Epistemic view of the wave function leads to superluminal signal

[MichPod]

Hope, I do not violate any forum rules here, this is not a discussion topic, mostly. I am just asking for help looking for a specific article/work.

I just remember reading somewhere that there is a QM theorem or article saying smth. in a sort that if the same physical "ontic" state would be represented in QM by two distinct wave functions, then the superluminal communication could be made possible. Can somebody remind me a reference to this work? I did a search with google for no result.

Beyond this very specific question, here is one that may be of some common interest. Could you recommend any resource which reviews or lists modern topics/articles/results in QM foundations, like recent PBR theorem for instance? As a layman not related to scientific society, I many times realized of how mahy things I do not know just because I did not have any chance to know such a thing exists.

 

[A. Neumaier]

Could you recommend any resource which reviews or lists modern topics/articles/results in QM foundations

As a start, I'd recommend to read in the reprint book by Wheeler and Zurek ''Quantum theory and measurement'' which gives the sources of the discussion up to around 1982. For newer stuff look at https://arxiv.org/abs/quant-ph/0312059. from 2005.

 

[Demystifier]

The PBR theorem says something similar to your bold claim, but as you seem to be familiar with the PBR theorem, you probably look for something else.

 

[A. Neumaier]

Superluminal features are built into Born's rule, independent of the interpretation. See
https://www.physicsforums.com/posts/5923754/
This shows that Born's rule cannot be valid in the relativistic regime, where the speed of light limits material transport.

 

[Demystifier]

Superluminal features are built into Born's rule, independent of the interpretation. See
https://www.physicsforums.com/posts/5923754/
This shows that Born's rule cannot be valid in the relativistic regime, where the speed of light limits material transport.

That sounds very much like the Einstein's incompleteness argument.

 

[A. Neumaier]

That sounds very much like the Einstein's incompleteness argument.

Can you point to what is similar in his and my argument? As far as I can tell, nobody before has noticed this problem of Born's rule. Thus I'd be very interested in pointers to the contrary.

 

[MichPod]

The PBR theorem says something similar to your bold claim, but as you seem to be familiar with the PBR theorem, you probably look for something else.

Well, I remember PBR did not talk about superluminal communication, but Wikipedia looks to say exactly what I was looking for: "The [PBR] theorem states that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance." Looks like that is the original quote I remembered and was searching for. That's funny.

Thank you for the help.

 

[Demystifier]

Can you point to what is similar in his and my argument? As far as I can tell, nobody before has noticed this problem of Born's rule. Thus I'd be very interested in pointers to the contrary.

Well, I am not saying that your complete argument is similar to the Einstein's. I am just saying that the two sentences above sound similar to his argument. And by that I mean the EPR argument, which I believe you are familiar with. You both start from the assumption of locality and conclude that then standard QM must be wrong in some sense.

 

[A. Neumaier]

Well, I am not saying that your complete argument is similar to the Einstein's. I am just saying that the two sentences above sound similar to his argument. And by that I mean the EPR argument, which I believe you are familiar with. You both start from the assumption of locality and conclude that then standard QM must be wrong in some sense.

Well, standard QM is nonrelativistic QM, and we all know what is wrong with it: It doesn't account - and doesn't claim to account - exactly for relativistic effects. Everything is assumed to happen instantaneously, including measurements and collapse.

Only relativistic QFT makes the claim to fully account for relativistic effects. But relativistic QFT uses only the special case of Born's rule where it applies to the interpretation of scattering amplitudes, and this use is covariant since the S-matrix is. Unlike Born's rule, QFT makes no claim about what happens when measuring arbitrary observables.

Thus QFT avoids the problems that plague the nonrelativistic theory when one imposes upon it arbitrarily a finite speed limit. Complaining about causality problems in nonrelativistic quantum mechanics because of superluminal effects is like complaining that the classical heat equation (which is manifestly nonrelativistic) is faulty since it allows for faster than light communication.

 

[A. Neumaier]

Wikipedia looks to say exactly

Please edit your post by adding a link to the source you were using.

 

[MichPod]

Please edit your post by adding a link to the source you were using.

Done.

 

[Demystifier]

Unlike Born's rule, QFT makes no claim about what happens when measuring arbitrary observables.

Suppose that we have an entangled pair of spatially separated particles.
1) What happens with the second particle when we measure the first, according to non-relativistic QM?
2) What happens with the second particle when we measure the first, according to relativistic QFT?

 

[A. Neumaier]

Suppose that we have an entangled pair of spatially separated particles.
1) What happens with the second particle when we measure the first, according to non-relativistic QM?
2) What happens with the second particle when we measure the first, according to relativistic QFT?

1) According to which interpretation?
2) What do you mean by a measurement of a particle, in terms of quantum fields?

