Hidden Assumptions in Bell's Theorem?

[mattt]

I guess we all agree on the mathematics, but different people describe this mathematical piece with very different words.

Some questions to try to reach an agreement:

1. Do Alice and Bob ( communicating among themselves, but not with Victor) have a way of knowing if Victor made/is making/will make a BSM measurement on pairs 23 ?

If not, even if our description of the state of a subensemble has really changed, are we comfortable saying that "something has changed/is changing/will change backwards for Alice and Bob 14 particles", even if there is no way to verify ( by means of measurements) this claim?

 

[PeterDonis]

I guess we all agree on the mathematics

Please note that equations in images are not acceptable. Please use the PF LaTeX feature to post equations directly. There is a "LaTeX Guide" link at the bottom left of each post window.

 

[vanhees71]

In single pair experiment, yes. Do you even realize that in swapping 1&4 are NOT entangled ? which is the point ?

Sigh, I repeatedly explained this. The point of swapping is that you start with a state of the form
$$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34},$$
i.e., in the initial state photons 1 and 2 are not entangled in any way with photons 3 and 4. Photons 1&2 and photons 3&4 are maximally entangled in the polarization-singlet state.

When projecting photons 2&3 to the polarization-singlet state, which occurs in 1/4 of the cases, the so prepared ensemble is in the state
$$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

Nobody is interested by explanation. Actually there is NONE. You opinions about instantaneous action, whatever that means, are immaterial.

Then, why do you deny the simple fact that in QED there are no actions in a distance, i.e., no FTL signals, etc? If it's anyway immaterial you need not to deny mathematical properties of the theory!

The same as everybody else, including you. Example:

But as usual, in the very next sentence you contradict yourself

No, in every sense possible, those observations and ticks are non-local. That's why you cannot observe Bell's violation but by waiting for those non-local records, to be confronted/compared (by non-FLT/classical means)). Only then non-local correlation are observed. Only the final merging of those non-local post observation actually reveal entanglement.

That's not, what I wrote.

Correct

Now, who is contradicting himself again ?So it's not classical, but not spooky, and NATURE behave like QM predicted, and not the other way around ?I follow the thread. Do you ? 2&3 ordering with 1&4 is IRRELEVANT. In other word acausal

What do you mean by ordering?

Don't worry, cryptographer, quantum-computer scientist, and bankers do.

 

[vanhees71]

View attachment 320844
I guess we all agree on the mathematics, but different people describe this mathematical piece with very different words.

Some questions to try to reach an agreement:

1. Do Alice and Bob ( communicating among themselves, but not with Victor) have a way of knowing if Victor made/is making/will make a BSM measurement on pairs 23 ?

If not, even if our description of the state of a subensemble has really changed, are we comfortable saying that "something has changed/is changing/will change backwards for Alice and Bob 14 particles", even if there is no way to verify ( by means of measurements) this claim?

I can't read the image, but I hope that all agree on the mathematics, although several people seem to contradict mathematical facts (microcausality) of QED. I've no clue why.

ad 1) No Alice and Bob need to know, whether the photons they discover are chosen due to Victor's Bell measurement, i.e., if the photons they consider are only those, where Victors pair 2&3 has been found to be in the polarization-singlet state (i.e., whether both of his detectors registered a photon). To see the violation of Bell's inequality you have to communicate the outcomes of all three, Alice, Bob, and Victor.

Of course the state has changed, because we have chosen a subensemble due to Victor's projection measurement. You can say that this is a preparation procedure for the new state given the original state of the four photons, and QED predicts that for this subensemble the pair 1&4 is also in a polarization-singlet state.

 

[Simple question]

Spoiler alert: a contradiction is coming.

Sigh, I repeatedly explained this. The point of swapping is that you start with a state of the form
$$\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_{34},$$
i.e., in the initial state photons 1 and 2 are not entangled in any way with photons 3 and 4. Photons 1&2 and photons 3&4 are maximally entangled in the polarization-singlet state.

And you are telling us that QFT/QED allows you to evolve that prepared state deterministically, and microcausaly, leading to an absolute determination of what can be observed.

