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I still think the psychophysical connection is one of these problems. See my recent paper:
https://link.springer.com/article/10.1007%2Fs11229-017-1476-y
Dear Bob,
Thanks for your comments! I am sorry for not discussing your ideas in detail in my book. The reason is that I have not studied your CH solution very deeply, and I cannot give my own opinions on it. I will try to study your solution in the near future.
Best,
ShanHi Jiri,
Thanks for your comments. I think you misunderstood the main idea of my paper. It does not aim to argue the impossibility of the psi-epistemic view based on the Kochen-Specker theorem. It only argues that the psi-epistemic view does not provide a straightforward resolution or a dissolution of the measurement problem, as I clearly stated in the abstract of the paper.
Best,
ShanHi Ken,
Thanks again for your very detailed reply! I learned a lot about the retrocausal quantum models from them. I feel that such models seem more complex than Bohm’s theory. Maybe the reason is that there are no wave functions in them?
Best,
ShanHi Matt,
Thanks again for your further comments, most of which I agree. There is only one minor point I disagree. I still think the ontological models framework is more specific than Bell’s framework due to its second assumption. Even in the proof of the CHSH version of Bell’s theorem, although the ontic state λ is a random variable, it still determines the outcome of a projective measurement on the system, not the probability of different outcomes for a projective measurement on the system.
Best,
ShanHi Matt,
Thanks for your interesting comments, some of which I basically agree.
But I think you misunderstood my paper. The paper does not aim to show the (realist) psi-epistemic view cannot solve the measurement problem. Rather, it only shows that the psi-epistemic view does not provide a straightforward resolution or a dissolution of the measurement problem, as I clearly stated in the abstract of the paper. This result removes the main motivation to assume the psi-epistemic view.
In fact, the writing of this paper is mainly motivated by your words in your review paper. You said, “A straightforward resolution of the collapse of the wavefunction, the measurement problem, Schrodinger’s cat
and friends is one of the main advantages of psi-epistemic interpretations…. The measurement problem is not so much resolved by psi-epistemic interpretations as it is dissolved by them. It is revealed as a pseudo-problem that we were wrong to have placed so much emphasis on in the first place.” It seems that your view expressed in your comments here is different from your view in your review paper.Here are my concrete replies to some of your comments.
“Namely, in situations like Schroedinger’s cat, where there is a macroscopic superposition of distinct states like an alive and a dead cat, we require that the ontic state occupied by the system is one in which the cat is either definitely alive or definitely dead. This certainly does not entail that all observables need to have pre-existing values. For example, a preferred observable, such as position as in Bohmian mechanics, would do the job just fine.”
*** I agree. But my point is that if not all observables have pre-existing values, then the psi-epistemic view will not provide a straightforward resolution or a dissolution of the measurement problem. In other words, it will have no advantages in solving the measurement problem when comparing with the psi-ontic view.
“Finally, you seem to think that models like Bohmian mechanics cannot be fit into the ontological models framework because they are deterministic. Of course this is wrong. Although ontological models need not be deterministic, they can be just by allowing some of the probabilities to have value 0 and 1. Bohmian mechanics would not actually be fully outcome deterministic when written as an ontological model, because when you measure an observable other than position, the outcome depends on the ontic state of the measurement device, which is not included in our description of the ontic state of the system. Thus, you would get a probabilistic answer from averaging over the possible states of the measurement device for a given measurement procedure.”
*** I cannot agree with you. First, when one measures position, the outcome is completely determined by the ontic state of the system, and the theory is deterministic. In particular, the probability of the measurement outcome is not determined by the ontic state of the system, but by the initial position probability distribution. In some models without the quantum equilibrium hypothesis, the probability of the measurement outcome is even different from the Born probability. This is inconsistent with the second assumption of the ontological models framework. Next, even when one measures an observable other than position, the outcome depends on the ontic state of the measurement device, but this only reflects the contextuality of the measured property. Moreover, even if there is a probabilistic answer in this case, the probability is not the Born probability either.
“That people have these misconceptions about the ontological models framework continues to surprise me. The framework is essentially the exact same framework that Bell used to prove Bell’s theorem, with a few bits of terminology added (such as system, preparation, measurement, etc.). But pretty much every valid criticism against the ontological models framework could be levelled against Bell’s work instead, so if you think that the setup of Bell’s theorem is valid and interesting, then you should have the same opinion of ontological models in general.”
*** I think the ontological models framework is not the same framework that Bell used to prove his theorem. In the former, the ontic state of a system determines the probability of different outcomes for a projective measurement on the system (which is the second assumption of the framework). While in the latter, the ontic state of a system determines the outcome of each projective measurement on the system (this assumption is consistent with Bohm’s theory). Moreover, the proof of Bell’s theorem does not require the second assumption of the ontological models framework.