 

[Demystifier]

1) According to which interpretation?
2) What do you mean by a measurement of a particle, in terms of quantum fields?

1) Your interpretation.
2) The thing measured in the Aspect's experiment.

 

[A. Neumaier]

QUOTE="Demystifier, post: 5986841, member: 61953"]Suppose that we have an entangled pair of spatially separated particles.
1) What happens with the second particle when we measure the first, according to non-relativistic QM?
2) What happens with the second particle when we measure the first, according to relativistic QFT?[/QUOTE]
1) According to which interpretation?
2) What do you mean by a measurement of a particle, in terms of quantum fields?

1) Your interpretation.
2) The thing measured in the Aspect's experiment.

1) Nothing. In my thermal interpretation, particles are properties of quantum fields manifesting themselves only in the detectors. Before detection, one just has beams of light in an entangled state.
2) I still cannot tell what you mean. In relativistic QFT, particles and their states are derived, asymptotic and hence approximate concepts. For particles, the only thing conventional QFT says is something about the probability of a large ensemble of equally prepared scattering events. Thus if you can give me a description of ''The thing measured in the Aspect's experiment'' in terms of such an ensemble, I can tell you what happens.

 

[Demystifier]

2) I still cannot tell what you mean. In relativistic QFT, particles and their states are derived, asymptotic and hence approximate concepts. For particles, the only thing conventional QFT says is something about the probability of (a large ensemble of equally prepared) scattering events. Thus if you can give me a description of ''The thing measured in the Aspect's experiment'' in terms of such an ensemble, I can tell you what happens.

But the theory should explain the experiment, not the other way around.

 

[Demystifier]

1) Nothing. In my thermal interpretation, particles are properties of quantum fields manifesting themselves only in the detectors. Before detection, one just has beams of light in an entangled state.

So what replaces the Born rule in your interpretation?

 

[A. Neumaier]

But the theory should explain the experiment, not the other way around.

It is explained by making the conventional nonrelativistic approximation, idealizing the measurement process, and avoiding saying what happens to individual particles. In this way you get an approximate description sufficient to explain the statistics and to see the difference to the predictions of local hidden variable theories.

So what replaces the Born rule in your interpretation?

I had explained it a number of times in various threads here where you participated in the discussion. Maybe you should read the page I linked to; there is a complete description (look for Uncertainty principle and Measurement rule).

 

[Demystifier]

and avoiding saying what happens to individual particles.

But something does happen to individual particles, doesn't it? So would you say that quantum theory is an incomplete theory in your interpretation? (Which, by the way, was also an Einstein's conclusion, which makes another similarity with his views.)

 

[A. Neumaier]

But something does happen to individual particles, doesn't it?

Yes - they are detected. That's the only thing that happens to particles. They are idealizations that don't exist before the detection event. In the beams there are no particles, only quantum fields. This is how one can uphold the Copenhagen interpretation in the strong form that particles have no properties unless detected, without having to give up a sense of reality for the time in between preparation and detection or for macroscopic objects.

So would you say that quantum theory is an incomplete theory in your interpretation?

Yes if you mean by ''quantum theory'' just fixed-particle number quantum mechanics: It is incomplete in that the quantum fields are missing that mediate the detection events.

 

[bhobba]

"The [PBR] theorem states that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance."

Read the paper - not commentary on it - it's not hard:
https://arxiv.org/pdf/1111.3328.pdf

Here is the relevant bit:
Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes. The other main assumption is that systems that are prepared independently have independent physical states.

See the bold bit - many interpretations do exactly that. Basically PBR says even if you think the state is real in a quite weak sort of sense then it must actually be real is a much stronger sense. But the out is you do not have to think of it as real at all - you can think of it like probability - just as an aid to calculation. That would be the view of approaches like the Baysian Interpretation which relies on Gleason's famous theorem - a proof of which I posted ages ago:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

See post 137.

Now the issue becomes - what is real? That is philosophy pure and simple and we do not get into here. But most would not consider probabilities as real - just an aid to calculate certain things. That may be right, or wrong, but those that use it don't really worry about it - most have a frequentest sort of view on it and some prefer Bayesian - me - I choose the one appropriate to the problem - which is nearly always frequentest. The Ensemble interpretation of QM is basically frequentest.

Thanks
Bill

 

[bhobba]

As a layman not related to scientific society, I many times realized of how mahy things I do not know just because I did not have any chance to know such a thing exists.

Well first you have to decide if you are serious about this or not.