When projecting photons 2&3 to the polarization-singlet state

When what ? Stop hand-waving. Show me your computations that tell when this happens. It follows microcausality remember ? It must be easy for you.

, which occurs in 1/4 of the cases, the so prepared ensemble is in the state
$$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

Not it is not. Update of knowledge is not part of your favorite philosophy.

Then, why do you deny the simple fact that in QED there are no actions in a distance

I don't, but you do. You've just written that "projection" change preparation state.

Here. Let me help you out with words: QM include spooky correlation at a distance. And they cannot be causally ordered, they just are non-local.

, i.e., no FTL signals, etc? If it's anyway immaterial you need not to deny mathematical properties of the theory!

I don't deny that either, so your point is moot.
What is not, is that you don't understand the implication of micro causality, beyond the no FLT signaling.

That's not, what I wrote.

I quoted verbatim your post #262.
But I am not the only one noticing you also have an idiosyncratic way to understand what "quoting" means.

 

[Fra]

QM include spooky correlation at a distance. And they cannot be causally ordered, they just are non-local.

I guess I do not understand the phrasings.

FTL influence would indeed be "spooky", but we agree there is no such thing.

But what part of a plain correlation deserve to be labeled spooky? Is it spooky we have a hard time to understand a mechanism that violated bells inequality? Is that it? Spooky as in not obeying bell realism?

/Fredrik

 

[Simple question]

I guess I do not understand the phrasings.

FTL influence correlation would indeed be "spooky", but we agree there is no such thing.

Fixed. And this is tested in the lab. So why bother mincing words ?

But what part of a plain correlation deserve to be labeled spooky?

The part that bothered Einstein.

Is it spooky we have a hard time to understand a mechanism that violated bells inequality? Is that it?

Yes, entanglement is spooky.

Spooky as in not obeying bell realism?

or Einstein locality. As per Bell's theorem.

 

[Fra]

FTL influence correlation would indeed be "spooky", but we agree there is no such thing.

Fixed. And this is tested in the lab. So why bother mincing words ?

I try to avoid mincing words, on the contrary do I try to understand the meaning behind. But your editing above still makes we wonder. Am I right to think that you by "FTL correlation" means "spacelike correlation"?

Using the FTL word seems to imply a communication, why else use the term. The only communication I see going on here is the between the observer Victor to the Observer that compares observations from Alice, and Bob (1&4) and the KEY info from Victor that is required to define the postselected ensemble. This is supposedly a classical message. Without receiveing this key, no observer can infer any entanglement.

The part that bothered Einstein.

Ok, we can call this part spooky.

or Einstein locality. As per Bell's theorem.

For me Einstein locality just means there are no FTL causations between remote systems? But where correlations have a previous common cause, they are not a violation of Einstein locality.

While a Bell style HV might have been one way to solve Einsteins original issue. Give his record of doing away with the realism of space and time, not once but twice, had he lived on and digested bells theorem, my bet is that he would have done away with realism of HV as well. Doing away with realism is possibly "spooky".

/Fredrik

 

[vanhees71]

Spoiler alert: a contradiction is coming.

And you are telling us that QFT/QED allows you to evolve that prepared state deterministically, and microcausaly, leading to an absolute determination of what can be observed.

After projecting (2&3) to the polarization-singlet state also (1&4) are in this state. That's due to the interaction of photons (2&3) with the beam splitter and the detectors. This is, of course, in principle described by QED since QED of course also applies to interactions of the em. field with matter.

When what ? Stop hand-waving. Show me your computations that tell when this happens. It follows microcausality remember ? It must be easy for you.

There's no need to do any calculations to know that there's no instantaneous interaction between the photons (2&3) and the equipment used to project them to the said polarization-singlet state with photons 1&4 and the equipment used to measure their polarization at their far-distant places. That's implemented in QED via the microcausality condition. If the registration events of photons (2&3) and 1 and 4 are space-like separated there cannot be causal influences between these measurements.