To sum up, maybe the view I objected in my paper is a bit of a straw man view as Ken said. But the paper does emphasize a few unsolved problems of the psi-epistemic view (which may be not clearly realized by some people who believe in the view), and shows that the psi-epistemic view does not provide a straightforward resolution or a dissolution of the measurement problem.
Thanks Arthur for your very detailed and helpful comments. I have learned much from these comments. I will improve my paper according to them. Best, Shan
Thanks Mark and Ken for your further comments. I have not thought too much on retrocausal models. I would like to know whether quantum randomness is also inherent in these models, and how these models account for the randomness of measurement results. Best, Shan
Thanks Mark and Ken for your very helpful comments. I will need more time to think about them. For now I think Ken’s explanation seems to require the deny of the existence of free fill and essential randomness and have to resort to superdeterminism. Best, Shan
Thanks for your comments, Kelvin. It seems that you did not really understand my solution, which is different from the solution discussed in your paper. In my solution, there are no “zombie tails”. The observer being in the superposition has only one mind with the unique mental content. The key point is that according to my assumption about vividness, below a certain threshold of amplitude the observer may not be consciously aware of the mental content corresponding to the low-amplitude branch.
Thanks for your further clarification, Peter. I still think that your assumption that the relative positions of the particles determine the measurement outcome requires a wholly new hidden-variables theory which is different from Bohm’s theory.
Consider your example. If after being measured by the Stern-Gerlach magnet, the two separated wave packets of the first particle are reflected by two mirrors so that their vertical positions are exchanged (during which the first particle in one packet will also be reflected along with the packet, and the position of the second particle is not changed), then according to your assumption, the measurement result will be changed. But this is not the case. The key point, in my view, is that the spin-magnetic field interaction is described by the wave function, and thus the measurement result being spin-up or spin-down is essentially encoded in the wave function too. (I think this also means that your assumption requires a new theory, in which, for example, the spin-magnetic field interaction is directly described by the particles.)
In addition, I think the concepts of “empty” and “occupied” wave packets are still valid at least in the context of measurement. For one, the Bohmian particle residing in one of many separated wave packets will ensure that the measurement record can be stable. If all wave packets greatly overlap and interfere with each other, then the motion of the Bohmian particles in the overlap region will in general be very chaotic and not stable, and thus their relative position can hardly represent a stable measurement record.
Finally, even if your assumption is true, you still need a detailed theory to give the corresponding relationship between different relative positions of the Bohmian particles and different measurement outcomes. In my view, this theory will be very different from SQM and Bohm’s theory, since the wave function will play minor or even no role in determining the appearance of a measurement outcome in the theory.
Thanks for your insightful comments, Peter. I should have made my argument more accurate. I agree that if assuming the measurement outcome supervenes on a pattern among a number of Bohmian particles, then Bohm’s theory can solve the measurement problem. But I think the assumption seems inconsistent with SQM. Let me restate my argument more clearly.
Consider a simple example in which a measuring device is composed of two Bohmian particles. In this case, the relative position of the two particles may indicate the measurement outcome. Now consider two post-measurement situations in two experiments: in one situation the two Bohmian particles reside in the branch $\ket{up}_M$ after the measurement, and the experiment obtains the x-spin up result; while in the other situation the two Bohmian particles reside in the branch $\ket{down}_M$ after the measurement, and the experiment obtains the x-spin down result. Since each Bohmian particle can be in any position in the region where the corresponding wave function spreads, which is the whole space in realistic situations, it is always possible that the relative positions of the two Bohmian particles in the two post-measurement situations are the same. This is irrelevant to the overlap of the two branches $\ket{up}_M$ and $\ket{down}_M$. Then if assuming the relative position of the two Bohmian particles indicates the measurement outcome, then these two experiments will obtain the same result. But this is not the case; the first experiment obtains the x-spin up result, while the second experiment obtains the x-spin down result.
In my view, in order to solve this problem a new hidden-variables theory is needed, which replaces the wave function with some other variables and thus will be quite different from Bohm’s theory. However, since there are already several proofs of the reality of the wave function, such as my recent argument in terms of protective measurements, this seems to be not a promising solution either.
Hi Peter, thanks a lot for your very helpful comments. Your questions are closely related to the understanding of RDM (random discontinuous motion) of particles. RDM gives an ontological interpretation of the wave function, but the instantaneous picture cannot explain interference and measurement. To explain the former, we still need the law of motion, which is supposed to be the linear Schrodinger equation for the wave function (which describes the state of RDM during a time interval dt). For the latter, we still need a solution to the measurement problem. Here RDM may help. My idea is that RDM may be the source of the randomness of measurement results, and especially, if wavefunction collapse is real, RDM may be the random noise that collapses the wave function. I proposed a model here (http://rspa.royalsocietypublishing.org/content/469/2153/20120526). No doubt further study is needed for my idea of RDM. Best, Shan
Hi Ken,
Many thanks for your reply and explanation! I would like to learn more details about your retrocausal theory by reading these two papers.
