Can Special Relativity Explain the Alice and Bob Spin Measurement Paradox?

[AndrzejB]

TL;DR Summary

measurement in frame of reference

Alice measures the spin, also Bob measures.
If we assume that the signals (from Alice to Bob) were sent, they had to be with the speed e.g. 10 c
But in another frame of reference Bob first measures, next Alice.
Measurement of Alice was cause and was sent back in time, or measurement of Bob was cause.
Since Alice and Bob case is symmetrical, it cannot be said that the first measurement reduced the wave function and the second was just a formality.
We have paradox.

 

[PeroK]

Alice measures the spin, also Bob measures.
If we assume that the signals (from Alice to Bob) wwere sent

There are no signals between entangled particles in QM.

 

[StevieTNZ]

There are no signals between entangled particles in QM.

Solves the apparent paradox. "Assume x, therefore y. It is, further, a fact there is a paradox." Work that out.

 

[AndrzejB]

I knew there were no signals, I put myself wrong, I meant that the time distance between the events was small and the spatial distance was large, so that if there were signals they would have to be> c which is impossible.
Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

 

[PeroK]

Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

The collapse of the wavefunction is not a physical process. It's an interpretation of the mathematics of QM.

The important point here is that the measurement results are correlated. QM does not specify a mechanism by which that correlation is achieved.

 

[Demystifier]

Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

You tacitly assume that cause must be before the consequence, i.e. that there is a time arrow that distinguishes the past from the future. But an arrow of time is an emergent phenomenon making sense only at the macroscopic level. At the fundamental microscopic level there is no arrow of time, i.e. one cannot distinguish the past from the future. From that point of view, there is no paradox.

Note also that the notion of signal assumes a time arrow. So the solution of the paradox can also be expressed by saying that there are no superluminal signals between the two systems. However, it does not mean that there are no superluminal influences. The influence, unlike signal, is a fundamental microscopic notion that does not need a time arrow; a microscopic event can influence both the future and the past. So it's possible that the two systems are correlated because they influence each other faster than light, without sending signals faster than light. An explicit model for such influences is provided by Bohmian interpretation, where special relativity is violated at the fundamental microscopic level, but in such a way that those violations cannot directly be observed in outcomes of macroscopic measuring apparatuses.

 

[vanhees71]

The collapse of the wavefunction is not a physical process. It's an interpretation of the mathematics of QM.

The important point here is that the measurement results are correlated. QM does not specify a mechanism by which that correlation is achieved.

Of course QM does specify "a mechanism" by which that correlation is achieved. It's due to the preparation of the system in an entangled state. E.g., you get entangled photon pairs using parametric down conversion, i.e., shouting with a laser on certain birefringent crystals and select the entangled pairs:

https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion

When thinking about the question of locality or non-locality one has to use relativistic QT since in non-relativistic physics there's no constraint for the signal speed to begin with. Now the only successful relativistic QT is local (sic!) relativistic QFT, which is constructed such that the causality structure of special relativistic spacetime is fulfilled. This is done by defining only such self-adjoint operators as representing observables which lead to local observables (like energy, momentum, charge densities), i.e., for which the operators commute if their arguments are space-like separated. This implies that there cannot be any causal influences between any two space-like separated events. Particularly signaling cannot be achieved at speeds faster than light (in vacuo).

 

[vanhees71]

You tacitly assume that cause must be before the consequence, i.e. that there is a time arrow that distinguishes the past from the future. But an arrow of time is an emergent phenomenon making sense only at the macroscopic level. At the fundamental microscopic level there is no arrow of time, i.e. one cannot distinguish the past from the future. From that point of view, there is no paradox.

The causality of the natural phenomena is a prerequisite for any natural science to make sense to begin with. If there were no laws of nature to discover, you'd not need any natural sciences, and the causal arrow of time is thus just one of the basic postulates underlying all of physics. Maybe that changes in the future when a quantum theory of gravitation and thus most probably also a quantum theory of spacetime has been found, but as long as this is not the case, all such statements are just speculative.

Given this "causal arrow of time", all the other "arrows of time" (like the "thermodynamic arrow of time" and the "radiation arrow of time") then follow. The thermodynamic arrow of time follows, e.g., from coarse graining of microscopic descriptions to effective descriptions of collective, macroscopic observables (Boltzmann's H theorem). The radiation arrow of time is of pretty similar origin: It's simply impossible FAPP to prepare the time-reversed solution of the Maxwell equations to the retarded solution for radiating out from a localized charge-current distribution.

Note also that the notion of signal assumes a time arrow. So the solution of the paradox can also be expressed by saying that there are no superluminal signals between the two systems. However, it does not mean that there are no superluminal influences. The influence, unlike signal, is a fundamental microscopic notion that does not need a time arrow; a microscopic event can influence both the future and the past. So it's possible that the two systems are correlated because they influence each other faster than light, without sending signals faster than light. An explicit model for such influences is provided by Bohmian interpretation, where special relativity is violated at the fundamental microscopic level, but in such a way that those violations cannot directly be observed in outcomes of macroscopic measuring apparatuses.

There are no "superluminal influences" by construction in local relativstic QFTs. There are strong correlations between far-distant observations on entangled quantum systems, but correlations are no causations!