Not it is not. Update of knowledge is not part of your favorite philosophy.

Of course, as soon as for a given photon pair (2&3) the observer at the place knows that also (1&4) are entangled in the polarization-singlet state. Of course is an update of knowledge part of the minimal interpretation of QT, which I'm follow as an interpretation. That's not philosophy that's physics!

I don't, but you do. You've just written that "projection" change preparation state.

Of course, selecting a subensemble from a given ensemble leads to another state of the subensemble. That I've written.

Here. Let me help you out with words: QM include spooky correlation at a distance. And they cannot be causally ordered, they just are non-local.

Correlation but no interaction/causation! So indeed, finally you agree with what I say for years!

I don't deny that either, so your point is moot.
What is not, is that you don't understand the implication of micro causality, beyond the no FLT signaling.

If there's no FTL (faster-than-light) signalling, then space-like separated detection events cannot cause each other. That's a tautology.

I quoted verbatim your post #262.
But I am not the only one noticing you also have an idiosyncratic way to understand what "quoting" means.

 

[vanhees71]

FTL influence correlation would indeed be "spooky", but we agree there is no such thing.

Fixed. And this is tested in the lab. So why bother mincing words ?

I try to avoid mincing words, on the contrary do I try to understand the meaning behind. But your editing above still makes we wonder. Am I right to think that you by "FTL correlation" means "spacelike correlation"?

The editing in fact is crucial! There's no FTL influence due to microcausality, but there are correlations between far-distant parts of an entangled quantum system. It's of course pretty misleading to call that "FTL". It's just described by the state of the system at a given time (in some arbitrary reference frame).

 

[Fra]

It's of course pretty misleading to call that "FTL".

I totally agree.

But I was trying to be diplomatic in my comment as there seems to be disagreement what is misleading and what is clarifying I suspect this itself is conditional on ones particular state of confusion.

/Fredrik

 

[WernerQH]

After projecting (2&3) to the polarization-singlet state also (1&4) are in this state. That's due to the interaction of photons (2&3) with the beam splitter and the detectors.

Is this "projecting" something physical or mathematical? Have you changed your position with respect to the "collapse of the wave function"?? The word "after" is misleading here. I think QED forces us to consider the entire pattern of events in space-time, and their possible causal connections. The entire sequence, or "history", if you like. The sub-ensemble then encompasses only those sequences where something special (the "Bell state measurement") happened.

The way QED does its magic of correctly mirroring Nature's fine book-keeping has to do with the propagators reaching also into the backward light cone. I don't think you can make the book-keeping consistent if you allow only a local, continuous description that can only evolve forwards in time.

 

[gentzen]

Is this "projecting" something physical or mathematical? Have you changed your position with respect to the "collapse of the wave function"??

I don't think that vanhees71 has changed his position. As he said, he always uses the minimal statistical interpretation. There is no "collapse of the wave function" in that interpretation, but the ensembles and subensembles are of prime importance, and are what gets assigned a state (and what gets "prepared").

The way QED does its magic of correctly mirroring Nature's fine book-keeping has to do with the propagators reaching also into the backward light cone. I don't think you can make the book-keeping consistent if you allow only a local, continuous description that can only evolve forwards in time.

I guess you are simply thinking of something else here than vanhees71. His description is just QED, and not something "local" in the typical Bell-theorem interpretation of that word.

 

[vanhees71]

Is this "projecting" something physical or mathematical? Have you changed your position with respect to the "collapse of the wave function"?? The word "after" is misleading here. I think QED forces us to consider the entire pattern of events in space-time, and their possible causal connections. The entire sequence, or "history", if you like. The sub-ensemble then encompasses only those sequences where something special (the "Bell state measurement") happened.

The way QED does its magic of correctly mirroring Nature's fine book-keeping has to do with the propagators reaching also into the backward light cone. I don't think you can make the book-keeping consistent if you allow only a local, continuous description that can only evolve forwards in time.

It's something physical, because you select only those four photons to be measured, for which the pair (2&3) was found to be in the polarization-singlet state.

