Exploring Measurements in Quantum Field Theory: From Light Cones to Bell Tests

[Delta Kilo]

TL;DR Summary

How is measurement of entangled particles treated in relativistic QFT?
With reference to https://arxiv.org/abs/2304.13356

Hello, I'm interested in how measurement, entanglement, bell test etc are handled in QFT.
It seems most QFT texts are being quite light on details on the subject. There would be is a preparation step as the start followed by some interaction and a measurement at the end. Interaction is usually where interesting stuff happens. The preparation is assumed to put the fields into some initial configuration and measurement gets the values of some observables and that's about it, there are no further details.

But there must be a lot of interesting things to say about measurement in QFT. For one, any effect of it is confined to future light cone.
Two space-separated measurements do not interact until their respective light cones intersect. Then a measurement has to have some minimal duration until the corresponding light cone encompass a portion of the measuring apparatus with enough degree of freedoms so we can say measurement has happened. It all has implications for both collapse models and MWI.

So far I found this: Measurement in Quantum Field Theory
Unfortunately I'm not versed in Algebraic QFT (to put it mildly) so it's hard for me to tell if what they do is trivial or ground-breaking.
But I appreciate general direction in which they are going, it sort of all makes sense.

I'd like to see QFT treatment of a standard bell test scenario where 2 maximally entangled particles fly from origin O to spacelike separated Alice and Bob who measure then along angles $\alpha$ and $\beta$ and send their results to Charlie for comparison. I am prepared to invest efforts into learning new stuff to get through it.

 

[A. Neumaier]

I'd like to see QFT treatment of a standard bell test scenario

What about the following?

• Summers, Stephen J., and Reinhard Werner. "Bell’s inequalities and quantum field theory. I. General setting." Journal of Mathematical Physics 28, no. 10 (1987): 2440-2447.

and the papers citing it according to Google Scholar.

 

[DrChinese]

What about the following?

• Summers, Stephen J., and Reinhard Werner. "Bell’s inequalities and quantum field theory. I. General setting." Journal of Mathematical Physics 28, no. 10 (1987): 2440-2447.

and the papers citing it according to Google Scholar.

1. I found some of the related work by Summers and Werner here, also from 1987:
https://www.researchgate.net/publication/225241368_Maximal_violation_of_Bell's_inequalities_is_generic_in_quantum_field_theory
Maximal violation of Bell's inequalities is generic in quantum field theory (Note: select the "Read Full Text" option)

​

2. This article - only partially available - references @a-neumaier 's citation:

https://www.sciencedirect.com/science/article/abs/pii/S1355219813000683
Bell inequality and common causal explanation in algebraic quantum field theory (2013)

 

[Delta Kilo]

What about the following?

• Summers, Stephen J., and Reinhard Werner. "Bell’s inequalities and quantum field theory. I. General setting." Journal of Mathematical Physics 28, no. 10 (1987): 2440-2447.

and the papers citing it according to Google Scholar.

Yes, thank you. I was going to read it, after I saw a follow-up:
Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets
(I learned a new word: bumpification )

From Summers' paper:

It is not our intent to enter into a philosophical discussion of Bell's inequalities in this forum. Our aim is to show that, just as quantum mechanics does, quantum field theory (QFT) predicts a maximal violation of Bell's inequalities, and that in
fact, unlike quantum mechanics, QFT predicts that this maximal violation is generic in a sense we shall explain.

That QFT predicts the same maximal Bell violation as QM is good to know but not really a surprise.
(the rest of the paper is way over my head)
The other paper shows the construction of explicit test functions in a toy model to achieve maximal violation.
They evaluate expectation value for the Bell-CHSH correlator:
$$\langle C \rangle = \langle 0|i[(\mathcal A_f + \mathcal A_{f'}) \mathcal A_g + (\mathcal A_f - \mathcal A_{f'}) \mathcal A_{g'}]|0 \rangle$$ where $f, f'$ and $g,g'$ are Alice and Bob's test functions for different angle settings. I guess it's all fine but it does not tell how to go about doing it in a lab.

This is actually part of my problem, when I read something like "to measure blah we apply operator foo to particle wavefunction and..." how exactly do you apply an operator to a particle wavefunction in a lab?
Well, the only way I can think of is to couple it to another system (measurement apparatus) in a certain way but then it gets a whole lot more complicated...