 

[Demystifier]

and the causal arrow of time is thus just one of the basic postulates underlying all of physics.

Given this "causal arrow of time", all the other "arrows of time" (like the "thermodynamic arrow of time" and the "radiation arrow of time") then follow.

No. Causal arrow of time is not a postulate, but an observed phenomenon. The standard view is that the causal and other arrows of time emerge from the thermodynamic one. The thermodynamic arrow of time can be traced back to a low entropy initial condition. Why the initial entropy was low? That question does not have a standard or widely accepted answer, it's one of the deepest unsolved problems in physics. The microscopic postulates as we know them are equations of motion which do not have any a priori causal arrow of time. Solving those equations requires fixing initial conditions, but in general we don't have a law telling us how to fix them. The observed phenomenon of thermodynamic time arrow tells us the initial condition must have a low entropy, but that of course does not fix the initial condition uniquely.

 

[vanhees71]

The fact that indeed the microscopic equations are time-reversal invariant (neglecting the weak interaction here) implies that we have to take the assumption of a causal arrow of time as a postulate. For me that's the most fundamental arrow of time since it's really to be assumed, and all the other arrows of time follow from it. Of course the arrow of time we experience in everyday life indeed is the thermodynamic arrow of time and is due to the macroscopic nature of our surroundings.

I cannot judge your cosmological argument. Do you have any references for this?

 

[Demystifier]

I cannot judge your cosmological argument. Do you have any references for this?

- A general introduction is wikipedia https://en.wikipedia.org/wiki/Past_hypothesis
- Particularly lucid and clear discussion is given in the book R. Penrose, The Emperor's New Mind, Chapter 7.
- See also my https://arxiv.org/abs/gr-qc/0403121 Sec. 2, where I give more references and briefly explain how causal time arrow emerges from the thermodynamic one (and not the other way around).

 

[vanhees71]

Hm, I still think, it's the other way around since you want to understand the macroscopic phenomena from the fundamental elementary building blocks, and to establish relativistic QFT as a theory about these elementary building blocks (i.e., the particles of the standard model) a basic ingredient is the causal arrow of time, and then by statistical arguments you derive the H-theorem and thus show that the so defined thermodynamic arrow of time is the same as the causal arrow of time, but also here you introduce the asymmetry between future and past by hand, i.e., you through away information in the future, i.e., going forward in time in the sense of the causal arrow of time (e.g., when deriving the Boltzmann equation from QFT, the Schwinger-Keldysh timepath uses the causal direction of time and leads to an increase of entropy in this direction of time).

The same holds for the radiative or electrodynamic arrow of time, i.e., the fact that we choose the retarded solution of Maxwell's equations to describe wave fields radiating out from compact distributions of charges and currents. The time-reversed situation is not impossible as far as we know, but it's FAPP impossible to realize since one is unable to construct over a far distance a wave field in an accurate way that is so finetuned that it's completely absorbed by some localized charge distribution.

 

[Demystifier]

The time-reversed situation is not impossible as far as we know, but it's FAPP impossible

You would probably agree with me that the time-reversed situation violates the causal time arrow. But if the causal time arrow was fundamental, then it would be absolutely impossible, not merely FAPP impossible. On the other hand, FAPP impossibility, rather than absolute impossibility, implies that it's a consequence of a FAPP law, not of an absolute law. This is a clear indication that the reason for impossibility of time-reversed situation lies in the thermodynamic time arrow, which is a FAPP statistical law, not an absolute law.

since one is unable to construct over a far distance a wave field in an accurate way that is so finetuned that it's completely absorbed by some localized charge distribution.

I agree, but there is always a small probability that the fine tuned configuration will be realized by chance. This is again a clear indication that the FAPP impossibility has a statistical origin, namely in the thermodynamic time arrow.

But here is a crucial detail that may confuse you. By "thermodynamic" time arrow in this context one does not assume that the system has a well defined temperature. It is really a generalized "thermodynamic" time arrow, which states that a coarse grained entropy increases, but in general this entropy does not need to be thermodynamic entropy. The usual thermodynamic time arrow, in which entropy is thermodynamic entropy, is just a special case.

Or to make the long story short, the causal time arrow is a FAPP statistical law. It emerges from a more general FAPP statistical law saying that coarse grained entropy increases. This general statistical law is misleadingly called thermodynamic time arrow, even though it refers to general systems that do not need to be thermodynamic systems with a well defined temperature.

 

[vanhees71]

You would probably agree with me that the time-reversed situation violates the causal time arrow. But if the causal time arrow was fundamental, then it would be absolutely impossible, not merely FAPP impossible. On the other hand, FAPP impossibility, rather than absolute impossibility, implies that it's a consequence of a FAPP law, not of an absolute law. This is a clear indication that the reason for impossibility of time-reversed situation lies in the thermodynamic time arrow, which is a FAPP statistical law, not an absolute law.

Why should the time-reversed situation violate the causal arrow of time? If I'd be an almighty experimentalist, able to prepare a spherical ingoing wave in such a precise manner that it's the time reversed wave of the outgoing wave from a charge-current distribution this same charge-current distribution would completely absorb the wave precisely. It's only because of the complexity of this initial state of the ingoing wave that we are practically unable to prepare it.

