QM–helping oneself to measurement results that are inexplicably just ‘there’ in the world–that SR is at least not violated. Richard noted earlier (if I understand correctly) his assumption that the existence of a measurement result in the world has no relation to whether anyone knows what it is, nor to any particular physical condition of the system under study. So it seems that when one party engages in what they consider a ‘measurement’, that doesn’t erase a measurement result that is simply out there in the world. That would be according to this ontology–which as I’ve noted seems ad hoc and lacks a physical account of ‘measurement.’
But once again, IF Nature behaves according to the direct-action theory, then there is no need for any of the above: measurement is defined in a specific physical theory that contains genuine non-unitarity; measurements have results that correspond appropriately to the physical nature of the systems under study; the Wigner’s Friend paradox never arises (because neither does the Schrodinger’s Cat paradox); the micro-world domain of applicability of QM is well-defined in contrast to the macro-world domain of relativity, and we have a way forward for quantum gravity in terms of spacetime emergence from the quantum level. (As an extra dividend we gain a fully non-circular explanation of the second law of thermodynamics: https://arxiv.org/abs/1612.08734 )November 6, 2018 at 1:11 am #5257
Thanks, Ruth. Your pointed out a potential issue. My argument does not reply on Alice’s result being erased, but relies on the state of the particles being recovered before Bob’s measurement. ShanNovember 6, 2018 at 5:58 pm #5258
Thnx, Richard. I figured that was the answer, but I wanted to make sure before I fashioned a response (forthcoming).November 7, 2018 at 3:54 pm #5259
I quote two sentences from your draft paper:
In Bob’s frame, since after the superobserver’s reset measurement the states of Alice and the particles are the same as their initial states, the result of Bob’s measurement has no correlation with the result of Alice’s measurement. Then we have E(a,b)=0 for any a, b.
I think these two sentences incorrectly derive a lack of correlation between Alice’s outcome and Bob’s in Bob’s frame.
The state Bob assigns after (in his frame) the superobserver has undone Alice’s measurement is irrelevant to Bob’s use of QM to calculate the correlation between Alice’s and Bob’s actual outcomes. That state would be relevant to the correlation of Bob’s outcome with a hypothetical $second$ measurement by Alice: it would predict $E(a,b)=-cos(a-b)$ for the correlation between Bob’s outcome and the outcome of Alice’s hypothetical second measurement.
To correctly calculate the correlation between his outcome and the outcome of Alice’s actual measurement, Bob must assign a state at a time (in his frame) before the superobserver’s intervention. He can assign the state (1) to the pair of spin 1/2 particles on a spacelike hypersurface prior to his own(Bob’s) measurement, and thereby correctly predict the same correlation $E(a,b)=-cos(a-b)$ as Alice. (For simplicity I assumed here that the spin state of the pair is invariant under Lorentz boosts. This may be false for the state (1), but if the relative velocities are small enough this won’t matter. If you replace the + with a – in the spin state (1) I think the assumption would be true. If the relative velocities were large enough to matter for the state (1), Bob would have to make sure to transform the directions a, b correctly, thereby reaching exactly the same predicted correlation as Alice.)
When Alice and Bob correctly apply QM to this scenario they make identical predictions for the correlation between the outcomes of their measurements. There is no contradiction between unitary QM and relativity.November 7, 2018 at 4:20 pm #5264
Let me comment on something you said in your last post:
Richard noted earlier (if I understand correctly) his assumption that the existence of a measurement result in the world has no relation to whether anyone knows what it is, nor to any particular physical condition of the system under study. So it seems that when one party engages in what they consider a ‘measurement’, that doesn’t erase a measurement result that is simply out there in the world. That would be according to this ontology–which as I’ve noted seems ad hoc and lacks a physical account of ‘measurement.’
The understanding you express in the first sentence is almost right. The qualifications are that in many circumstances the existence of a measurement result in the world does have a relation to whether anyone knows what it is ((s)he’s the one who performed the measurement!), and in some circumstances this measurement result is represented by the physical condition of the system under study.