Best,
ShanHi Ken,
This is a very interesting paper. I would like to know whether a retrocausal explanation has the ability to derive the Born rule. I think this question is closely related to the missing account of how a future measurement setting influences the measured system physically (which has been referred to by you). It seems that only after we know the underlying mechanism, can we answer similar questions. Here I am also curious about the underlying mechanism. Is there some particle or wave which transfers the retrocausal influence? What equation of motion does it obey? Can we test its existence by experiments? etc.
Best,
ShanI think my new strategy to prove nonlocality may be more helpful for understanding the nature of nonlocality, e.g. determining whether the nonlocality requires the existence of a preferred Lorentz frame.
It is noncontroversial that the existence of the above hypothetical superluminal signaling is incompatible with the theory of relativity, and it will lead to the existence of a preferred Lorentz frame. No matter which convention of synchrony is adopted, the preferred Lorentz frame can always be defined as the inertial frame in which the one-way speed of light is isotropic and the superluminal signaling is transferred instantaneously in space.
Now, the superluminal signaling is composed of two processes: a nonlocal process and a local subluminal process. Obviously, the local subluminal process does not lead to the existence of a preferred Lorentz frame. Thus the process leading to the existence of the preferred Lorentz frame must be the nonlocal process. In other words, quantum nonlocality must lead to the existence of a preferred Lorentz frame.
Note that this argument for preferred Lorentz frame is independent of whether my proof of nonlocality is valid, though they use the same strategy: nonlocality + locality -> superluminal signaling.
Hi Shelly,
Thanks again for your further comments! I still think my proof of nonlocality does not depend on the meaning of the wave function. No matter the wave function is epistemic or ontic or something else, the wave function may be changed in a linear way by an usual external potential according to the Schrodinger equation, and it is also possible that the wave function may be changed in a nonlinear way by a special hypothetical external potential. The above proof only relies on the possible existence of the nonlinear evolution of the wave function (besides the collapse postulate and the Born rule). [If one thinks the proof depends on the meaning of the wave function, then whether or not nonlinear evolution may exist will depend on the meaning of the wave function, which seems to be implausible.]
Certainly, this new proof of nonlocality in standard quantum mechanics does not establish that our world is nonlocal. But the above result, if it is valid, may be still a surprise for some orthodox physicists. For the proof shows that no matter how to interpret the wave function, nonlocality always exists in standard quantum mechanics; one cannot resort to the possible lack of counter-factual definiteness or non-contextuality to avoid the nonlocality, though one might avoid it in another different quantum theory.
Best, Shan
Hi Richard,
Many thanks for your kind reply! I will consider my argument more deeply. But I still have a question for your reply. I think the existence of precise anticorrelation requires that the wave function of the photon on every side need to be collapsed as in standard quantum mechanics. I would like to know what you think about this point.
Best,
ShanHi Richard,
I have a short comment on your very intriguing paper. It seems that in your formulation of QM there is still the collapse of the wave function, though the wave function is not ontic. Then it seems that my new proof of the quantum nonlocality also applies to your theory. My proof does not depend on the meaning of the wave function, but depend on the existence of the collapse of the wave function.
Best,
ShanHi Travis,
I agree that finding an image of the familiar 3D world is an issue for the Everettians. I also hope Chris can clarify some of these things.
Best,
ShanHi Shelly,
Many thanks for your very helpful comments on my new proof of Bell’s theorem. You pointed out a very important potential issue, and I should have clarified my argument concerning this point. Here are my answers.
First of all, as you may admit, when assuming that the wave function is ontic, my proof is valid. I think this is still an interesting result. But certainly, as you have emphasized, it is not a proof of Bell’s theorem.
Next, I think the psi ontology assumption may be avoided in my proof, since nonlinear evolution of the wave function may be not needed in my proof. Here I should have made my point clearer. It is also logically possible to introduce certain hypothetical local interaction with particle 2 or even with the device, which may change the outcome distributions to lead to nonlocal signaling. Certainly, if the wave function indeed represents the physical state of particle 2 (i.e. if the wave function is ontic), then such interaction may be equivalent to nonlinear evolution of the wave function.
Thirdly, I think even if my proof resorts to nonlinear evolution of the wave function, it does not necessarily assume psi ontology. The reason is that that different evolution of the wave function leads to physically different results or states of device does not necessarily require that the wave function is ontic. In standard quantum mechanics, different linear evolution of the wave function also leads to physically different results of measurement.
Lastly, I agree that physical differences out would require physical differences in. For example, if there is nonlocal signaling, then a and a’, which are physical different, can lead to physically different situations. But the wave function is a description of the in-between process involving the particles, and it is not necessarily physical or ontological only because the input and output are physical. Otherwise we will have a very simple proof of psi ontology.