Of course you have to consider the entire pattern of events in spacetime, and what's for sure within standard local (=microcausal) QFT is that space-like separated events cannot in any way causally influence each other.

The history is (in any reference frame)

at ##t=t_{12}## pair (1&2) was created in an entangled state (say the polarization-singlet state for simplicity) at a place A'
at ##t=t_{34}## pair (3&4) was created in an entangled state (say the polarization-singlet state for simplicity) at a place B'

The time order of this creation processes is irrelevant. To have them for sure not in causal contact (that's what's aimed at in the entanglement-swapping experiment) you must ensure these creation events to be space-like separated. That can be achieved by simply choosing the inertial reference frame (lab frame) such that ##t_{12}=t_{34}=0##.

Photon 1 will be manipulated with beam-splitters/polarizers and detected at time ##t_1## at a far distant place A

Photons (2&3) will be subject to the projection measurement to the polarization-singlet state at a place C, which can be very far distant from A, at times ##t_{2C}## and ##t_{3C}##

Photon 4 will be manipulated with beam-splitters/polarizers and detected at a far distant place B at time ##t_B##.

For sure for both photons (23) to be detected at C it needs at least a time ##\text{max}(A'C,B'C)/c## since the corresponding wave packets travel with ##c##.

It's also for sure that photons 1 and 4 need the minimal times to reach their detectors given by the speed of light and the distances from their point of creation to the place of detection.

The temporal order of all these measurements is, however, completely irrelevant for the outcome of the photon statistics of the pair (14) given that you select only those for which the pair (23) was found to be in the polarization-singlet state. The result of all measurements on (14) is that they are also in the polarization-singlet state.

The fact that the time order for all these measurement is completely irrelevant for this outcome together with the assumption that standard QED is correct and thus that space-like separated events cannot be causally connected then ensures that all the measurements cannot causally influence in any way each other. Nevertheless through the selection of the pairs for which (23) was found to be in the polarization-singlet state also the before completely uncorrelated pairs (14) are foudn to be in the entangled (and thus maximally correlated) polarization-singlet state.

These arguments show clearly that under the assumption that standard QED is right that these correlations are not due to a causal influence of the measurements, and indeed QED, which was used to come to this prediction, tells us that the correlations are due to the preparation of the pairs (12) and (34) in the polarization-singlet state in the beginning, but these pairs being completely uncorrelated, i.e., in the initial state ##\hat{\rho}=\hat{\rho}_{12} \otimes \hat{\rho}_34}##.

 

[WernerQH]

I guess you are simply thinking of something else here than vanhees71. His description is just QED, and not something "local" in the typical Bell-theorem interpretation of that word.

No, I was thinking of QED. It is true that the field operators satisfy local and even deterministic equations. But they are only statistical representations of possible field configurations. There's more to QED than field operators and their equations of motion: the Born rule forms an integral part of the theory. And applying the Born rule breaks the "locality" of the theory. What's been causing this ongoing kerfuffle is vanhees71's insistence on calling the entire theory "local" based on a heuristic used in the derivation of just a piece of it.

Consider one radioactive atom surrounded by several detectors. At most one of them can register the decay. How do the detectors "negotiate" which one will do this?
Of course, total energy has to be conserved. But adding up the energies absorbed by different detectors is definitely a nonlocal operation.

 

[WernerQH]

It's something physical, because you select only those four photons to be measured, for which the pair (2&3) was found to be in the polarization-singlet state.

[...]

These arguments show clearly that under the assumption that standard QED is right that these correlations are not due to a causal influence of the measurements [...]

I have absolutely no doubts about QED. Thank you for explaining everything once again, but I'm still unable to see your statements as a coherent whole.

 

[gentzen]

No, I was thinking of QED. It is true that the field operators satisfy local and even deterministic equations. But they are only statistical representations of possible field configurations. There's more to QED than field operators and their equations of motion: the Born rule forms an integral part of the theory.

And vanhees71 agrees with this statement. He uses the minimal statistical interpretation to interpret the probabilities from the Born rule.