If serious read Dr Susskinds books - The Theoretical Minimum:
https://www.amazon.com/Books-Theore...bin:The Theoretical Minimum&tag=pfamazon01-20

If not then Omnes book is reasonably up to date for lay persons:
https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20

BTW even though I haven't commented on it Dr Neumaier is correct in emphasizing understanding QM is not really the critical thing - QFT is. But in that he has left me far behind as my knowledge of QFT is not on a par with his. But first try to understand normal QM as much as you can - going to QFT without a good foundation in ordinary QM is not advisable.

Thanks
Bill

 

[A. Neumaier]

Well, I remember PBR did not talk about superluminal communication, but Wikipedia looks to say exactly what I was looking for: "The [PBR] theorem states that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance."

But this is the opposite of what the authors claim. In the abstract of their paper https://arxiv.org/abs/1111.3328 (published in Nature Phys. 8, 475 (2012)),

we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions which contradict those of quantum theory.

Thus assuming each object has its own state, they claim to get a contradiction (though I didn't check their arguments). If only the ensemble has a state, nothing is claimed. For an ensemble is traditionally supposed to consist of identically and independently prepared systems, which is the exact opposite of the second assumption stated in the abstract.

 

[bhobba]

Thus assuming each object has its own state, they claim to get a contradiction

The implications of PBR is rather complex. Schlosshauer has shown that for each interpretation where it holds you can find one it doesn't, and if I remember conversely:
https://arxiv.org/pdf/1203.4779.pdf

He also thinks it is not quite what it seems when examined carefully enough and is, in his words, a bit of an overreach:
https://arxiv.org/pdf/1306.5805.pdf

Personally I was very enthused with the theorem when I first saw it, but am now not that enamoured.

Thanks
Bill

 

[MichPod]

Read the paper - not commentary on it - it's not hard:
https://arxiv.org/pdf/1111.3328.pdf

I actualy did read PBR article, at least some parts of it to understand the idea of the proof. It's just that I was now looking for something else which turned out to be a wikipedia quote on the same subject.
True, I did not realize in the beginning its results are not universal or limited i.e. do not rule out non-ontic theories as many people say.

Btw, how is understanding of QFT may be more important/critical than of QM? I thought that they both have basically the same foundational problems i.e. that QFT does not resolve any foundational problem QM has, just inherits all of them.

Btw2. Going back to my original message (looking for a resource which reviews or lists modern topics/articles/results in QM foundations), I once tried to start a page on a wikiversity site "https://en.wikiversity.org/wiki/Quantum_Mechanics_Beyond_Textbooks" referencing partly advanced partly not well known stuff in QM from a layman/QM student perspective. I think that may be quite an interesting idea, useful for the QM students. I had many references to put in yet unfortunately I realized in the end that this project is much above my competence to select the right topics. I did not want to produce some unreliable low quality resource, so I abandoned making it. I thougt may be somebody here could be interested in contributing to this project https://en.wikiversity.org/wiki/Quantum_Mechanics_Beyond_Textbooks . It could IMO become a very useful page filling some gap between the standard QM books and real research.

 

[bohm2]

Were you looking for this:

The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, it is always possible, in principle, to explain such experimental violations through models based on hidden influences propagating at a finite speed v > c, provided v is large enough. Here, we show that for any finite speed v > c, such models predict correlations that can be exploited for faster-than-light communication. This superluminal communication does not require access to any hidden physical quantities, but only the manipulation of measurement devices at the level of our present-day description of quantum experiments. Hence, assuming the impossibility of using quantum non-locality for superluminal communication, we exclude any possible explanation of quantum correlations in term of finite-speed influences.

https://arxiv.org/pdf/1110.3795v1.pdf

 

[bohm2]

The other main assumption is that systems that are prepared independently have independent physical states.

Can you do science without this assumption?

 

[MichPod]

Were you looking for this: https://arxiv.org/pdf/1110.3795v1.pdf

No. I think I already found what I looked for. That was probably some quote in wikipedia about PBR :-).
Your reference looks interesting, though. Thank you for sharing this.

 

[MichPod]

Well first you have to decide if you are serious about this or not.

If serious read Dr Susskinds books - The Theoretical Minimum:

Bhobba, I already promissed you to read Ballentine, and I am now working through a very nice list of QFT books which you gave me.

 

[bhobba]

Btw, how is understanding of QFT may be more important/critical than of QM? I thought that they both have basically the same foundational problems i.e. that QFT does not resolve any foundational problem QM has, just inherits all of them.

QM has a couple of meanings depending on context. One is the non relativistic theory in beginning/intermediate textbooks. The other meaning is that plus theories that incorporate relativity. If you want to speak of QM+Relativity you call it Quantum Field Theory (QFT). Ordinary QM is a limiting case of QFT. Some believe that it's easier to solve the issues of interpretation in QM by using QFT - here is an example:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

I personally think there may be something to it - but it is advanced - best to understand ordinary QM first. Dr Neumaier's thermal interpretation is of the QFT type.
http://arnold-neumaier.at/physfaq/cei

I freely admit to not fully understanding it, but as an approach it certainly is interesting.