Thanks again for your very helpful criticisms! Your further comments and criticisms are very welcome.
Best,
ShanPS. It is a fundamental and widely accepted assumption that a measurement result exists universally, and in particular, it exists for every observer, independently of whether the observer makes the measurement or knows the result. But the Everettian theory violates this assumption.
Hi Travis,
I think the authors are right in suggesting that the correlations in question don’t yet exist (when the state is 0.9) but do exist (when the state is 0.10). The reason is that in Everettian theory a measurement result exists only relative to the systems which are decoherent with respect to the measurement result, and it does not exist for nondecoherent observers who does not make the measurement or know the result. Although people including me may not like such relativity of worlds, it is required by the theory, for which I have given a simple argument based on protective measurements (http://philsci-archive.pitt.edu/9790/1/mwi_relativity.pdf).
Best,
ShanHi Gregg,
I fully agree with Bell and you that if quantum theory is to serve as a truly fundamental theory, conceptual precision in its interpretation is not only desirable but paramount. In my view, even in current realistic quantum theories, there is still conceptual imprecision. For example, in collapse theories favored by me, the source that collapses the wave function still needs to be specified in physics. On the other hand, I also think experimental tests are very important and can help improve the conceptual precision.
Best,
ShanHi Matt,
Thanks for this! I look forward to reading your final paper.
Yes, I agree that “the operational argument does not depend in any way on what the protective measurement scheme tells Bob to do.”
But in your note, you say: “But since protective measurement uses exactly the same resources, how can it lead to a radically different conclusion about the role of the wave-function?”
My point is that what Bob has done in your scheme is not a PM, and protective measurement does not use exactly the same resources. So, if this is true, it will influence your operational argument.
Best,
ShanPS. I noticed another feature of your scheme last night (when I am near sleeping). It seems that your scheme cannot measure the expectation value of an observable with arbitrary accuracy, and the state of the ensemble will be largely mixed in the end. Suppose the first weak measurement leads to small probability 1/n to collapse to other states, then after n steps the probability to stay in the initial state is (1-1/n)^n, which is not close to one when n approaches infinity. I hope this point may be useful for your further analysis.
Here is my further idea (gotten on the bus to my office), which shows that there are more differences:
(1) The first one concerns the weak measurements (with readouts). These weak measurements result in strong wavefunction collapse. Here the strongness means that the probability to collapse most of the outcome states is large, although the initial state and the final state are almost the same. It is this feature makes your scheme be more like or even equivalent to projective measurements (as you have proved in your notes).
I think it is also this feature that makes your scheme different from Zeno-type PM. In a Zeno-type PM, the wavefunction collapse is very weak in the sense that the probability to collapse the wrong outcome states is very small, and can be made arbitrarily small in principle.
In other words, wavefunction collapse has no role in obtaining the right expectation value in an (ideal) Zeno-type PM. But, as you also noted in the end of your notes, wavefunction collapse has a significant role in obtaining the weak measurements results, from which the right expectation value is re-constructed. This also leads to the second difference.
(2) It is that your scheme relies on the Born rule (so does the PBR theorem? I am not sure). This is not unexpected as it relies on wavefunction collapse. Imagine that the Born rule assumes a different form, e.g. not |psi|^2, then it seems possible that the right expectation value cannot be re-constructed from the weak measurements results.
By contrast, a Zeno-type PM does not replies on the Born rule. (It may only require that very small probability amplitude has small probability collapse outcome.) The right expectation value is obtained independently of the Born rule in a Zeno-type PM. In fact, the expectation value is generated from the continuous Schroeinger evolution. (It is also this avoidance of wavefunction collapse that makes PM probably have direct implications on the reality of the wave function)
It is these differences that makes one doubt the equivalence of your scheme and Zeno-type PM.
I would like to know your further thoughts.
Best,
ShanDear Matt,
I must say that your scheme let me think more deeply about PM. I am very grateful to you for this.
I think we should not make assertions quickly; we need a more careful analysis and more effective discussions, especially because we have different opinions from the beginning.
Here is my current thoughts:
1. Your scheme is not the same as adiabatic PM (as Max also noted). I think you should agree with this. It is unclear whether you can find a psi-epistemic model of adiabatic PM. So, it is fair to say that there is still no firm basis to reject the possible implications of such PMs.
2. Whether your scheme is equivalent to or similar to Zeno-type PM is a very interesting question, which certainly needs a careful analysis. I think they are different. My previous analysis is:
Your scheme is equivalent to many weak measurements of an ensemble of identically prepared systems. In your scheme, one get many inaccurate expectation values, from which the right expectation value is re-constructed.
By contrast, in a Zeno-type PM, although there are also frequent projective measurements (as a protection), one directly get the right expectation value with arbitrary accuracy in a single measurement.
Matt #1101:
Thanks for your further comments!