 

[vanhees71]

It becomes "practical" now:

https://physicsworld.com/a/quantum-entanglement-observed-in-top-quarks/

and the scientific paper (open access):

https://link.springer.com/article/10.1140/epjp/s13360-021-01902-1

 

[DrChinese]

It becomes "practical" now:

https://physicsworld.com/a/quantum-entanglement-observed-in-top-quarks/

and the scientific paper (open access):

https://link.springer.com/article/10.1140/epjp/s13360-021-01902-1

A follow-up (updated?) paper is essentially the same research as the Springer 2021 paper cited above, whose authors are a part of the ATLAS collaboration. I assume they were the leads on the newer paper.

https://arxiv.org/abs/2311.07288
ATLAS Collaboration
Observation of quantum entanglement in top-quark pairs using the ATLAS detector (2023)
"The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes both the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement to date."

Pretty impressive stuff. And just as predicted per Afik and de Nova in a 2020 proposal.

 

[WernerQH]

I'm interested in how measurement, entanglement, bell test etc are handled in QFT.

For me, quantum (field) theory is a microscopic theory, and there is no place for a concept like "measurement" in a fundamental theory. I think this is what John Bell expressed in his article "Against Measurement". It should be possible to describe what happens in a Bell-type experiment without worrying about every detail of the macroscopic detectors, and describe it more directly in terms of the photon propagators.

In the double-slit experiment there is an amplitude for a photon to go from the source S through slit A to the detector D: $( S \to A ) \times ( A \to D )$, and similarly $( S \to B ) \times ( B \to D )$ for going through the second slit B. As is well known, the probability that the photon arrives at the detector D is proportional to $$ \left| ( S \to A ) \times ( A \to D ) + ( S \to B ) \times ( B \to D ) \right|^2 \qquad . $$ The amplitude for the inverse process $( A \to S )$ is the complex conjugate of $( S \to A )$, so the probability can be rewritten as $$ \begin{align*} & ( S \to A ) \times ( A \to D ) \times ( D \to A ) \times ( A \to S ) \\ + & ( S \to B ) \times ( B \to D ) \times ( D \to B ) \times ( B \to S ) \\ + & ( S \to A ) \times ( A \to D ) \times ( D \to B ) \times ( B \to S ) \\ + & ( S \to B ) \times ( B \to D ) \times ( D \to A ) \times ( A \to S ) \end{align*} \quad , $$ the third and fourth line representing interference terms, where the return path is different from the forward path. This is how the Born rule (which is often associated with the concept of measurement) enters QFT. In the Schwinger-Keldysh formalism it is built-in through integration over a "closed time-path". In quantum optics people refer to it as the Klyshko picture. It's the integral over a closed time-path that gives us directly the probability of a particular pattern of events.

In the case of a Bell-type experiment with two photons emitted from a source S arriving at two detectors A and B you can write down an analogous probability: $$ ( S \to A ) \times ( A \to S ) \times ( S \to B ) \times ( B \to S ) \quad , $$ expressing the correlations at the two remote detectors. The point is that the photon propagator also extends into the backward light cone, something you might interpret as backward causation. But it is misleading to think of one event "causing" another. The formalism just ensures that the pattern of events is always consistent, that conservation laws are satisfied (e.g. that a single photon emitted by one atom can be detected by at most one detector).

Hope this clarifies how QFT can be local and violate the Bell inequalities at the same time. I don't think that there's anything traveling from the source to the detectors, neither waves nor (entangled) particles. What is called photon propagator is just a mathematical expression that allows us to compute correlations between events.

 

[DrChinese]

1. Hope this clarifies how QFT can be local and violate the Bell inequalities at the same time.

2. I don't think that there's anything traveling from the source to the detectors, neither waves nor (entangled) particles. What is called photon propagator is just a mathematical expression that allows us to compute correlations between events.

1. It might be fair to use this explanation for an ordinary Bell setup - which was the original question as you note. However, all of this falls apart (IMHO) when you start talking about Bell tests in which there is no common backwards light cone.

Characterizing the nonlocal correlations of particles that never interacted (2018)
"Starting from two independent pairs of entangled particles, one can measure jointly one particle from each pair, so that the two other particles become entangled, even though they have no common past history. The resulting pair is a genuine entangled pair in every aspect, and can in particular violate Bell inequalities."
Note that the entanglement operation (Bell State Measurement) itself can be performed outside of the backwards light cone of the final entangled particles. For that matter, it can be performed outside the forward light cone of those same entangled particles as well. So there is neither forward or backward overlapping time cones.