It's as with the time-reversed process of a shattering glass: If we'd be able to prepare precisely the time reversed final state, the glass would reassamble completely, but that's of course impossible because of the complexity of this initial state.

In general it's very difficult to prepare initial states which lead to a time evolution of decreasing entropy when described in the coarse-grained manner of statistical physics. This is the reason, why almost always we observe states with increasing entropy and that's why the causal arrow of time usually coincides with the thermodynamic arrow of time, i.e., the state in the future has larger entropy than the initial state.

I agree, but there is always a small probability that the fine tuned configuration will be realized by chance. This is again a clear indication that the FAPP impossibility has a statistical origin, namely in the thermodynamic time arrow.

Sure, but the probability is really very small.

But here is a crucial detail that may confuse you. By "thermodynamic" time arrow in this context one does not assume that the system has a well defined temperature. It is really a generalized "thermodynamic" time arrow, which states that a coarse grained entropy increases, but in general this entropy does not need to be thermodynamic entropy. The usual thermodynamic time arrow, in which entropy is thermodynamic entropy, is just a special case.

Of course not. If the initial macroscopic state is equilibrium, it's static, but entropy is not only defined in equilibrium.

Or to make the long story short, the causal time arrow is a FAPP statistical law. It emerges from a more general FAPP statistical law saying that coarse grained entropy increases. This general statistical law is misleadingly called thermodynamic time arrow, even though it refers to general systems that do not need to be thermodynamic systems with a well defined temperature.

We agree to disagree. For me the causal arrow of time is a fundamental postulate of our physical theories, and the thermodynamical arrow of time can be shown to coincide with this causal arrow.

 

[Demystifier]

We agree to disagree. For me the causal arrow of time is a fundamental postulate of our physical theories

Fair enough. But I don't see this postulate explicitly stated in any of our fundamental theories. When I read a list of postulates for the Standard Model, or for quantum mechanics, or for general relativity, or for classical electrodynamics, or for classical mechanics, I don't see the causal time arrow postulate. Do you know any textbook, or lecture notes, or even a research paper, that states this postulate explicitly?

This, perhaps, is a meta-postulate, that is, a postulate that lies behind "ordinary" postulates. If so, then it belongs to meta-physics, rather than "ordinary" physics. But I know that you don't have a high opinion on meta-physics, so it's a bit ironical that you put such a strong emphasis on a postulate that seems to be a meta-postulate.

Can you imagine a though experiment that, in principle, could decide whether the causal time arrow postulate is true or false? In other words, can you describe at least one example of how the world look like if this postulate were wrong? If not, then it's another indication that it is a non-scientific postulate belonging to meta-physics.

 

[vanhees71]

Of course, it's not stated explicitly, because it's taken for granted, because it's the prerequisite for natural science, i.e., if there were no causal laws, there'd be no natural science. It's of course used all the time. The first expclicit need to use it usually occurs in classical electrodynamics, where you solve the time-reversal invariant wave equation, and where you have to choose the retarded Green's function from all the other possible Green's functions of the d'Alembert operator. Of course, you could as well introduce this idea of the retarded Green's function already much earlier, i.e., when you discuss the harmonic oscillator with an external force (or even the free particle with a given external force as a function of time).

 

[gentzen]

Of course, it's not stated explicitly, because it's taken for granted, because it's the prerequisite for natural science, i.e., if there were no causal laws, there'd be no natural science.

I guess you are talking about "the causal time arrow postulate". (I am glad that nearly nobody is following your example of not quoting what you are responding to.)

There are two things I don't get about your argument:

1. Why should a FAPP causal time arrow not be sufficient for natural science?
2. Why should we be able to conclude anything from "it's the prerequisite for natural science"? You probably know my example of the placebo effect in medicine (together with the fact that experiments are not repeatable), which of course makes everything much harder, but not impossible. But let me try a more physical example instead: The closed timelike curves in general relativity seem incompatible with a causal time arrow.

While I am at general relativity, let me just test the general ability to accept incompatibilities of general relativity with other "principles": For example Daniel Greenberger thinks that the equivalence principle of general relativity is incompatible with quantum mechanics:

If you put a particle into a really strong external gravitational field, it should behave like any other particle in that field and its mass should drop out, according to the weak equivalence principle. But quantum mechanically, that doesn’t happen. We give the particle a mass at the beginning, and the mass enters the calculation, and this violates weak equivalence.

And since this thread was about compatibilty between special relativity and quantum mechanics, let me just mention that the predicted phenomenology of quantum mechanics is compatible with special relativity, independent of whether "local relativistic QFT" can be extended (or used) beyond scattering of asymptotic states or not. At least no incompatibilities are currently known.

 

[vanhees71]

I guess you are talking about "the causal time arrow postulate". (I am glad that nearly nobody is following your example of not quoting what you are responding to.)

If I don't quote what I'm responding to I respond to the posting directly before the new posting. We are discussing the causal arrow of time indeed.

There are two things I don't get about your argument:

1. Why should a FAPP causal time arrow not be sufficient for natural science?

I think one needs causality to have natural sciences to begin with. If there were no causal laws, we couldn't discover them. Whether it's FAPP or not, I don't care.

