I Entanglement and FTL signaling in professional scientific literature

[Delta2]

TL;DR Summary

Is it absolutely certain according to our current best understanding, that entanglement doesn't imply faster than light signaling?

According to professional scientific literature and to our best understanding, are there any suggestions that entanglement might imply some sort of faster than light signaling between the entangled particles?

I know that according to relativity nothing can travel faster than light, but what about according to quantum physics?

Thanks, Dimitrios.

 

[vanhees71]

It is "absolutely certain" that there are no faster-than light causal actions by construction of relativistic local QFT, which is the only (utmost) successful relativistic QT we have. On its very foundations one assumes that the operators representing local observables commute at space-like separated arguments. This holds particularly for the Hamilton density (energy density) and any other local observable, and thus there cannot be faster-than-light interactions by construction. This assumption is quite strong, leading to massive and massless particles but no tachyons, the spin-statistics theorem, and the PCT theorem, all of which are empirically valid with very high confidence.

 

[Delta2]

by construction of relativistic local QFT

Ehm , by construction of relativistic QFT you simply mean that you take it as an axiom of the theory that the speed of light is the upper limit for all sorts of speeds (let it be wave/fields or particles) in the universe.

Are there any theories where it is not taken as an axiom? What about non relativistic QFT?

 

[vanhees71]

In non-relativistic QFT you cannot even formulate such an axiom, because there are no time-like, light-like, and space-like four-vectors. The spacetime manifold is a completely different one, and of course, there is no limit on the speed for causal signal propagation. That's also, why there is no spin-statistics theorem, no necessity for antiparticles and thus also no CPT theorem in non-relativistic Q(F)T.

On the other hand, in relativistic (Q)FTs there occur "speeds" larger than the speed of light, like the phase and/or group velocities in dispersive media, but they do not violate the absence of faster-than-light causal-signal propagation. For classical electrodynamics this has been solved in a 1.5-column article by Sommerfeld in 1907 (answering a question by Willy Wien concerning the faster-than-light group velocity in the region of anomalous dispersion) and has been further worked out by Sommerfeld and Brillouin in 1914.

I don't know, where to find English translations of these papers, but I guess there must be one at least for the latter two very famous ones!

A. Sommerfeld, Ein Einwand gegen die Relativtheorie der
Elektrodynamik und seine Beseitigung, Phys. Zeitschr. 8, 841
(1907),
https://archive.org/details/bub_gb_Vy0KAAAAIAAJ

L. Brillouin, Über die Fortpflanzung des Lichtes in
dispergierenden Medien, Ann. Phys. (Leipzig) 349, 203
(1914), https://doi.org/10.1002/andp.19143491003

A. Sommerfeld, Über die Fortpflanzung des Lichtes in
dispergierenden Medien, Ann. Phys. (Leipzig) 349, 177
(1914), https://doi.org/10.1002/andp.19143491002

 

[PeroK]

Are there any theories where it is not taken as an axiom? What about non relativistic QFT?

There's a basic derivation of a) Newtonian space and time and b) Lorentzian spacetime from fundamental principles of homogenity and isotropy of space and time. From that perspective, these are the only two possibilities.

And, by experiment, it appears that our universe has a Lorentzian spacetime with the speed of light as the maximum, invariant speed.

If you want something different, you need to go beyond these basic principles and postulate some alternative structure for space and time. And then you would have to formulate QT within your exotic spacetime.

Non-relativistic QFT, by definition, assumes speeds that are sufficiently low for relativistic effects to be neglected. It certainly isn't an alternative for high-energy physics where there is no maximum speed!

Moreover, none of this helps the fundamental issue that you would need to postulate a FTL communication mechanism to explain entanglement. And, this is back to the issue that comes up time and again on this forum: do we accept what QM is telling us about the universe? Or, do we assume that we have an a priori insight into the causal structure of the universe (due to our innate human intelligence) and interpret QM as experimental results that mislead us about the true nature of reality?

And, as Scott Aaronson asks, when has that approach been a successful means of furthering science? I.e. deciding that nature cannot be the way the experiment evidence indicates.