[Note: @vanhees71 has attempted to explain this using QFT a number of times, primarily by invoking arguments such as "local causality is built into QFT, and QFT is the best theory we have". You can imagine how well that goes over in the experimental world, in which quantum nonlocality is generally accepted (often mentioning that "local causality" cannot hold post-Bell). But his argument is actually circular, as he assumes that which he seeks to prove.] 2. I don't see how this follows from the rest of your post. Photons are exactly what travel from a source to a detector. They are "real" in any sense I can think of, and are not merely mathematical abstractions. Whether or not they follow a single specific path is a different question.

 

[PeterDonis]

"local causality is built into QFT, and QFT is the best theory we have"

The issue with this claim of his is not that it's circular, but that it uses a different definition of "local" than you (and most of the experimental literature that you reference) use. Your definition of "local" is basically "does not violate the Bell inequalities". His definition of local is basically "spacelike separated measurements commute". Both of your claims are true with the appropriate definitions: QM (and QFT) are nonlocal because they violate the Bell inequalities, but QFT (and QM in these cases since non-relativistic QM also says the measurements involved in these experiments commute) are local because spacelike separated measurements commute. (In fact in the experiments you have referenced, the measurements commute regardless of whether they are spacelike, null, or timelike separated.) So when he says "QFT is local", he is actually not disagreeing with you (though he often claims that he is, or at least implies it). He's just focusing on an aspect of QFT which is, for all practical purposes, irrelevant to the experiments you are referencing.

 

[DrChinese]

1. The issue with this claim of his is not that it's circular, but that it uses a different definition of "local" than you (and most of the experimental literature that you reference) use. Your definition of "local" is basically "does not violate the Bell inequalities". His definition of local is basically "spacelike separated measurements commute". *

2. He's just focusing on an aspect of QFT which is, for all practical purposes, irrelevant to the experiments you are referencing.

1. Most experimental literature is the same as my usage. That's because I follow the literature closely, as I am not original enough to invent my own lingo.

J.S.Bell (and requoted by Alain Aspect): "It has been argued that quantum mechanics is not locally causal and cannot be embedded in a locally causal theory." And of course, this is certainly in the Bell sense.2. Correct (i.e. I agree his QFT argument does not fit the example at hand). We have agreed here that the usage by @vanhees71 of "local causality" in the sense that there must be "signal locality" as reasonable and acceptable. As you say, I'm not objecting to that. I am objecting to the idea that there is a QFT explanation for the experiments demonstrating entanglement of particles which never existed in a common light cone. Search as I might, I have seen no convincing QFT papers on this. It's all just plain QM.

So I give @WernerQH due credit for directly addressing Bell in the first place.

---

* Help me out here. The phrase "spacelike separated measurements commute" seems to lack useful meaning, certainly in the context of entanglement. If something commutes locally, then it also commutes nonlocally, agreed?

So... what is there that commutes nonlocally, but that does not commute locally? I cannot think of an experimental setup that would demonstrate this. Thanks in advance...

 

[gentzen]

* Help me out here. The phrase "spacelike separated measurements commute" seems to lack useful meaning, certainly in the context of entanglement. If something commutes locally, then it also commutes nonlocally, agreed?

Take a step back, and look at "timelike separated measurements". In that case it is always clear which measurement came first, and which later. So testing experimentally whether those measurements commute or not seems possible. Because the whole thing involves statistics, it is not so clear cut, but in the end it somehow works in practice. However, for "spacelike separated measurements", it depends on the inertial frame which ones comes first, and which later. So if those measurements would not commute, then you would have serious trouble if you wanted to claim Lorentz invariance.

 

[PeterDonis]

I am objecting to the idea that there is a QFT explanation for the experiments demonstrating entanglement of particles which never existed in a common light cone. Search as I might, I have seen no convincing QFT papers on this. It's all just plain QM.

Since QM is just the non-relativistic limit of QFT, a QM explanation of an experiment where relativistic effects are negligible (and you have already agreed that this is the case for the experiments we are discussing here) is a QFT explanation. The lack of papers that explicitly use QFT to analyze such experiments is simply because nobody has the copious free time to go and re-derive QM as the non-relativistic limit of QFT again and again in order to explain each new experiment.

 

[DrChinese]

Take a step back, and look at "timelike separated measurements". In that case it is always clear which measurement came first, and which later. So testing experimentally whether those measurements commute or not seems possible. Because the whole thing involves statistics, it is not so clear cut, but in the end it somehow works in practice. However, for "spacelike separated measurements", it depends on the inertial frame which ones comes first, and which later. So if those measurements would not commute, then you would have serious trouble if you wanted to claim Lorentz invariance.