1. Why should we be able to conclude anything from "it's the prerequisite for natural science"? You probably know my example of the placebo effect in medicine (together with the fact that experiments are not repeatable), which of course makes everything much harder, but not impossible. But let me try a more physical example instead: The closed timelike curves in general relativity seem incompatible with a causal time arrow.

While I am at general relativity, let me just test the general ability to accept incompatibilities of general relativity with other "principles": For example Daniel Greenberger thinks that the equivalence principle of general relativity is incompatible with quantum mechanics:

I don't understand, what Greenberger means, because there's QFT in curved spacetimes, describing particles in a given general relativistic "background spacetime". Why should this be incompatible with the (weak) equivalence principle. A quantum gravity of the gravitational interaction doesn't exist yet, and it may well be that the equivalence principle is not valid any more in such a theory.

And since this thread was about compatibilty between special relativity and quantum mechanics, let me just mention that the predicted phenomenology of quantum mechanics is compatible with special relativity, independent of whether "local relativistic QFT" can be extended (or used) beyond scattering of asymptotic states or not. At least no incompatibilities are currently known.

Of course. What has this to do with the causality principle, which is an important ingredient to establish local relativistic QFTs to begin with?

 

[gentzen]

Of course. What has this to do with the causality principle, which is an important ingredient to establish local relativistic QFTs to begin with?

It is unrelated to the causality principle. It is just my opinion regarding the original question of this thread.
(And I wanted to make it clear that while I am open to the possibility that general relativity might be incompatible with other "sacred physical principles" including quantum mechanics, I am strictly opposed to suggesting a similar possible incompatibility for special relativity.)

 

[PeterDonis]

Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function

That's because it doesn't matter. Since the measurements are spacelike separated, they commute: their results do not depend on the order in which they are made. Which is good because the order in which they are made is frame dependent.

That is usually taken to mean that there cannot be any cause and effect relationship between them, since any such relationship would require the order of the measurements to be invariant, and it's not.

 

[Demystifier]

Of course, it's not stated explicitly, because it's taken for granted, because it's the prerequisite for natural science, i.e., if there were no causal laws, there'd be no natural science.

Then it belongs to philosophy of science, not to physics proper. But physics, as the most fundamental science, often has aspirations to explain some general scientific principles from more fundamental physics principles. The causal time arrow is certainly one of them. Another example is the "free will" postulate, namely the phenomenological fact that experimentalists have some freedom to choose initial conditions at will. This principle seems to be contradicted by both deterministic and probabilistic fundamental laws of physics, so many physicists believe that "free will" postulate, similarly to the causal time arrow postulate, cannot be fundamental bust must emerge somehow at the macroscopic level only.

 

[malawi_glenn]

Almost all threads in this subforum ends up in a battle between demyst and vanhees :)

 

[vanhees71]

Then it belongs to philosophy of science, not to physics proper. But physics, as the most fundamental science, often has aspirations to explain some general scientific principles from more fundamental physics principles. The causal time arrow is certainly one of them. Another example is the "free will" postulate, namely the phenomenological fact that experimentalists have some freedom to choose initial conditions at will. This principle seems to be contradicted by both deterministic and probabilistic fundamental laws of physics, so many physicists believe that "free will" postulate, similarly to the causal time arrow postulate, cannot be fundamental bust must emerge somehow at the macroscopic level only.

The causality principle clearly belongs to physics proper, because it is used to select the physical from all possible solutions of the equations of motion. That's why we discuss it to begin with.

That you can choose initial conditions "at will" is also an empirical fact, and that's part of why the physical laws look as they look, i.e., why you have, e.g., second-order differential equations for the coordinates of a mechanical system.

 

[martinbn]

I don't think the arrow of time is relevant here. Two events can be cause effect related if there is a causal curve connecting them. The time orientation only determines which can be the cause and which the effect. But if the two events are space-like separated, then all this is irrelevant. Part of the confusion comes from treating coordinate time as some sort of classical absolute time. You chose a frame in which one event is first and the other second, in the sense that one has smaller value of the chosen time coordinate, then you fool yourself that there might be an influence from the first to the second event because the first event was in the past. But it isn't in the past, they are space-like. Coordinates are just lables. This is either due to missunderstanding of relativity, or simply being careless and slipping into thinking norelativistically (could also be deliberate). Same for the retrocausality. If the events are space-like choosing a frame doesn't make one in the future of the other.

 

[vanhees71]

Nevertheless, relativistic spacetimes admit a causality structure (at least locally), and you can always choose your time-like coordinate such that the causal ordering is as usual, i.e., if two events have a cause and effect relation you can always make the time-like coordinate such that the event at the smaller time coordinate must be the cause.

 

[Demystifier]

Almost all threads in this subforum ends up in a battle between demyst and vanhees :)

But this a friendly battle, we respect each other, often like each other, and agree on most physics issues (except those on which we have a battle).

 

[Demystifier]

Whether it's FAPP or not, I don't care.

That's it! That's the single most important reason why we have "battles" in this subforum at all. Almost all the "battles" we had in this subforum originate from the the deep difference between you and me that you don't care much about the difference between FAPP and "truly" fundamental laws, while I do.