And applying the Born rule breaks the "locality" of the theory. What's been causing this ongoing kerfuffle is vanhees71's insistence on calling the entire theory "local" based on a heuristic used in the derivation of just a piece of it.

No, the kerfuffle is pretty independent of vanhees71's use of the word "local". He even admits the existence of that non-local part of QM (or QFT), he just prefers to call it "far-distant correlations":
https://www.physicsforums.com/threa...ntum-foundations.1045477/page-10#post-6812647

The question which caused the kerfuffle is more subtle. Even if vanhees71, or martinbn, or I, or LittleSchwinger, or ... would explain it in perfectly clear words, it is still not sure that those who didn't find the answer themselves would get it. vanhees71 is just more motivated to try to explain it, so you get the impression that the problem would be with him.

Consider one radioactive atom surrounded by several detectors. At most one of them can register the decay. How do the detectors "negotiate" which one will do this?
Of course, total energy has to be conserved. But adding up the energies absorbed by different detectors is definitely a nonlocal operation.

There is just one particle from the decay, so the different detectors don't need to negotiate. (Or at least there will be just one particle, if you really have a one-particle state. But your question basically already presupposes that.) Of course, that particle doesn't have properties like a classical particle. It has fewer properties, and those fewer properties even can have strange non-local quantum correlations with properties of other particles. You want to know where those non-local correlations and their quantum randomness comes from? In the end, the information content of the particles must be limited, at least if the energy is limited. So they share their randomness... And where does the randomness itself comes from? I don't know.

 

[WernerQH]

There is just one particle from the decay, so the different detectors don't need to negotiate.

So it's the particle that decides? Does it send out tentacles to each detector? In a continuous, tentative way? Sorry about the sarcasm, I'm too much afflicted with classical thinking.

Of course, that particle doesn't have properties like a classical particle. It has fewer properties, and those fewer properties even can have strange non-local quantum correlations with properties of other particles.

I have no problem with non-local correlations. I think that's what QFT is about. But we should be more explicit about the "correlata". What is it that is correlated? "Particle" is a classical concept, and talk about particle properties (undefined? uncertain? non-local?) just confuses the issues. I'm very much in favour of the (minimal) statistical interpretation. But I think it needs to be supplemented with a minimal ontology: that there are no particles, but just emission and absorption events (localized short-lived currents). Those events are what is correlated, and QED describes just that. What we call photons or electrons is something that we read into the patterns of events in space-time.

You want to know where those non-local correlations and their quantum randomness comes from? In the end, the information content of the particles must be limited, at least if the energy is limited. So they share their randomness... And where does the randomness itself comes from? I don't know.

I don't believe in particles, and therefore they don't need to carry information.
QFT is just fine as statistical theory.

 

[gentzen]

So it's the particle that decides? Does it send out tentacles to each detector? In a continuous, tentative way? Sorry about the sarcasm, I'm too much afflicted with classical thinking.

The way you formulated your question, the implicit assumption of a one-particle state was already there. That is the reason why you know that at most one of the detectors can register the decay. So the property that there is only one particle is certain, and hence that is also the explanation for what you would observe in that case.

But we should be more explicit about the "correlata". What is it that is correlated? "Particle" is a classical concept, and talk about particle properties (undefined? uncertain? non-local?) just confuses the issues.

I don't believe in particles, and therefore they don't need to carry information.

It is not really important whether it is a particle, a quasi-particle or an excitation which carries energy, momentum, spin, and information. The preparation is such that the environment (say a crystal) is in its ground state, and therefore cannot carry information. Only the particle/quasi-particle/excitation has the energy to be in that non-ground state, and therefore carries information. So the particle does not need to be real here, it is sufficient that it is a suitable concept to describe the physical situation caused by the preparation.

I'm very much in favour of the (minimal) statistical interpretation. But I think it needs to be supplemented with a minimal ontology: that there are no particles, but just emission and absorption events (localized short-lived currents).