And yet: what's an example of something in which the statement "spacelike separated measurements commute" is relevant? AFAIK, any pair of spacelike measurements commute (or don't commute) equally in QM or QFT. Lorenz invariance is not a factor in the expectation value. Locality is not an issue.

 

[PeterDonis]

what's an example of something in which the statement "spacelike separated measurements commute" is relevant?

Timelike or null separated measurements can be causally connected in the ordinary way, in which case they certainly will not commute. "Spacelike separated measurements commute" is basically a way of ruling out ordinary causal connections between those events, so that ordinary causality respects the light cone structure of spacetime. That's a brief response, anyway. For a more detailed one, you might try, for example, the introduction to Volume I of Weinberg's classic The Quantum Theory of Fields.

(I say "ordinary causality" to avoid taking any position here on whether whatever kind of connection there is between entangled particles that enforces correlations that violate the Bell inequalities is a "causal" connection. If it is, it certainly isn't an "ordinary" one since it has to work even though the measurements commute. But it's logically possible that there are other kinds of causal connections besides the "ordinary" kind.)

 

[PeterDonis]

AFAIK, any pair of spacelike measurements commute (or don't commute) equally in QM or QFT.

Huh? All spacelike separated measurements commute in QFT, by construction. In non-relativistic QM, you can take a pair of measurements that don't commute, and make them spacelike separated, and they still won't commute. Non-relativistic QM has no way of ruling that out unless you add auxiliary assumptions.

A better question might be whether there are any meaningful cases in QFT where the non-commuting measurements aren't on the same particle, since in QFT two measurements made on the same particle cannot be spacelike separated, since the particle has to travel between them and it can't travel faster than light. In non-relativistic QM there is no such restriction, so we could conceive, for example, of measuring spin-z and spin-x on the same spin-1/2 particle at spacelike separated events, and those measurements would not commute.

 

[vanhees71]

1. Most experimental literature is the same as my usage. That's because I follow the literature closely, as I am not original enough to invent my own lingo.

J.S.Bell (and requoted by Alain Aspect): "It has been argued that quantum mechanics is not locally causal and cannot be embedded in a locally causal theory." And of course, this is certainly in the Bell sense.

But that's obviously not true, because relativistic QFT is a locally causal theory by implementing the microcausality constraints for local observables. Of course quantum mechanics, as a non-relativistic theory is not local, but that's not the point. The point is that there is a consistent relativistic, causal formulation of a QT, and the causality is realized, as in classical relativistic physic, by using fields and a pretty strict "locality principle", i.e., microcausality.

2. Correct (i.e. I agree his QFT argument does not fit the example at hand). We have agreed here that the usage by @vanhees71 of "local causality" in the sense that there must be "signal locality" as reasonable and acceptable. As you say, I'm not objecting to that. I am objecting to the idea that there is a QFT explanation for the experiments demonstrating entanglement of particles which never existed in a common light cone. Search as I might, I have seen no convincing QFT papers on this. It's all just plain QM.

So I give @WernerQH due credit for directly addressing Bell in the first place.

Of course, all the experiments you quote, particularly those with photons, which cannot be described in any other way than local relativistic QFT, are described correctly by this QFT. We have discussed this over and over again, and I thought finally you accepted these mathematical facts.

The possibility of entanglement swapping, i.e., entangleling two photons which never have been in direct causal contact, is fully compatible with relativistic QFT. It's possible because the two independently prepared photon pairs where each prepared in a Bell state, and that preparation is in the past lightcone of each of the local measurements necessary to select (or even post-select!) the subensemble, where the two photons, before being completely uncorrelated, are in a Bell state. There's no violation of Einstein-causality whatsoever, and even the argument that the two photons, which are entangled in these sub-sensembles, were "never in causal contact" is based on the assumption that Einstein-causality, i.e., that space-like separated events (the local measurements on the four photons at far distant places) cannot be causally connected!

---

* Help me out here. The phrase "spacelike separated measurements commute" seems to lack useful meaning, certainly in the context of entanglement. If something commutes locally, then it also commutes nonlocally, agreed?

So... what is there that commutes nonlocally, but that does not commute locally? I cannot think of an experimental setup that would demonstrate this. Thanks in advance...