But I don’t see why your second sentence follows from this understanding. I think all measurement results are “out there in the world”, in that every measurement result is represented/determined by a true magnitude claim about some system. There is nothing ad hoc about this: if there were no true magnitude claims then an application of the Born rule would have nothing to which to assign probabilities! Only if one were to take a quantum state to correspond to “an element of physical reality” would it be reasonable to expect QM itself to yield a physical account of ‘measurement’. In my view quantum states are objective in just the same sense that Born probabilities are objective: but neither correspond to “elements of physical reality”.
(By the way, I don’t see why anyone would think that merely making a measurement would erase the result of a previous measurement.)November 8, 2018 at 1:08 am #5265
Thanks Richard, let me address your comment that:
… if there were no true magnitude claims then an application of the Born rule would have nothing to which to assign probabilities!
The above statement/position depends on the notion of ‘magnitude claim’. That’s a linguistic entity, and I think we earlier agreed that QM doesn’t demand or depend on linguistic entities. And indeed the Born Rule does have something to which it assigns probabilities in an approach that doesn’t assume that measurement outcomes are ‘given’ as part of a 3+1 spacetime manifold.
Specifically: if quantum states represent propensities for the actualization of outcomes, then the Born probabilities describe (quantify the weights of) those propensities. This reflects an ontology in which measurement outcomes dynamically arise out of fundamental ontological uncertainty, so that they are not ‘given’ a priori.
The ontological presupposition lurking in the background of the apparent discrepancy in our approaches is that of actualism (which I dispute). Taking all measurement results as actual and given, such that the Born probabilities are only epistemic, is what I claim is ad hoc. The approach is ad hoc because it helps itself to a set of measurement results as a brute fact about the world for which there is no physical account. But that isn’t necessary, since (in the direct-action picture of fields) there is a physical account of the conditions under which measurement outcomes arise and of what they consist.
(Re erasing measurement results: I agree with you here, and of course I didn’t claim that measurements erase previous results. I was commenting on something that Shan said above.)November 8, 2018 at 11:40 am #5269
In your post, you said: “To correctly calculate the correlation between his outcome and the outcome of Alice’s actual measurement, Bob must assign a state at a time (in his frame) before the superobserver’s intervention.” Could you explain why? Thanks!
PS. Gijs Leegwater has just posted a paper in arXiv (https://arxiv.org/abs/1811.02442), in which he discussed a similar thought experiment as your third argument, but he reached the same conclusion as mine. He may later participate in our discussions.November 11, 2018 at 12:40 am #5272
I much prefer your presentation of FR in Quantum Theory and the Limits of Objectivity (2018), so I will refer to that. Looking at your Eq (13) and understanding that there exists an objective fact of the matter about what Xena and Yvonne have recorded for their measurements (h or t and + or -, respectively), it seems unavoidable that what Wigner and Zeus decide to measure bears on Xena and Yvonne’s records (what you refer to as “retrocausality”). Suppose we prepare many states Psi per your Eq (13) and collect all of the same X and Y cases together for W and Z to measure. Eq (13) says we could have collected h- or t+ or t- and it’s up to W and Z to figure out which one we picked (of course, this could be self-selected by X and Y, too). Because it’s an objective fact of the matter, we can use this to replace counterfactual measurements. Now, suppose Z decides to measure z and obtains OK. Then W decides to measure y, so he has to obtain +. From Eq (13) we then know (as you point out) that our fact of the matter for this collection of trials is t+. They then make measurements on another Psi in the collection, just to make sure. This time W measures w and obtains OK then Z decides to measure x, so he has to obtain h. From Eq (13) we then know (as you point out) that our fact of the matter for this collection of trials is h-, contrary to what W and Z determined by deciding to make different measurements. It looks like what Z and W decide to measure determines an otherwise objective fact established before Z and W started making measurements. Do you agree? If not, why not?November 11, 2018 at 11:07 pm #5275
No, I don’t agree. I regard retrocausation here as a desperate and unnecessary response to the situation you present. (Though I’m happy to entertain this as a conceptual possibility in other contexts and for other reasons.)