 

[malawi_glenn]

But this a friendly battle, we respect each other, often like each other, and agree on most physics issues (except those on which we have a battle).

But maybe the OP become "discouraged" to continue?

 

[vanhees71]

That's it! That's the single most important reason why we have "battles" in this subforum at all. Almost all the "battles" we had in this subforum originate from the the deep difference between you and me that you don't care much about the difference between FAPP and "truly" fundamental laws, while I do.

But the point is that whatever "truly fundamental laws" might be, they cannot be checked by experiments and thus are fictions which are not subject of a natural science. At best they provide some interesting pure math (like "string theory" et al).

 

[Demystifier]

But the point is that whatever "truly fundamental laws" might be, they cannot be checked by experiments and thus are fictions which are not subject of a natural science. At best they provide some interesting pure math (like "string theory" et al).

True, but one can always think about what is fundamental according to a given theory, even if this is not a theory of everything. For example, if one imagines that classical electrodynamics is fundamental, then, since it is a deterministic theory in which all variables are determined by initial conditions in the far past, then human experimentalists cannot have a fundamental ability to choose initial conditions at will. It's a clear logical consequence of this theory, so within this theory one must accept it even if this contradicts our common sense. In particular, if our common sense tells us that our free will is fundamental, one must reject the common sense and accept that free will is somehow emergent, not fundamental. Or alternatively, if one insists that free will is fundamental, then classical electrodynamics cannot be. Similar conclusions can be made about quantum electrodynamics, Standard Model, string theory, etc. We cannot check these conclusions by experiments, but we can think logically and trust our logical conclusions. If logic is not science, that's a deficiency of science, not of logic.

 

[DrChinese]

That's because it doesn't matter. Since the measurements are spacelike separated, they commute: their results do not depend on the order in which they are made. Which is good because the order in which they are made is frame dependent.

That is usually taken to mean that there cannot be any cause and effect relationship between them, since any such relationship would require the order of the measurements to be invariant, and it's not.

I agree with your conclusion about commuting measurements. And yet...

When the outcomes DON'T commute in QM: the order of measurements STILL does not demonstrate a cause and effect relationship, and it is quite impossible to prove Alice (measured first*) influenced Bob more than Bob (measuring second*) influences Alice. @RUTA labels this result as "acausal". @Demystifier says there are superluminal influences but there is no possibility of signaling. @vanhees71 believes all quantum action respects c (implying there is a causal direction) [although how this squares with Bell has always been unclear to me, and probably anyone else who cares to probe his perspective].

@malawi_glenn I think you are right: we lost the OP @AndrzejB a while back... It was around the time he stated "if there were signals they would have to be> c which is impossible. Problem is that it is impossible to say which measurement was the cause of the reduction of the wave function."

He's actually correct: There may not be signals >c, but there could be "influences" >c. And it is in fact impossible to say which measurement is the cause of the "wave packet reduction" (assuming that is a physical process). Clearly, these are interpretation dependent; and that should be our answer.*Of course, non-commuting measurements can be performed that are in the same reference frame... and thus would not be frame dependent in determining sequence order. These might or might not be "spacelike" separated (I would prefer the term "spacetime-like" separated here), depending on your perspective on (or definition of) such requirement. The counter-example I would give is measurements on 2 entangled photons that never co-existed (reference available), but are measured sequentially in the same place. There is no way to conclude the first measurement influences the second any more than vice versa - except by assumption. QM is otherwise silent on this point.

 

[vanhees71]

I agree with your conclusion about commuting measurements. And yet...

When the outcomes DON'T commute in QM: the order of measurements STILL does not demonstrate a cause and effect relationship, and it is quite impossible to prove Alice (measured first*) influenced Bob more than Bob (measuring second*) influences Alice. @RUTA labels this result as "acausal". @Demystifier says there are superluminal influences but there is no possibility of signaling. @vanhees71 believes all quantum action respects c (implying there is a causal direction) [although how this squares with Bell has always been unclear to me, and probably anyone else who cares to probe his perspective].

But that's very easily understood: The violation of Bell's inequality is because of the preparation of the system in an entangled state, i.e., the long-ranged correlations are there because of the preparation of the system. No causal influence of A's on B's or B's on A's measurement is necessary to explain it within relativistic local QFT.

The argument is usually the other way around: One says that there cannot be causal influences between the measurements, because the measurement events are space-like separated, i.e., one takes indeed the microcausality condition for be fulfilled in Nature.

 

[DrChinese]

But that's very easily understood: The violation of Bell's inequality is because of the preparation of the system in an entangled state, i.e., the long-ranged correlations are there because of the preparation of the system. No causal influence of A's on B's or B's on A's measurement is necessary to explain it within relativistic local QFT.

The argument is usually the other way around: One says that there cannot be causal influences between the measurements, because the measurement events are space-like separated, i.e., one takes indeed the microcausality condition for be fulfilled in Nature.

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution). Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).

For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion. To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted [and could therefore not have been prepared initially in the synchronized state vanhees71 imagines], our results directly confirm the quantum nature of teleportation."

To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.