 

[martinbn]

This might be helpful

https://en.wikipedia.org/wiki/No-communication_theorem

 

[Delta2]

Ehm sorry @PeroK are you saying that the speed of light as upper limit can be proved by the principles of homogenity and isotropy of space?

 

[martinbn]

Ehm sorry @PeroK are you saying that the speed of light as upper limit can be proved by the principles of homogenity and isotropy of space?

No, he said that those principles imply that there are only two options, the a) and b) he listed. And that experiments/observations rule out a). Hence b) is left.

 

[Demystifier]

Summary: Is it absolutely certain according to our current best understanding, that entanglement doesn't imply faster than light signaling?

According to professional scientific literature and to our best understanding, are there any suggestions that entanglement might imply some sort of faster than light signaling between the entangled particles?

I know that according to relativity nothing can travel faster than light, but what about according to quantum physics?

Thanks, Dimitrios.

One should distinguish faster than light (FTL) signaling from FTL influences. Signal is something that a complex system (e.g. a human, an animal, or a human made machine) produces to send information, which was previously created by the complex system in a controllable way. Influence is more general, it can be a signal created by the complex system, but it can also be an influence of one particle on another. By this definition, "signaling between the entangled particles" is a nonsense because one particle cannot be sufficiently complex to create a signal, but we can talk about influences between the entangled particles.

With this distinction, entanglement does not allow FTL signaling, but it allows FTL influences. For example, Alice can use quantum measurement to create a random number and use entanglement to instantaneously share this random number with Bob. But random number is not a signal.

 

[Delta2]

No, he said that those principles imply that there are only two options, the a) and b) he listed. And that experiments/observations rule out a). Hence b) is left.

Yes ok I understood that, but something that is not clear to me, since I never got my hands on a good textbook on relativity, can we have Lorentzian spacetime with faster than light speeds?

 

[Delta2]

But random number is not a signal

Well I don't know how is signaling defined in professional scientific literature (and to be honest when I was writing my post, I had in mind that there might be some unknown field (not EM or gravity) that has waves that travel FTL). But anyway for me personally the example you gave with Alice sharing a random number with Bob in an FTL way counts as some sort of signaling. Thanks!

 

[martinbn]

One should distinguish faster than light (FTL) signaling from FTL influences. Signal is something that a complex system (e.g. a human, an animal, or a human made machine) produces to send information, which was previously created by the complex system in a controllable way. Influence is more general, it can be a signal created by the complex system, but it can also be an influence of one particle on another. By this definition, "signaling between the entangled particles" is a nonsense because one particle cannot be sufficiently complex to create a signal, but we can talk about influences between the entangled particles.

I think this is not the point.

With this distinction, entanglement does not allow FTL signaling, but it allows FTL influences. For example, Alice can use quantum measurement to create a random number and use entanglement to instantaneously share this random number with Bob. But random number is not a signal.

I disagree with this. I think that the use of the word share is incorrect here.

 

[Motore]

Yes ok I understood that, but something that is not clear to me, since I never got my hands on a good textbook on relativity, can we have Lorentzian spacetime with faster than light speeds?

Sure, but it must be finite speed. We denote that with c. And in our universe c = speed of light in vacuum.

 

[Grinkle]

I never got my hands on a good textbook on relativity

I find this (Gao) derivation very digestible, myself. There is no paywall, but you do need to create a log in.

https://www.academia.edu/38454021/Why_special_relativity

Regarding a more complete textbook on SR, maybe this one (Rindler)?

https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20

 

[PeroK]

Ehm sorry @PeroK are you saying that the speed of light as upper limit can be proved by the principles of homogenity and isotropy of space?

http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

 

[Demystifier]

I think that the use of the word share is incorrect here.

What word would be better?

 

[PeroK]

Well I don't know how is signaling defined in professional scientific literature (and to be honest when I was writing my post, I had in mind that there might be some unknown field (not EM or gravity) that has waves that travel FTL). But anyway for me personally the example you gave with Alice sharing a random number with Bob in an FTL way counts as some sort of signaling. Thanks!