2) Are you saying the same protection can apply to two non-orthogonal states? Can you give an example of how that would work?
No, we need two different protections for two non-orthogonal states. The protection is taken as part of the state preparation procedure.
1) Why couldn’t somebody also run your argument using the tomography-of-protector then projective measurement-of-system scheme?
This needs a more careful analysis. My answer is negative. One reason is that scuh a scheme is not a usual measurement, like projective meaurement or PM. The result of your scheme is re-consctructed from many inaccurate WM results. In this case, I don’t know whether it is meaningful to say “the same physical state $\lambda$ yields the same probability distribution of measurement results.” Moreover, even if one can run my argument using your scheme, it seems that this does not refute the argument either. I will say more about your scheme later.
Best,
ShanMy answers to these questions are as follows:
1. We don’t need new experimental observations to understand the wave function. This is different from the case of the measurement problem. This is why I think we should first solve this problem.
2. Although we cannot exclude the anti-realist view, I believe we can find the true meaning of the wave function when assuming a realist view. In particular, I think we can determine which of the three views: epistemic, nomological, and ontic, is right. In my opinion, protective measurement (PM) provides a strong support for the ontic view.
3. However, I think an ontic interpretation of the wave function is not necessarily a continuous field in cf space (as usually thought). There are good arguments for the view that the wave function describes motion of particles in real space, and the motion is random in nature. For instance, the modulus squared of the wave function may give the probability density that the particles appear in certain positions in space. In this sense, we may say that the wave function describes the statistical property of the motion of a single system. (At a deeper level, I think it may represent the dispositional property of the particles that determines their random discontinuous.)
4. I think the true meaning of the wave function will have deep implications for solving the measurement problem (this is also the reason why I think the meaning of the wave function is an extremely important problem). The epistemic view is a good example. My opinion is that even for the ontic view, making sense of the wave function will also help solve the measurement problem. For example, if the Born probabilities originate from the objective probabilities inherent in the random motion of particles described by the wave function, then all existing realistic alternatives to quantum mechanics need to be reformulated. The reformulation may be easier for some alternatives, but more difficult for others. For example, it is relatively easy to find a dynamical collapse model where the chooser or the noise source that collapses the wave function is the underlying random motion of particles. However, it seems difficult to find a new formulation of Bohmian mechanics in which the probabilities of measurement results are objective and come from the wave function. Moreover, it seems that the many-worlds interpretation and the many-minds interpretation cannot be reformulated in terms of the objective probabilities inherent in the random motion of particles either.
Hi Bob and Matt,
Thanks again for your very helpful discussions! I think both of you may be sympathy with my interpretation of the wave function in terms of random discontinuous motion of particles (see http://philsci-archive.pitt.edu/10659/), as you already presented similar examples.
I will catch a bus now. Your later comments and criticisms are very welcome!
Best,
ShanHi Bob,
Thanks for your further comments!
I think the point is that people usually believe that a wave function ONLY describes an ensemble, but if the psi-ontic view is right, a wave function also describes a SINGLE system. This is new. Certainly, a wave function can still describe an ensemble.
Shan
Matt #1094:
In my picture of random motion of particles, it seems that we may say that classical probability distributions are also properties of individual systems. The word “classical” is in the sense of an ergodic, random motion of individual particles.
Shan
I agree with most of your analyses in your ergodic motion example.
In my interpretation of the wave function in terms of random motion of particles, what PM measures is indeed a probability distribution, such as the position probability density of a particle. But this probability density describes the single particle, not an ensemble. This probability should be better understood as an indeterministic dispositional property of the particle that determines its random discontinuous motion. This is consistent with the conclusion of my PM argument.
Dear Matt,
Thanks for your very helpful criticisms!
I am not familiar with the equivalence between quantum mechanics and classical Liouville mechanics. But I think this equivalence will not imply the physical interpretations of these two theories must be the same; otherwise will already has a classical int. of QM. (Moreover, I think your objection is not only for my argument, but also for the psi-ontic view.)
I will respond to your second objection below.
Shan
Dear Bob,
Thanks for your very helpful comments!
Yes, I agree that PMs can also measures <P_j>. My point is that these measured quantities describe a single quantum system, and not just an usual probability distribution in QM. The latter interpretation depends on what happens during a conventional measurement.
As to the second comment, I would like give an example. In my interpretation of the wave function (as said above), the wave function of an N-body quantum system describes the state of random discontinuous motion of N particles (which is composed of density and flux density in configuration space), and in particular, the modulus squared of the wave function gives the probability density that the particles appear in every possible group of positions in space. At a deeper level, the wave function may represent the indeterministic dispositional property of the particles that determines their random discontinuous motion.
I hope these answers may be helpful.
Best,
ShanI should clarify one point for my argument. My argument, if valid, only says that the wave function describes certain state or property of a single quantum system, and it does not imply that the wave function itself is real, e.g. the wave function describes a continuous field a la Albert.