I do think we have answered the OP. If we want another go at whether QFT demands local causality, that discussion belongs in the Interpretations subforum.

 

[PeterDonis]

Moderator's note: Thread moved to QM interpretations subforum.

 

[PeterDonis]

Since Alice and Bob case is symmetrical, it cannot be said that the first measurement reduced the wave function

In fact, we cannot even say that "reducing the wave function" happens at all (except as a calculational convenience) unless we adopt an interpretation of QM that includes that. Not all interpretations do.

In other words, how the "paradox" you describe is resolved depends on which interpretation of QM you adopt. That is why this thread has been moved to the interpretations subforum.

 

[bobob]

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution).

If the two photons have a spacelike seperation when measured, the two photons were always spacelike seperated. The two photons produced by parametric down conversion have never interacted with each other.

Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).

I think the use of the term "non-local" is not helpful here. It is used inconsistently to mean different things in different articles.

For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion.
To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations.

Again, I don't think the use of "non-local" here means what you are trying to suggest.

Thus, by demonstrating quantum nonlocality for photons that never interacted...

Why do you think the above implies what you have in brackets below?

[and could therefore not have been prepared initially in the synchronized state vanhees71 imagines],

First, the use of synchronized here doesn't relate to the standard usage (as Einstein used it) of the word in which synchronization takes place via causal processes. The two photons are created with a spacelike seperation, so I don't know what synchronization means in that context.

The following article on parametric down conversion might be interesting:

https://arxiv.org/ftp/arxiv/papers/1809/1809.00127.pdf

To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.

In an earlier post you mentioned "influences" as different from "cause."
How are those not synonymous here? In Bell's type experiments, the measurements are independant of each other, which by definition means the measurements are not causally connected.

 

[gentzen]

I think the use of the term "non-local" is not helpful here. It is used inconsistently to mean different things in different articles.

Sorry, but I find the sentence from DrChinese perfectly understandable. You are free to suggest a reformulation of his sentence. If it should be indeed more understandable, or at least not significantly less understandable to me, than I could be willing to revise my opinion.
Of course, the word "local" means different things in different contexts. But that does not yet imply any inconsistency, or that the word would be "not helpful".

Again, I don't think the use of "non-local" here means what you are trying to suggest.

Can you enlighten me what DrChinese is trying to suggest, from you point of view?

I am neither a fan of bashing the word "local", nor of concluding wrong things from a statement like "QM is nonlocal". I am especially opposed to conclude the false statement "QM is incompatible with special relativity" from the true statement "QM is nonlocal".

 

[martinbn]

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. ...

I don't understand why you disagree with that! Surely the state the system is in is due to the preparation. The state contains all the information about the measurement outcomes. All predictions are based on it and the experiments confirm them.

 

[martinbn]

Nevertheless, relativistic spacetimes admit a causality structure (at least locally), and you can always choose your time-like coordinate such that the causal ordering is as usual, i.e., if two events have a cause and effect relation you can always make the time-like coordinate such that the event at the smaller time coordinate must be the cause.

Coming back to this, which of course is true. The point that I was trying to make was different. Given an event A, all other events can be divided into those in the future of A, in the past of A, and the rest. You can also choose a time coordinate, which gives a label to all events. Then all events can be divided into those with time coordinate bigger than that of A, smaller than that of A or equal to that of A. In classical physics these two divisions are the same (or at least they can be, it depends on how you choose the time parameter). In relativity they are definitely not the same. My statement is that often in the Bell type discussion people forget that. In classical physics if an event B has time coordinate bigger than that of A, then B is in the causal future of A and can be influenced by A. In relativity if B has bigger time coordinate it doesn't mean that it is in the causal future of A. But in these discussions some people try to use that as one of their steps in their arguments to conclude that there are possible influences from A to B.

 

[vanhees71]

What you mean - and I vehemently disagree with - is: "the long-ranged correlations are there because of the [initial local] preparation of the system. Words in brackets added by me to your statement. Of course, the entangled system has spatial (I would call it "spatiotemporal") extent. And all the questions we have pertain to how we get perfect correlations from the expanded system WITHOUT some kind of FTL influence - since the measurements are made independently later (than your locally prepared solution). Since the entangled system itself has spatial extent and is therefore nonlocal from one spot to another, there is something "nonlocal" going on - which is termed "quantum nonlocality" (because we do not further understand the nature of the nonlocality).

There is no FTL influence. The correlations are there due to the preparation made before the measurements. Of course the entangled state has spatial extent, because photons are not localizable at all.

Now we entering the endless debate about locality, and I use locality always in the sense it's understood in the relativistic-QFT community, i.e., a local QFT is a QFT, where the Hamilton density is a function of the field operators and their derivatives at one spacetimepoint and field operators representing local observables, among them the Hamilton density (energy density), commute at space-like separated arguments. This excludes the posibility of faster-than-light causal influences.

There are long-ranged correlations, i.e., observables on a quantum system taken at far-distant places can be strongly correlated although the observables are maximally uncertain due to the preparation of the system. That's what's described by entanglement.

The alleged tension between locality (in the above precise mathematical sense) and long-range correlations are thus not there in relativistic local QFTs, and these theories are in accordance with all observations.