Equation (13) and its equivalents represent probabilistic correlations between the outcomes of possible measurements on X and Y, not between the values of magnitudes in/on X and Y (including whatever magnitudes record the outcomes of Xena’s and Yvonne’s measurements in their labs.) So it is only in thought that we can collect all of the same X and Y cases together for W and Z to measure: not even Xena and Yvonne can physically collect them together, since any attempt to do so by observing X and/or Y would disrupt the sensitive correlations coded in the superposed state (13). But we can still consider how to handle the cases you mention.
Once Zeus has measured z and obtained OK, Wigner is indeed sure to get + if he measures y (as long as Zeus’s measurement has not disturbed Y), and (provided he trusts Zeus’s measurement report—see Step 1 of my reconstruction of the argument) he may infer that Xena’s outcome was t.
Consider instead the case in which Wigner first measures w and obtains OK, and then Zeus measures x. This time it is not Wigner’s perspective but Zeus’s that we should take when insisting on unitary evolution of the total quantum state. From that perspective, Wigner’s measurement of w yields a state in which Zeus’s overall probability of getting an outcome of +1 in a measurement of x is 1/3 (without regard to Wigner’s outcome). At first sight it looks like Zeus is certain to get an outcome +1 conditional on Wigner’s getting an outcome OK, thereby certifying the prior outcomes of Xena’s and Yvonne’s measurements as h-. But this assumes both that Wigner’s intervening measurement on Y has not uncorrelated the outcome of Zeus’s subsequent measurement of x from Xena’s actual outcome when measuring f, and that Zeus can trust Wigner’s report of his own measurement outcome.
Both these assumptions are questionable. I think the first rests on what I called Intervention Insensitivity and argued against in my paper. The second may seem more plausible, and I made an analogous assumption in step 1 of Wigner’s reasoning in my paper. But notice that Zeus’s representation of Wigner’s state following Wigner’s prior measurement is entangled with that of Y (as well as X). So one could argue that whatever Wigner says about his outcome (more carefully, whatever Zeus measures Wigner’s outcome to be) is not a reliable guide to Wigner’s actual outcome. In particular, even if Zeus takes Wigner’s outcome to have been OK (because that’s what he observes it to be in a hypothetical future measurement on W) Wigner’s actual outcome might equally well have been FAIL. In that case, Zeus’s probability of getting h when measuring x would again be 1/3 (not 1) when conditionalized on the outcome of a measurement of Wigner’s outcome.
As you see, the assigned quantum states play a more important role in predicting measurement outcomes than the assumed unique outcomes of prior measurements. That’s why it’s not necessary to make a desperate appeal to retrocausation.
PS I’m not confident that this is the clearest response to your interesting question, but I don’t have time to improve on it right now!November 15, 2018 at 1:57 am #5277
Thnx for the detailed response, Richard. Let me see if I totally understand it.
The state given by your Eq 13 applies to any of the three possibilities for the definite, single outcomes recorded by Xena and Yvonne in one world, i.e., heads- or tails- or tails+, respectively, prior to Zeus and Wigner making their measurements.
Eq 13 says that if Zeus measures z he can obtain OK, which is compatible with any of the three single recorded values heads- or tails- or tails+. If that happens and Wigner subsequently measures y, Wigner will obtain + (due to quantum interference). But, that means Yvonne’s single recorded outcome is and always was + (no rewriting history, no retrocausality). But, that violates our assumption that Eq 13 and Zeus’s OK outcome apply to ANY of Xena/Yvonne’s three definite, single outcomes in one world because two of the three single recorded values heads- or tails- or tails+ contain – for Yvonne’s recorded outcome.
You avoid this conclusion by saying Zeus could measure z and obtain OK followed by Wigner measuring y and obtaining + while Yvonne’s recorded outcome is actually -. In other words, it’s simply the case that Wigner’s measurement outcome of Yvonne’s y measurement record does not agree with Yvonne’s y measurement record.
Is that your claim?November 24, 2018 at 4:02 pm #5284
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