You are in favor of a statistical interpretation. My impression is that neither vanhees71 nor you fully grasp that "minimal" part. A. Neumaier repeatedly tried to explain that it doesn't apply to the continuous evolution in time of a single system (like the universe), but only to ensembles. But with an ontology, I don't see what would stop you to apply it precisely to such a situation. Or maybe I don't grasp the "minimal" in your minimal ontology.

P.S.: I doubt that anybody else in this thread had this sort of objection to the position of the "postselection" camp. Your objection seems pretty independent of the kerfuffle to me.

 

[vanhees71]

There is just one particle from the decay, so the different detectors don't need to negotiate. (Or at least there will be just one particle, if you really have a one-particle state. But your question basically already presupposes that.) Of course, that particle doesn't have properties like a classical particle. It has fewer properties, and those fewer properties even can have strange non-local quantum correlations with properties of other particles. You want to know where those non-local correlations and their quantum randomness comes from? In the end, the information content of the particles must be limited, at least if the energy is limited. So they share their randomness... And where does the randomness itself comes from? I don't know.

This randomness is just a generic property of Nature. You could as well ask in classical physics, why particles have properties like mass, electric charge, etc. Of course in both classical an quantum physics the "answer" to that question according to modern physics is that a great deal follows from symmetry principles, but then you can ask, why the symmetry principles are the specific ones that describe Nature. In this sense the symmetries are just a description of basic properties of Nature, which cannot be explained by any "more simple" other generic feature of Nature.

After all physics is an empirical science, i.e., its descriptions of phenomena in terms of mathematical theories/models are based on quantitative observations of phenomena, often in experiments, where a well-defined sufficiently separated piece of matter is accurately investigated, and what came out of many such observations in connection also with theoretical analysis and theory/model building is the inherent randomness of Nature, which is described by quantum theory. In this sense QT is just a very efficient book-keeping tool of a vast of single empirical discoveries in a handful of "fundamental rules" or "postulates". That this works for such a vast number of observations is simply a miracle, which cannot be explained. Wigner called it "the incomprehensible effectiveness of mathematics in the natural sciences". Not also Weinberg's dictum about "the incomprensible ineffectiveness of philosophy in the natural sciences", which is, however, another story ;-).

 

[WernerQH]

So the particle does not need to be real here, it is sufficient that it is a suitable concept to describe the physical situation caused by the preparation.

Exactly. It is a way to describe the regularities, the correlations between what is called "state preparation" and "measurement".

A. Neumaier repeatedly tried to explain that it doesn't apply to the continuous evolution in time of a single system (like the universe), but only to ensembles. But with an ontology, I don't see what would stop you to apply it precisely to such a situation. Or maybe I don't grasp the "minimal" in your minimal ontology.

I can't make sense of Neumaier's view at all. For me an ensemble just serves as a "fuzzy" description of its members, (thought) copies of one and the same physical system. Of course, the mathematical description of the ensemble as a whole can have features that are vastly different from that of its members (e.g. continuous and deterministic evolution instead of random jumps, or irreversible instead of reversible dynamics).

P.S.: I doubt that anybody else in this thread had this sort of objection to the position of the "postselection" camp. Your objection seems pretty independent of the kerfuffle to me.

Indeed, I'm not sure to which camp I belong. I just wanted to point out what in my mind is the most "hidden" of the assumptions of Bell's theorem: the existence of particles.

 

[WernerQH]

Of course, that particle doesn't have properties like a classical particle. It has fewer properties, and those fewer properties even can have strange non-local quantum correlations with properties of other particles.

Isn't it absurd to insist on having a "local" theory, and introduce* such bizarre non-local "objects" at the same time?

"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them."

(George Orwell, 1984)

*Actually, they are not introduced, but are leftovers from classical physics, superfluous metaphysical baggage like the ether.

 

[vanhees71]

Exactly. It is a way to describe the regularities, the correlations between what is called "state preparation" and "measurement".

The quantum state operationally describes the preparation procedure, and its meaning is solely probabilistic, i.e., it is a mathematical tool to calculate the probabilities for the outcome of measurements on the so prepared system.