For other readers: the statements of vanhees71 are his opinion, and virtually all those studying Bell and QFT do not share his opinion. To date, he has not produced a single quotation from any well respected source echoing his viewpoint - he just says it is "obvious" from QFT. On the other hand, the statements affirming the existence of "quantum nonlocality" are legion. 2022 Nobel winner Zeilinger: "The nonlocality is confirmed by observing a violation of Bell’s inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted [and could therefore not have been prepared initially in the synchronized state vanhees71 imagines], our results directly confirm the quantum nature of teleportation."

Here, Zeilinger uses another notion of locality than that used in relativistic QFT. If you read Zeilinger's scientific papers, it's pretty clear that he is pretty much a follower of the standard Copenhagen interpretation. That "locality" is used with different meanings in different scientific communities is not my fault!

To the OP: there is no paradox. Relativistic QM does not offer a local causal mechanism/explanation for Bell type entanglement, and does not offer an FTL signaling mechanism that would violate relativity. Quantum nonlocality coexists with relativity, they operate in different domains.

I do think we have answered the OP. If we want another go at whether QFT demands local causality, that discussion belongs in the Interpretations subforum.

Now you precisely say, what I'm saying, i.e., you are contradicting yourself. Since this thread is now in the interpretation subforum, I refrain from further following it.

 

[gentzen]

That "locality" is used with different meanings in different scientific communities is not my fault!

Fully agreed. And it is not a problem anyway, in my opinion. Locality is a general concept, not a technical term.

Since this thread is now in the interpretation subforum, I refrain from further following it.

Wow, this sounds to me like you are intentionally bringing up interpretational issues in answers to beginners questions. The corresponding "irony" was already pointed out earlier in this thread:

This, perhaps, is a meta-postulate, that is, a postulate that lies behind "ordinary" postulates. If so, then it belongs to meta-physics, rather than "ordinary" physics. But I know that you don't have a high opinion on meta-physics, so it's a bit ironical that you put such a strong emphasis on a postulate that seems to be a meta-postulate.

Then it belongs to philosophy of science, not to physics proper. But physics, as the most fundamental science, often has aspirations to explain some general scientific principles from more fundamental physics principles.

I guess your reasoning is that other answers already brought it up, and therefore you were kind of forced to react. But I think the deeper issue for you is about how to teach and explain relativistic QT. You somehow believe that teaching QFT right from the start is the only valid answer:

Now the only successful relativistic QT is local (sic!) relativistic QFT, which is constructed such that the causality structure of special relativistic spacetime is fulfilled.

 

[vanhees71]

Fully agreed. And it is not a problem anyway, in my opinion. Locality is a general concept, not a technical term.Wow, this sounds to me like you are intentionally bringing up interpretational issues in answers to beginners questions. The corresponding "irony" was already pointed out earlier in this thread:

This is not an interpretational issue. It's a mathematical issue. Relativistic QFT in its usual form as a local QFT excludes faster-than-light propagation of causal effects/signals. That's not an interpretational but a mathematical fact. Of course we use it to construct the "right" relativistic QTs, because we want to be able to interpret the formalism physically, and physics in the form we know it, implies causality! If you call this an interpretational issue, fine with me.

I guess your reasoning is that other answers already brought it up, and therefore you were kind of forced to react. But I think the deeper issue for you is about how to teach and explain relativistic QT. You somehow believe that teaching QFT right from the start is the only valid answer:

Indeed this horse is beaten to death in this forum, and that's why I don't need to repeat these mathematical arguments again and again.

 

[DrChinese]

1. There is no FTL influence. The correlations are there due to the preparation made before the measurements.

2. Of course the entangled state has spatial extent, because photons are not localizable at all.

3. Here, Zeilinger uses another notion of locality than that used in relativistic QFT. If you read Zeilinger's scientific papers...

1. As I have pointed out a zillion times, the entanglement can be created AFTER Bell measurements are performed. That shows how absurd your argument is.

There is no experimental evidence that indicates that the quantum world respects local causality. And I don't know of any respected author in the field that would agree with you on this point.2. The component photons in actual Bell experiments are localizable to relatively small sections of spacetime. True, they are not exact point particles in the usual sense. But that is NOT the spatial extent I am referring to.

A biphoton has spatial (actually spatiotemporal) extent as its path is shaped by the experimenter on its way to Alice (in one place) and Bob (in another). This is the spacelike separation. Somehow the biphoton is able to "collapse" into 2 separable photons that are consistent with joint measurements by Alice and distant Bob, but are NOT consistent with independent (and therefore separable) measurements by Alice and distant Bob. That's the quantum nonlocality Zeilinger refers to.3. And again, no quotes to support your position. Your quotes are always: a) trust me as I quote myself; or b) read every book or paper ever written, and trust me, there's a quote somewhere. A call for a relevant quote should not go unanswered in PF, and you get away with it far too often.

-DrC

 

[vanhees71]

ad 1) I have repeatedly argued that also entanglement swapping doesn't imply any non-local causal influences. The entanglement swapping is by selecting events based on measurements on entangled systems, i.e., the entanglement of the corresponding subensembles is as well explained by the entanglement of the original systems, and this entanglement was due to the preparation of these systems.