You don't need QM to do that. Just send a pair of numbers ($0$ and $1$) to A and B randomly. If A gets $0$, then she knows immediately that B got $1$. And, that can be useful. But, A and B have no control over the information, so it can't be a signal. E.g. if A and B agree that $0$ means "he/she does nothing" and $1$ means "he/she does something", then they know who is doing what, but neither can signal the other FTL that "I'm tired today, I'll take $0$ and you take $1$".

 

[gentzen]

One should distinguish faster than light (FTL) signaling from FTL influences. Signal is something that a complex system (e.g. a human, an animal, or a human made machine) produces to send information, which was previously created by the complex system in a controllable way.

The no FTL signaling property is stronger than just "created by the complex system in a controllable way." You cannot learn anything about what happened FTL.

For example, if Alice and Bob agree beforehand how they will measure their entangled particle(s), then the random number(s) they will end-up sharing could have been "created already" at the moment where their respective particles received their entanglement.

But anyway for me personally the example you gave with Alice sharing a random number with Bob in an FTL way counts as some sort of signaling.

It would be better to not call this "some sort of signaling". Most important, the word signaling is used intentionally to not apply to this "sharing of a random number". And it also risks to obscure the special nature of non-locality provided by entanglement.

 

[vanhees71]

Well, I think any theory should be in accordance with the empirical evidence. The natural sciences are about theories describing objective, reproducible observations of nature.

Relativity has been discovered by adapting the theory about electromagnetism to the empirical evidence, particularly the null result of the Michelson-Morley experiment. This lead Einstein to his special-relativistic spacetime model.

Then, of course, also QT had to be formulated to be compatible to this spacetime model, and after some quibbles with non-relativistic quantum mechanics ("first quantization formalism") the now standard formalism in terms of a local relatistic QFT has been established, and the microcausality constraint is imposed in the postulates precisely to ensure relativistic causality as well as other formal properties like a unitary S-matrix, the cluster-decomposition principle (which is closely related to the impossibility to send causal faster-than-light signals).

 

[Demystifier]

For example, if Alice and Bob agree beforehand how they will measure their entangled particle(s), then the random number(s) they will end-up sharing could have been "created already" at the moment where their respective particles received their entanglement.

By "could have", I guess you mean it's possible to construct a local hidden variable theory in which it is so. I agree with that. But the interesting thing here is that local explanation requires the existence of hidden variables. From a Copenhagen point of view which denies the existence of hidden variables, namely the existence of random numbers before they were measured, one cannot avoid the existence of nonlocal influence. This, indeed, is very similar to the EPR argument.

 

[vanhees71]

But the theory, relativistic local QFT, describing these experiments does not admit nonlocal influence by construction and also doesn't introduce hidden variables. So there must be a flaw in the argument. With the minimal interpretation there's no such problem of course, because there's no non-local collapse when doing a local measurement (or local measurements at two distant places on one entangled quantum system). QFT doesn't give up locality and Einstein causality but determinism ("realism"), i.e., observables which do not take determined values due to the state preparation are "really irreducibly random", i.e., their values are "really undetermined", i.e., there's no missing information (given the preparation of the system in a pure state, which by definition indeed defines "complete information" about the system).

 

[Dale]

Please recall that this thread is NOT in the interpretations section.

 

[gentzen]

By "could have", I guess you mean it's possible to construct a local hidden variable theory in which it is so.

No, that is not what I mean, or rather not how I would use the word "theory".

What I mean that entanglement is subtle, and the example is intended to illustrate that no matter how you try to achieve it, you cannot learn anything about what happened FTL. So if Alice and Bob agree on a protocol before hand, then this enables "entanglement to have the last word" by moving "the moment of creation" of the randomness backward in time, thereby denying that anything was learned FTL.

It is similar to the argument made by PeroK. The goal is to convince Delta2 that he would better not call this "sharing of a random number" as "some sort of signaling".