For me, and other followers of the minimal statistical interpretation, this implies that the corresponding probabilistic predictions about the outcome of measurements can only be tested by repeating the measurement on an ensemble of equally prepared systems.

This means that on the one hand the quantum state refers to the single member of this ensemble, because it's the formal description of the properties this system has because of the corresponding preparation procdedure. On the other hand, concerning the meaning for measurements of observables of this system, it refers only to an ensemble.

I know that there are many physicists and almost all philosophers, who try to associate an extended meaning to the quantum state (formally described by a statistical operator) and the probabilities predicted by the quantum formalism. However, for me that's metaphysics, i.e., it's unnecessary for the application of the formalism to the real-world experiments.

I can't make sense of Neumaier's view at all. For me an ensemble just serves as a "fuzzy" description of its members, (thought) copies of one and the same physical system. Of course, the mathematical description of the ensemble as a whole can have features that are vastly different from that of its members (e.g. continuous and deterministic evolution instead of random jumps, or irreversible instead of reversible dynamics).Indeed, I'm not sure to which camp I belong. I just wanted to point out what in my mind is the most "hidden" of the assumptions of Bell's theorem: the existence of particles.

The question what "particles" are in connection with their description with relativistic QFT is another can of worms, which we should not open in this thread but in a separate one if needed.

 

[martinbn]

Isn't it absurd to insist on having a "local" theory, and introduce* such bizarre non-local "objects" at the same time?

I think it is inconvinient to use the same word "non-local" to mean different things. What is confusing is when some do so without specifying what they mean by it. What is absurd is when some specify that they mean one thing by that term, and then use a different meanings in their argumnets!

 

[WernerQH]

I think it is inconvinient to use the same word "non-local" to mean different things. What is confusing is when some do so without specifying what they mean by it. What is absurd is when some specify that they mean one thing by that term, and then use a different meanings in their argumnets!

Yes, it's the perfect method for making doublethink less obvious.

 

[vanhees71]

That's why I insist in using local/non-local in the clear mathematical way of relativistic QFT: The theory/interactions are local, because local observables/the Hamilton-density operator obey the microcausality principle, i.e., local-observable operators commute if their space-time arguments are space-like separated. This implies that there's no FTL-signalling and thus no causal connection between space-like separated measurement events (like detector clicks).

Then, of course, the in this sense local QFT should also describe the correlations between far-distant parts of a quantum system in an entangled state, and indeed there is no problem whatsoever, and these correlations have indeed nothing whatsoever to do with any "non-locality" (in the above sense), i.e., they describe not "spooky interactions at a distance" but the "inseparability" of entangled quantum systems.

One should note that the "spooky interactions at a distance" can only be an argument against QT, if one insists on a "collapse of a quantum state" as a physical event. There is no collapse in general, and it's only a description of how an observer, who takes note of an outcome of a filter measurement, i.e., a projection, i.e., it describes the update of the knowledge of this observer rather than a physical process on the measured system.

E.g., in the here discussed case of entanglement swapping: The observer who does the projection measurement of the pair (2&3) to the polarization-singlet state knows that he can describe the four-photon state in the so perpared subensemble (1/4 as big as the original full ensemble) by the state ##\hat{\rho}_{14} \otimes \hat{\rho}_{23}## (where ##\hat{\rho}_{jk}=|\Psi^{(-)} \rangle\langle \Psi^{-}|## are the polarization-singlet two-photon states).

However nothing can have happened to the photons 1 and 4 (at least not instantaneously) due to the measurement on the pair (2&3) due to the microcauslity constraint valid in QED. Indeed, to select the subensemble due to the filter measurement on (2&3), one has to communicate about the outcome of measurements on photon 1, of the filter measurement on (2&3), and on photon 4, which can only be done by comparing the corresponding measurement protocols, and this can be done only with usual communication, which can only be done with "signals" which propagate at most with the speed of light.

 

[Demystifier]

"Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them."