What physical state or property the wave function describes is a further question that needs to be studied. I do have an idea in this regard (http://philsci-archive.pitt.edu/10659/), which has been studied by me for 20 years. The idea is very similar to Bob’s picture of ergodic motion of particles.
According to this idea, the wave function of an N-body quantum system describes the state of random discontinuous motion of N particles, and in particular, the modulus squared of the wave function gives the probability density that the particles appear in every possible group of positions in space. At a deeper level, the wave function may represent the indeterministic dispositional property of the particles that determines their random discontinuous motion.
Matt #1079:
“But I still don’t see how this affects are operational argument, which is independent of the details of Bob’s strategy – we only need to to be right about what Charlie (the protector) does.”
Yes, this is the crux; what Charlie (the protector) does is not a PM. For example, in your scheme, one get many inaccurate expectation values, from which the right one is derived. But in a PM, one directly get the right expectation value with arbitrary accuracy.
SO, I think your argument is indeed valid, but your conclusion is not.
Best,
ShanHi Max and Ken,
Thanks for your comments! As to Ken’s question #1, I think the quantities measured by PMs are not probabilities. They are expectation values of observables.
As to Ken’s second question: yes, the argument, if valid, also establishes the reality of multi-particle entangled states. But this does not imply ehese configuration-space-states are somehow ‘real’, such as according to Albert’s view. The state may describes ergodic motion of particles in real space. As you may know, this is the interpretation of the wave fucntion I have been studied (http://philsci-archive.pitt.edu/10659/).
Best,
ShanHi Matt,
After I have re-read your notes, I still think that your scheme is different from the PM scheme in either form (Zeno or adiabatic). Your scheme is equivalent to weak measurements of an ensemble of identically prepared systems, as Bob noted. So, it might be not surprising that one cannot argue for the reality of the wave function based on the scheme.
In your scheme, one get many inaccurate expectation values, from which the right one is derived.
In a PM, one directly get the right expectation value with arbitrary accuracy.
I would like to know your further response.
Best,
ShanHi Max,
Thanks for your comments! I just noticed them. I am reading Matt’s notes about the toy model of PM.
I think your above worry in #1056 is right, which is still related to the limit problem we discussed in your presentation. I think I have two solutions: one is the new criterion, and the other is my PBR-like argument.
Yes, I still think a Zeno-type PM is equally indicative of the reality of the wave function as an adiabatic PM. I have argued that knowing the wave function beforehand does not influence my argument. The main reason, as you may know, is as follows:
The wave function is only a mathematical object associated with the prepared physical system, and we need to determine whether it refers to the physical state of the system or to the state of an ensemble of identically prepared systems. In this sense, although the wave function is known, the physical state of the system is still unknown. Thus, precisely speaking, what the protective measurements measure is not the known wave function, but the unknown physical state, which turns out to be represented by the wave function.
Best,
ShanMatt #1048:
I think there is an essential difference between we know nothing about the measured system and we know something about it.
If we know nothing about the measured system, then we cannot surely measure the wave function of a single system, and we cannot distinguish nonorthogonal states either, while if we know something about it, we may have enough information to do these by PMs.
I think this may influence your claim in 3.2.
Best,
ShanHi Max,
why not say something about Matt’s ideas. Please join in! We may extend our discussions if you have time.
Shan
Hi Bob,
Thanks for your further comments! I fully agree with you. Yes, what PMs measures are just the density and flux density. The wave function is then constructed from these. My conclusion from PMs is that the wave function describes a property of a single quantum system. But which property it describes is a further problem. I have even proposed an interpretation of the wave function in terms of ergodic motion of particles, which is quite like your picture (see http://philsci-archive.pitt.edu/10659/ or relevant papers).
Best,
ShanHi Matt,
Relative to #1041, I now think there are no essential difference, and yours may be regarded as an interesting extension of the original Zeno PM.
My another point is that even if your alternative protocol does not establish the reality of the wave-function, this does not necessarily imply that the original PM cannot do that.
Moreover, your claim “But the only POVM that can perfectly distinguish a set of basis states is the projective measurement in that basis” seems not right for PMs where we know the measured wave function beforehand.
Also, I think an adiabatic PM can obtain more information than logN bits from Alice’s system. One may not know the Hamiltonian and the wave function of the system beforehand, but one can obtain the values of the wave function in the whole space by PMs.
No doubt, I will need to think more deeply about your interesting ideas. I will get back to you when I have any other comments. Thanks again!
Best,
ShanHi Matt (P),
Thanks for your kind reply!