 

[vanhees71]

Please recall that this thread is NOT in the interpretations section.

Well, the microcausality constraint is a mathematical property of the the theory. There's not so much to "interpret" about it!

 

[Demystifier]

But the theory, relativistic local QFT, describing these experiments does not admit nonlocal influence by construction and also doesn't introduce hidden variables. So there must be a flaw in the argument.

There is a flaw in the argument, but on your side. Relativistic local QFT does not admit nonlocal signaling, but it admits nonlocal influences. Even Weinberg, in Lectures on Quantum Mechanics, says: "Copenhagen interpretation relies on something happening during a measurement that is outside the scope of quantum mechanics" (2nd edition, page 97).

 

[vanhees71]

Yes, the Copenhagen interpretation, but not the minimal interpretation! I also was very surprised about Weinberg's opinion on these problems in his quantum mechanics textbook. In his QFT books of course he "celebrated" the microcausality principle as the prime ingredient of the theory, deriving from it the basic properties of the theory, including the impossibility of nonlocal signaling, which for me is the same as nonlocal influence, or what difference should there be?

 

[Demystifier]

Yes, the Copenhagen interpretation, but not the minimal interpretation!

Your version of the minimal interpretation cannot be found in any book or peer reviewed paper. (My recent thread in which I proved inconsistency of your version of the minimal interpretation has been deleted for exactly this reason.) The closest published cousin of your version is the version by Ballentine, and according to Ballentine, the Bell's theorem proves nonlocality.

 

[vanhees71]

Where do you find this in Ballentine's book, which by the way is about non-relavistic quantum theory, where there is no microcausality principle and also no restriction in the velocity of signal propagation. I don't understand the claim that I propose something non-standard here. It's all consistent with modern QFT textbooks, including particularly Weinberg's!

 

[Demystifier]

I also was very surprised about Weinberg's opinion on these problems in his quantum mechanics textbook. In his QFT books of course he "celebrated" the microcausality principle as the prime ingredient of the theory, deriving from it the basic properties of the theory, including the impossibility of nonlocal signaling, which for me is the same as nonlocal influence, or what difference should there be?

Apparently, Weinberg changed his opinion when he grew older. You are still relatively young, so there are chances for you as well.

 

[vanhees71]

Now I'm really worried getting older...

 

[Demystifier]

Where do you find this in Ballentine's book,

I quoted it several times before for you, so I'll not do it again.

I don't understand the claim that I propose something non-standard here. It's all consistent with modern QFT textbooks, including particularly Weinberg's!

The standard QFT textbooks, including the Weinberg's, don't talk about the meaning of the Bell theorem in QFT. So whatever you say about their relation, right or wrong, is nonstandard.

 

[vanhees71]

Where do you find this in Ballentine's book, which by the way is about non-relavistic quantum theory, where there is no microcausality principle and also no restriction in the velocity of signal propagation. I don't understand the claim that I propose something non-standard here. It's all consistent with modern QFT textbooks, including particularly Weinberg's!

I looked it up. There's a statement about locality and contextuality on page 606, and as expected this is not nonlocality in the sense of microcausality of relativistic QFT but "nonlocality" in the sense of long-ranged correlations of measurement outcomes due to entanglement. That's of course non contradiction, because as with any quantum theory also in relativistic local (or better microcausal) QFT you can have such "long-range correlations" between entangled parts of a quantum system. These correlations are inherent in the state since it was prepared and is not caused in any way by the local measurements on the far-distant parts.

 

[vanhees71]

I quoted it several times before for you, so I'll not do it again.The standard QFT textbooks, including the Weinberg's, don't talk about the meaning of the Bell theorem in QFT. So whatever you say about their relation, right or wrong, is nonstandard.

Well, I don't think that Weinberg discusses Bell etc. in his QFT textbooks, but what he discusses at length is the microcausality principle and its meaning and its implications, and this implies that there is no faster-than-light influence between local measurements of local observables. I don't understand, why you think that were "nonstandard".