(George Orwell, 1984)

Copenhagen interpretation is full of doublethinks, here are some:
- A scientific theory only talks about what can be measured, the uncertainty principle is a fundamental scientific principle that says something about intrinsic properties of quantum systems irrespective of our measurements.
- The state ##\psi## provides a complete physical description of a single system, it determines a probability which is physically meaningful only for an ensemble of systems.
- The Hamiltonian describes a deterministic evolution of the state. Since the Hamiltonian is local, the probabilistic measurement outcomes cannot violate locality.

 

[vanhees71]

Well, yes, Heisenberg is utmost confusing, even more so than Bohr. SCNR.

The first point doesn't make sense. What's meant is that only such observables take determined values, if the system has to be prepared in a state describing this property. E.g., the helicity of a photon takes the determined value ##h=1## if this photon has been prepared to be in a left-circular state. All other observables may be indetermined. All the preparation in a given state tells are the probabilities for the value of an observable, when this observable is measured.

Concerning the second point I think there's some truth in this "doublethink", as I said in #303:

The quantum state operationally describes the preparation procedure, and its meaning is solely probabilistic, i.e., it is a mathematical tool to calculate the probabilities for the outcome of measurements on the so prepared system.

For me, and other followers of the minimal statistical interpretation, this implies that the corresponding probabilistic predictions about the outcome of measurements can only be tested by repeating the measurement on an ensemble of equally prepared systems.

This means that on the one hand the quantum state refers to the single member of this ensemble, because it's the formal description of the properties this system has because of the corresponding preparation procdedure. On the other hand, concerning the meaning for measurements of observables of this system, it refers only to an ensemble.

The third point is completed clear and valid. Due to the microcausality condition there cannot be a causal connection between a measurement in one region of spacetime and one in another region of space time that is spacelike separated to the former.

 

[martinbn]

Copenhagen interpretation is full of doublethinks, here are some:
- A scientific theory only talks about what can be measured, the uncertainty principle is a fundamental scientific principle that says something about intrinsic properties of quantum systems irrespective of our measurements.
- The state ##\psi## provides a complete physical description of a single system, it determines a probability which is physically meaningful only for an ensemble of systems.
- The Hamiltonian describes a deterministic evolution of the state. Since the Hamiltonian is local, the probabilistic measurement outcomes cannot violate locality.

Why are these double think? What exactly contradicts what?

 

[Demystifier]

Why are these double think? What exactly contradicts what?

Compare the italic words.

 

[martinbn]

Compare the italic words.

That is not double think, it's just being imprecise. Otherwise it is everywhere. For example: number theory, prime numbers are numbers that cannot be factorized. Primes of the form ##p=4k+1## factor in two distinct factors in the ring of Gaussian integers.

 

[Demystifier]

That is not double think, it's just being imprecise. Otherwise it is everywhere. For example: number theory, prime numbers are numbers that cannot be factorized. Primes of the form ##p=4k+1## factor in two distinct factors in the ring of Gaussian integers.

Fair enough! Can you rewrite my examples of "doublethinks" as precise statements?

 

[LittleSchwinger]

- The Hamiltonian describes a deterministic evolution of the state. Since the Hamiltonian is local, the probabilistic measurement outcomes cannot violate locality.

Well usually what is meant there is that the evolution of the quantum state is a Cauchy problem, i.e. the state at time t=0 fixes the state at later times, but that state itself describes probabilities. It's no different from classical stochastic processes like Black-Scholes. I don't really see it as double think.

Like martinbn I don't think the rest are doublethink either. In fact you're really just rephrasing common statements purposefully using the ambiguity of a single English word to make them appear silly.

 

[WernerQH]

I think you provided a perfect example, speaking of stochastic processes as deterministic and probabilistic at the same time.

 

[LittleSchwinger]

I think you provided a perfect example, speaking of stochastic processes as deterministic and probabilistic at the same time.

In books on Stochastic processes it's usually phrased with something like:
The initial probability state/distribution ##P(0)## determines/fixes the probability distribution ##P(t)## at later times...

To me it's as clear as day that this is referring to the evolution being a Cauchy problem and doesn't contradict in any way that the state encodes probabilities. If other people think this is "doublethink" fair enough.