My point is still that the resources provided by your protecting channel is not exactly those provide by a PM. An adiabatic PM can provide more resources (when the protection based on energy conservation is ensured, e.g. when a
lower bound of the energy gaps to other levels is known beforehand). These resources will allow the whole spatial wave function of the system to be measured points by points.Shan
Hi Matt (L),
Relative to #1033, I think it is an interesting idea, which has not been discussed in the literature. That will require to transform the time parameter in the adiabatic scheme into the frequency parameter in the Zeno scheme.
Shan
Hi Matt,
Thank you very much for your clarification!
I think the measurement in Matt’s notes is not exactly the Zeno-type PM either. There is at least one difference as far as I can see. In the Zeno version, there are indeed frequent projective measurements to protect the measured state. But the measurement of the studied observable is usually a strong measurement. Moreover, the frequency of the projective measurements is required to be very large to ensure the accuracy of the obtained expectation value of the measured observable. These features do not appear in your scheme of measurements.
I will think more about your scheme.
Shan
PS. There is an essential difference between a weak measurement and a protective measurement. The former, as you noted, can only provide an extremely inaccurate estimate of the expectation value of the measured observable, but the latter can obtain the expectation value of the measured observable with arbitrary accuracy.
Dear Matt,
I think your argument is valid. But I notice that, (I think Max will also agree with me), the measurement you discussed is not exactly the protective measurement, but a series of weak measurements (plus projective measurements) on one of a known set of orthogonal bases.
For an (adiabatic) protective measurements, the only information which is needed is that the system is in a nondegenerate eigenstate of its Hamiltonian (and a
lower bound of the energy gaps to other levels, which is enough to fix the strength and the adiabaticity of the measuring coupling), while the Hamiltonian and the state may be unknown. An example is a trapped atom, where the potential may not be known beforehand, but one does know that after a sufficiently long time the atom is to be found in the ground state.So, in my opinion, your analysis does not argue against the possible implications of PM for the ontological status of the wave function.
Shan
Dear Matts,
I just got up. I am reading your interesting paper, and trying to understand your ideas. I will respond soon.
Shan
A very short note: I have read to 3.1. I noticed that 2.2 and 3.1 may be problematic. The measurement you discussed is not precisely PM.
Hi Ruediger,
Thanks a lot for your answers to my questions!
I am sorry for the wrong schedule. May you be available this evening in Egham? I can set a new time slot suitable for you.
Best,
ShanThanks, Ken.
I’m also one of those (few?) realists who think we can force multiparticle QM back into ordinary spacetime (via random discontinuous motion of particles, in my case).
Hi Max,
Thanks for your answers! I admit one of your objections to the new criterion is valid; there are indeed two fundamentally different types of disturbance.
I think the new criterion can be further improved to avoid this new objection. It is:
“If, by disturbing a system with probability arbitrarily close to zero, we can predict with probability arbitrarily close to unity the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.”
Think about the modern definition of derivative. I think this criterion can be equivalent to the original EPR’s, and it is more suitable for the quantum cases.
Shan
PS. Based on your objections, I am also beginning to doubt the direct road from measurability to reality. I think an argument to absurdity like PBR argument is better. See my PBR-like argument for psi-ontology in terms of protective measurements. We will discuss this later.
Hi Ken,
This is an intriguing paper. It proposes some interesting novel ideas.
I have two general concerns. One is that the similarity between two math equations seems not to ensure these two equations have the same physical interpretation, as in the case of Nelson’s stochastic mechanics. The other is that Schrodinger’s original derivation of his equation is only a heuristic derivation. So, it seems debatable to draw fundamental physical implications from the derivation.
Thanks, Shan
Dear Lee,
Thanks a lot for your kind reply! I still has one concern. Imagine we prepare an energy eigenstate of an electron or atom in an extremely special and complex external potential. Such a potential can hardly be found in natural environment, and it is arguably that the potential can only be designed and generated by an intelligent being like our human beings. So, it seems that your interpretation still has certain implications for the existence oi aliens like us.
I would like to know what you think about this. Thanks!
Shan
Hi Ruediger and Chris,
I would like to know whether QBism has some unsolved problems in its current stage. I do think some of Bohr’s views on QM are deep, and searching for the ultimate reality may be “risky game”. But I also think that the beautiful mathematical formalism of QM, which was discovered by our intuition and lucky guess, already implies the existence of the underlying physical reality, and we do have abilities (though not logical) to discover some aspects of reality,
Shan
Moreover, I also addressed the scaling problem you pointed out in your PM paper.
I think in order to argue for the reality of the wave function in terms of protective measurements, it is not necessary to directly measure the wave function of a single quantum system, and measuring the expectation value of an arbitrary observable on a single quantum system is enough.
If the expectation values of observables are physical properties of a single quantum system, then the wave function, which can be reconstructed from the expectation values of a sufficient number of observables, will also represent the physical property or physical state of a single quantum system.
Shan
Hi Max,
As you may already know, I answered one of your objections in my edited PM book. Here is a brief summary. But I am not sure whether it is successful.