Bell's theorem and all that usually is discussed in Quantum Optics textbooks, which use "standard QED" too. So there's still nothing beyond nonstandard QFT in my arguments either!

 

[PeroK]

There is a flaw in the argument, but on your side. Relativistic local QFT does not admit nonlocal signaling, but it admits nonlocal influences. Even Weinberg, in Lectures on Quantum Mechanics, says: "Copenhagen interpretation relies on something happening during a measurement that is outside the scope of quantum mechanics" (2nd edition, page 97).

If we take entanglement at face value, then the measurement outcomes at A and B are spacelike separated and yet correlated. That only implies "things happening outside QM" and "nonlocal influences" if we do not accept non-locality as a building block of nature. I do not have the confidence to say either "well, of course non-locality (in this sense at least) can be a building block of nature - why not?"; nor to say "this sort of non-locality is sufficiently counterintuitive that there must be something wrong".

Whether threre is a problem with QM in this regard depends on what we are prepared to accept from nature. And I can't find within myself any clear argument that determines whether I can take quantum entanglement at face value without feeling a fool; nor, to reject it without feeling innately prejudiced!

 

[PeterDonis]

For example, Alice can use quantum measurement to create a random number and use entanglement to instantaneously share this random number with Bob.

Not quite. Bob can't know which random number Alice shared until he receives information from Alice by normal signals and combines that information with the information from the measurement he made on a particle entangled with Alice's particle.

 

[vanhees71]

There's nothing necessary "outside QM" or rather microcausal QFT to understand the long-ranged correlations, which are in full accordance with the microcausality principle. Here's a very nice answer about the issue on stackexchange:

https://physics.stackexchange.com/q...ith-or-even-predicted-by-quantum-field-theory

 

[Demystifier]

These correlations are inherent in the state since it was prepared and is not caused in any way by the local measurements on the far-distant parts.

That's your interpretation, not Ballentine's. At pages 609-610 (2nd edition) he says:
"Einstein’s locality postulate, which is the key to Bell’s theorem, is strongly
motivated by special relativity. Thus the conflict between quantum mechanics
and locality suggests a deep incompatibility between quantum mechanics and
relativity. ... It is not valid to object that we have based our analysis on nonrelativis-
tic quantum mechanics. In fact, only the properties of spin and polarization
have been used, and these are essentially identical in both the relativistic and
nonrelativistic theories."

 

[Demystifier]

Bell's theorem and all that usually is discussed in Quantum Optics textbooks, which use "standard QED" too. So there's still nothing beyond nonstandard QFT in my arguments either!

Can you quote some quantum optics book that confirms your interpretation of the Bell theorem?

 

[Demystifier]

Not quite. Bob can't know which random number Alice shared until he receives information from Alice by normal signals and combines that information with the information from the measurement he made on a particle entangled with Alice's particle.

You are simply wrong (in a way that, fortunately, does not depend on interpretation). For example, let the entangled state be $|0\rangle |0\rangle + |1\rangle |1\rangle$. Suppose that Alice performs a measurement at time $t$ and obtains the result $0$. (The chance for this result was 50%, so it's a random number.) Bob can know that this random number is $0$ by performing the measurement at the same time $t$, without any additional classical information.

Note that this is not quantum teleportation (which requires a classical information), because here Bob knows in advance the entangled state.

 

[PeterDonis]

this is not quantum cloning (which requires a classical information), because here Bob knows in advance the entangled state.

Ah, I see; yes, I was confusing this scenario with quantum teleportation (not "cloning" since cloning implies making a copy of a quantum state without changing the original, which is impossible by the no cloning theorem).

 

[PeterDonis]

Bob can know that this random number is $0$ by performing the measurement at the same time $t$, without any additional classical information.

The time when Bob makes his measurement doesn't matter, does it? The key thing is the direction of his spin measurement (it has to be the same as Alice's).

 

[Demystifier]

Ah, I see; yes, I was confusing this scenario with quantum teleportation (not "cloning" since cloning implies making a copy of a quantum state without changing the original, which is impossible by the no cloning theorem).