I don't know, what you'd accept as empirical evidence for the locality of interactions. The point is that with local relativistic QFT we have a theory, where all interactions are local, and today there's not a single experiment violating the predictions of local relativistic QFT, i.e., all phenomena can explained with this kind of theory, which is consistent with the relativistic causality structure of spacetime.

ad 2) Now you contradict yourself. In your posting before you emphasized the finite extension of the "wave packets". Now you make a point about the localization of the photons. Indeed what's "localized" are the detection events at A's and B's detectors, and these can indeed by space-like separated, which excludes a causal influence of one of these events on the other, and this assumption is usually made by all experimenters performing such experiments, and this is indeed justified, because these experiments are in accordance with local relativistic QFT! If you deny the validity of the locality (microcausality) principle, you also deny the validity of this argument, which for sure is not denied in all papers on the subject I'm aware of.

The experiments are also independent, as has been demonstrated by randomly choosing the observable measured at A's and B's place independently, again in a way, where relativistic causality excludes a mutual causal influence of one of these choices on the other.

3) As I said before, any paper I know, take the locality assumption as an argument rather than denying it. I think this is once more a misunderstanding, because you don't accept the precise definition of locality as used in relativistic QFT, but I defined precisely what I mean by locality, namely the validity of the microcausality condition for local observables.

 

[StevieTNZ]

Now you precisely say, what I'm saying, i.e., you are contradicting yourself. Since this thread is now in the interpretation subforum, I refrain from further following it.

So are you, by continuing to post in this thread.

 

[martinbn]

1. As I have pointed out a zillion times, the entanglement can be created AFTER Bell measurements are performed. That shows how absurd your argument is.

Correct me if I am wrong but some entanglement is created before the measurements. You cannot have all entanglement created after the measurements. And all swapping happens through local interactions. There is no swapping at a distance, is there?

 

[vanhees71]

Precisely that's my point!

 

[DrChinese]

Correct me if I am wrong but some entanglement is created before the measurements. You cannot have all entanglement created after the measurements. And all swapping happens through local interactions. There is no swapping at a distance, is there?

There is no requirement that the entangled system being tested (via a Bell test) be created before the swap (which creates the entanglement). The decision to do that can be done after the measurements. The swap can be done anywhere, and need not be close (local) to Alice or Bob's measurements. Yes, you are correct that there is some entanglement created before the swap - and keep in mind that the later swap also creates the final entanglement in an apparently retrocausal manner. An entangled system operates in spacetime that has no classical analogy. Alice can observe her particle before Bob's is ever created, and before a swap occurs. How can you begin to describe that in classical terms?

The thing to remember, when considering swapped entanglement experiments, is that the Bell statistics are respected regardless of ordering. Nothing changes when sequence changes, which you would absolutely expect (that it would change) if we were witnessing local causality (which was ruled out by Bell of course).

In any Bell test on a stream of biphotons (created by any means, and regardless of whether post-selection occurs), I can tell Alice and Bob to test polarization at any angle across 360 degrees (essentially a large/infinite number of possibilities). After the swap, we will see perfect correlations (a signature of entanglement) - despite the fact that Alice's portion of the biphoton never interacted in any manner with Bob's portion of the biphoton. The ONLY interaction that occurs is where the swap occurs, which is distant to both Alice and Bob. How is it that these perfect correlations ONLY occur when a swap occurs, despite the swap being distant? Oh, and AFTER the component photons observed have had a change to interact in the beam splitter (in the Bell State Measurement device). Because their interaction is an absolute requirement for us to see the perfect correlations elsewhere! If you sent those same 2 component photons through the BSM in manner in which they DON'T meet, then even when you get the same triggers in the BSM there is no entanglement (and therefore no perfect correlations).

Anyone who claims that post-selection changes the situation (as I have described above) is flat out wrong. The only requirement for swapping is that the component photons arrive together within a narrow time window - something that is a requirement for all Bell tests. And having this interaction occur AFTER the perfect correlations are already recorded proves that local causality cannot be present - and therefore cannot be a feature of QFT. Or any other theory, as we already knew post-Bell.

 

[vanhees71]

This is all clear, but indeed the point is that for entanglement swapping you need two entangled pairs prepared before all the manipulations for swapping are done. After the swapping you have entangled two photons that have never been in causal contact through local measurements.

 

[kurt101]

How can you begin to describe that in classical terms?

I think there is a simple classical explanation that preserves causality with the entanglement swapping experiment.

The entanglement swapping experiment case where the BSM test is done after the measurements can be thought of as the inverse of the basic EPR experiment. In the basic EPR experiment (like Alain Aspect 1983) the two photons are in the same state when they are created at the SPDC and then the "action" that changes the photon states happens afterwards. In the entanglement swapping experiment, in the case where the BSM test is done after the measurements, you are doing the inverse; the "action" happens first when the measurements are done and then the BSM test happens after when you are looking for the condition where the photons are in the same (or perpendicular) state.

In other words, with this explanation, it is the symmetry in the entanglement swapping experiment that tricks you into thinking that true entanglement swapping is happening in all cases, but it does not actually happen in the case where the BSM test is done last.