Thanks
Bill

 

[Fra]

Btw, how is understanding of QFT may be more important/critical than of QM? I thought that they both have basically the same foundational problems i.e. that QFT does not resolve any foundational problem QM has, just inherits all of them.

One note that i personally think is important if you have unification of interactions in mind is that the QM vs QFT foundation issue fades as you try to reconstruct state spaces from an abstract starting points and general informationspaces without assuming a classical spacetime index that is a priori separated from internal spaces.

In this sense, QFT just has more baggage which isn't necessarily helpful. Thats not to say Newtonian spacetime is better than relativity but just a note that spacetime itself as we know it may not come out in one piece in this quest at extreme energies and QFT cements more classical spacetime stuff into the picture and i am not sure that is the best approach.

/Fredrik

 

[A. Neumaier]

Formally there are no difficulties with QM - its what it means that's at issue and what the various interpretations grapple with. They all have problems - every single one of them.

I think Dr Neumaier has a good point - QFT may indeed be a better place for interpretations. I do not know enough of his thermal interpretation to comment on its specifics.

Dr Neumaier is correct in emphasizing understanding QM is not really the critical thing - QFT is. But in that he has left me far behind as my knowledge of QFT is not on a par with his. But first try to understand normal QM as much as you can - going to QFT without a good foundation in ordinary QM is not advisable.

how is understanding of QFT may be more important/critical than of QM? I thought that they both have basically the same foundational problems i.e. that QFT does not resolve any foundational problem QM has, just inherits all of them.

There is a basic difference between QM and QFT.

In QM, one prepares tiny systems with very few degrees of freedom, and one can prepare large ensembles of essentially independent systems in the same state. Thus the statistical interpretation makes sense. On the other hand, the question whether a state can be assigned to individual systems, or, if not, how measurements select individual results for each system, pose the well-known interpretational problems.

In (nonrelativistic or relativistic) QFT the fields are functions of space and time, and hence the associated observables can be measured at most once once. Thus the statistical interpretation of their ensemble mean (expectation) makes no experimental sense. However, this is not a problem since no use is made of it anywhere. Indeed, only two kinds of predictions are compared with experiments: Either S-matrix elements, which have an interpretation as transition amplitudes of asymptotic collision events of few particles (a case where Born's rule applies without the slightest philosophical problems), or field expectation values and field correlation functions, which are treated as macroscopic observables, without any statistics involved on the experimental side. Therefore as far as the relation to experiment is concerned, the interpretation of QFT poses no fundamental problems.

What requires interpretation is how the dynamics in the particle view of QM arises from interacting relativistic QFT, which has no number operator and hence no concept of particles at finite time. Related to this question are the issues involved in the measurement problem, since these are about mixing the particle view (for tiny systems) with the field theoretic view (for detectors).

 

[ftr]

one just has beams of light in an entangled state

Are you saying that there is no single particle double slit experiment. Or only in high energy experiments.

 

[A. Neumaier]

Are you saying that there is no single particle double slit experiment. Or only in high energy experiments.

In a double slit experiment, a monochromatic beam of light (i.e., an electromagnetic field in a special state deserving to be called a ''monochromatic beam of light'') passes through a screen with two slits and causes a response on a screen. That's all.

In the single particle case: If the beam of light before the screen can be approximated by a single wave packet (in a Fock state) whose total energy is $\hbar\omega$ where $\omega$ is the frequency (this is a ''single photon on demand''), then it can be approximated after the screen by a superposition of two wave packets (this is still a ''single photon''). The energy is enough to cause only a single detection event on the screen, with a probability proportional to the incident field energy. This implies that the event generated is consistent with the diffraction pattern generated by the slits. It this happens a number of times, the events will display the full diffraction pattern. This explanation works whether the field is treated classically or by QED.

In the multiparticle case: There is no consistent interacting relativistic multiparticle theory, neither in a classical nor in a quantum version. (This excludes for simplicity a trickle of papers not accounted for by the main stream.) Thus any consistent model featuring a natural speed limit will have to be a relativistic quantum field theory.

In the thermal interpretation, the only thing left of the particle picture is the detection event. One doesn't need more.

 

[MichPod]

The energy is enough to cause only a single detection event on the screen, with a probability proportional to the incident field energy.

But how does this "detection event" happen to appear only at one particular coordinate, while the quantum field is spread over the whole screen? I.e. what causes the "wave collapse" on measurement in your way of interpretation?

QM just postulates "measurement" and "wave collapse", at least in the Copenhagen interpretation. Is it not the case that you also postulate the existence of local detection events?