I think your objection based on the fact that a realistic protective measurement can never be performed on a single quantum system with absolute certainty does apply to the usual Einstein-Podolsky-Rosen criterion of reality. However, in my opinion, one may avoid this objection by resorting to a somewhat different criterion of reality, which seems more reasonable and also appropriate for realistic protective measurements.
The new criterion of reality is that if, with an arbitrarily small disturbance on a system, we can predict with probability arbitrarily close to unity the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.
Although a realistic protective measurement with finite measurement time T can never be performed on a single quantum system with absolute certainty, the uncertainty and the disturbance on the measured system can be made arbitrarily small when the measurement time T approaches infinity (in theory). Thus according to this criterion of reality, realistic protective measurements also support the reality of the wave function.
I would like to know your response.
Shan
Hi Lee,
In your real ensemble interpretation, a quantum system is one of N similarly constituted systems in the universe, which have been prepared in the same state and are subject to the same external forces as they evolve.
Since an external potential is usually classical and generated by a macroscopic system, this seems to require that there are also N similarly constituted macroscopic systems such as our human beings.
Thus, your interpretation seems to imply that there exist many other human beings living in other places of the universe.
Moreover, it seems that each of the N similar macroscopic systems also has a quantum wave function according to your interpretation, and their behaviors will be not classical.
Are these understandings right? Could you explain a little more detail about your interesting new idea?
Best,
ShanPS. Since the maximum file size allowed is 2148 KB, you will be unable to upload a larger pdf file. Sorry for the inconvenience.
Hi Richard,
Since I will be unable to participate in the text chat about your upcoming presentation, I give a few comments here in advance.
In my opinion, it seems difficult for such a view to explain the results of protective measurements.
During a protective measurement, the measured state is protected by an appropriate procedure (e.g. via the quantum Zeno effect) so that it neither changes nor becomes entangled with the state of the measuring device appreciably. In this way, such protective measurements can measure the expectation values of observables on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. Moreover, the whole wave function of the system can also be measured by a series of protective measurements as expectation values of certain observables (Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993).
So, if the wave function can be measured from a single quantum system (without disturbing the system), it seems that it should be regarded as something objective about the system. For a detail argument, please see my presentation.
I would like to know what you think about this. Thanks!
Shan
Further clarifications of the PBR-like argument
1. The above protective measurements on the two protected nonorthogonal states are the same. (The protection can be regarded as one part of the state preparation procedure.)
2. Although a realistic (adiabatic) protective measurement with finite measurement time T can never be performed on a single quantum system with absolute certainty, the uncertainty can be made arbitrarily small when the measurement time T is arbitrarily long according to QM.
3. Protective measurements generally require the measured states be known. But knowing the wave function beforehand is not a weak point in my argument.
The wave function is only a mathematical object associated with the prepared physical system. Although the wave function is known, the physical state of the system is still unknown. Thus, strictly speaking, what the protective measurements measure is not the known wave function, but the unknown physical state, which turns out to be represented by the wave function.
A PBR-like argument for psi-ontology in terms of protective measurements
For two arbitrary (protected) nonorthogonal states of a quantum system, select an observable whose expectation values in these two states are different. Then the overlap of the probability distributions of the results of protective measurements of the observable on these two states can be arbitrarily close to zero (e.g. when the measurement interval T approaches infinity for adiabatic measurements).
If there exists a non-zero probability p that these two (known) nonorthogonal states correspond to the same physical state λ, then when assuming the same λ yields the same probability distribution of measurement results as the PBR theorem assumes, the overlap of the probability distributions of the results of protective measurements of the above observable on these two states will be not smaller than p. Since p is a determinate number, this leads to a contradiction.
This argument only considers a single quantum system, and avoids the nontrivial assumptions used by the PBR theorem and improved theorems.
Protective measurements
During a protective measurement, the measured state is protected by an appropriate procedure (e.g. via the quantum Zeno effect) so that it neither changes nor becomes entangled with the state of the measuring device appreciably.
In this way, such protective measurements can measure the expectation values of observables on a single quantum system, even if the system is initially not in an eigenstate of the measured observable.
Moreover, the whole wave function of the system can also be measured as expectation values of certain observables in principle.
A long-standing question in QF is whether the wave function relates only to an ensemble of identically prepared systems or directly to the state of a single system.
Recently, Pusey, Barrett and Rudolph demonstrated that under an appropriate assumption, the wave function is a representation of the physical state of a single quantum system (Pusey, Barrett and Rudolph 2012).
This poses a further interesting question, namely whether the reality of the wave function can be argued without resorting to nontrivial assumptions (cf. Lewis et al 2012; Colbeck and Renner 2012; Schlosshauer and Fine 2012, 2013; Leifer and Maroney 2013; etc).
In this presentation, I will argue that protective measurements, by which one can measure the expectation values of observables on a single quantum system (Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993), already provide such an argument.