Yes, I meant teleportation, I've corrected it now.

 

[Demystifier]

The time when Bob makes his measurement doesn't matter, does it? The key thing is the direction of his spin measurement (it has to be the same as Alice's).

Yes.

 

[Demystifier]

There's nothing necessary "outside QM" or rather microcausal QFT to understand the long-ranged correlations, which are in full accordance with the microcausality principle.

Agree on that. But the point is that microcausality prevents FTL signaling, not FTL influences. Standard QFT does not prevent FTL influences simply because it does not say anything about influences. Influence is not a concept that you can define within standard QFT. That's because standard QFT is an instrumental theory, while influence (unlike signal) is not an instrumental concept. An instrumental theory is a theory talking only about how humans can use it, while influence refers to how nature itself behaves, irrespective of humans. You can say that "FTL influence" is philosophy and hence irrelevant, I'm fine with that, but you can't say that FTL influence is disproved by standard QFT. A theory cannot disprove something which is not even a well-defined concept in this theory.

 

[vanhees71]

Can you quote some quantum optics book that confirms your interpretation of the Bell theorem?

Good question. I don't know, whether there's a quantum-optics book which states the microcausality principle explicitly at all, but they use the standard QFT formalism to describe the violation of Bell's inequality etc. and this formalism fulfills the microcausality principle, be it mentioned explicitly or not, and this shows that non-local correlations are indeed compatible with the microcausality principle, which excludes faster-than-light signal propagation, i.e., it's not the measurement at A which causes the outcome of a measurement at B, when the measurement outcomes are registered at spacelike separated events. The observed correlations are due to the preparation of the system in the entangled state, and these correlations can only be observed by comparing the registered measurement results afterwards.

 

[vanhees71]

The time when Bob makes his measurement doesn't matter, does it? The key thing is the direction of his spin measurement (it has to be the same as Alice's).

Indeed, if you want to have 100% correlations A and B must measure the spin component in the same direction, and B knows what A will find as soon as he gets his measurement result given (!) that he knows that the particles are prepared before (!) in an entangled state. It doesn't matter whether A measures her spin before or after Bob or simultaneously. The microcausality principle implies that if the measurement outcomes are registered as space-like separated events, it cannot be B's measurement that causes A's outcome and vice versa. To verify the 100% correlation, of course A and B must share their measurement protocols, which cannot done with any faster-than-light communication either.

 

[vanhees71]

Agree on that. But the point is that microcausality prevents FTL signaling, not FTL influences. Standard QFT does not prevent FTL influences simply because it does not say anything about influences. Influence is not a concept that you can define within standard QFT. That's because standard QFT is an instrumental theory, while influence (unlike signal) is not an instrumental concept. An instrumental theory is a theory talking only about how humans can use it, while influence refers to how nature itself behaves, irrespective of humans. You can say that "FTL influence" is philosophy and hence irrelevant, I'm fine with that, but you can't say that FTL influence is disproved by standard QFT. A theory cannot disprove something which is not even a well-defined concept in this theory.

What then in fact IS "an influence"? For me signal and influence in this context are simply the same thing. We are talking about physics, not philosophy here. We are (still ;-)) in the scientific part of the quantum forum!

 

[PeterDonis]

What then in fact IS "an influence"?

It's whatever it is that allows correlations that violate the Bell inequalties, without FTL signaling taking place.

 

[vanhees71]

But the standard QFT doesn't need an influence, because the correlation is due to the state preparation and not due to some faster-than-light "influence" of one measurement on the other. This is, of course, argued within microcausal QFT. If you admit some "influences" outside the dynamics of this QFT you can claim anything you like, including FTL "influences", but the point is that microcausal QFT is a theory that is compatible with the impossibility of FTL "influences" on the one hand and the observed correlations described by entangled states.

 

[Demystifier]

But the standard QFT doesn't need an influence, because the correlation is due to the state preparation

No, standard QFT does not say that it's due to the state preparation. Standard QFT is agnostic on that, because it's a philosophical question and standard QFT is not philosophy.