Where is any lack of "userful meaning". A photon detection is a click of a detector at a certain time and a certain place, where this detector is located, and the setups of these Bell experiments have been made with a lot of effort such that these measurement events are space-like separated and thus that there's no causal influence of one measurment on the other done far away. In some experiments even the choices of which observable is measured at each place is constructed such as to be space-like separated, i.e., even the very choices of which observable is measured cannot causallyt affect each other. Again, in this argument Einstein causality is assumed (!) to hold!

 

[gentzen]

Of course quantum mechanics, as a non-relativistic theory is not local, but that's not the point.

That statement is wrong, at least if precedeed by "of course". Newtonian mechanics without gravitation and other non-locally acting forces is local, despite not being Lorentz invariant, i.e "relativistic". Non-relativistic quantum mechanics can be used to model quantum computing, and if one considers only one-qubit gates and locally acting two-qubit gates, then everything is in fact just as local (with respect to the connectivity struture of the quantum chip) as is Newtonian mechanics without gravitation.

 

[gentzen]

That statement is wrong, at least if precedeed by "of course".

It would be correct, if we focus on the way non-relativistic QM gets applied to atoms and molecules: There one directly plugs in the non-locally acting electrostatic potential as the interaction between the electrons and nuclei. But for macroscopic distances, one is normally more careful, and does not use such non-local stuff.

So for very short distances, it is true that non-relativistic QM is typically also used in a non-local manner. But that is not relevant for the experiments that DrChinese is interested in, where everybody is very careful to use non-relativistic QM only in a manner which respects locality.

 

[WernerQH]

1. It might be fair to use this explanation for an ordinary Bell setup - which was the original question as you note. However, all of this falls apart (IMHO) when you start talking about Bell tests in which there is no common backwards light cone.

Why? Using zig-zag lines with pieces going forward and backward in time you can, in principle, construct arbitrarily long spacelike "causal" chains. Of course the probabilities become very, very small as you add more and more pieces.

2. I don't see how this follows from the rest of your post. Photons are exactly what travel from a source to a detector. They are "real" in any sense I can think of, and are not merely mathematical abstractions.

You are right. Of course it's an absolutely compelling idea that photons "travel" from the source to the detector. As compelling as the idea that light waves cannot exist without an aether carrying them was for Maxwell. Like the aether, traveling photons have conflicting attributes: polarization is one of their fundamental features, but while the photons in the Bell-type experiment are on the way to the detectors, they are (according to @vanhees71) "completely unpolarized". I think it's more economical to define photons simply as pairs of emission and absorption events, rather than "entangled" entities with imprecise undefined properties. Moreover, these photons are identical: if you have one photon $A \to B$ and another one $C \to D$, the Feynman rules say that you also have to add the amplitudes $A \to D$ and $C \to B$. There aren't any facts of the matter "which" photon interacted with "which" electron. For this reason I prefer to think of distributed point-like events rather than some continuous "stuff" connecting them. After eons of evolution we have no difficulties detecting correlations between events, discerning patterns, or words in what are in fact only separate pixels on a computer screen. So my view of quantum theory is decidedly non-local!

For most physicists Wheeler-Feynman absorber theory has little appeal. But its mere existence shows that locality is not a strict conditio sine qua non for physics. Just like the gravitational potential can give Newtonian action at a distance a local flavour, we can introduce fields as a convenient book-keeping device. John Cramer created the Transactional Interpretation featuring forward running (in time) "offer waves" and backward running "confirmation waves". This is similar to what I described in my first post, but I cannot accept these waves as physically real. With more than one particle present they can only propagate in an abstract high-dimensional configuration space. I've never understood how exactly Cramer's transactions come about. My view is thus not only non-local but also non-realist, if you insist that continuous fields must exist. What I think of as real are only points in spacetime. Particles and fields are just names we give to special patterns of events.

 

[vanhees71]

Why? Using zig-zag lines with pieces going forward and backward in time you can, in principle, construct arbitrarily long spacelike "causal" chains. Of course the probabilities become very, very small as you add more and more pieces.

I don't know, what you are discussing here about. Which light cones are you referring to?

You are right. Of course it's an absolutely compelling idea that photons "travel" from the source to the detector. As compelling as the idea that light waves cannot exist without an aether carrying them was for Maxwell. Like the aether, traveling photons have conflicting attributes: polarization is one of their fundamental features, but while the photons in the Bell-type experiment are on the way to the detectors, they are (according to @vanhees71) "completely unpolarized". I think it's more economical to define photons simply as pairs of emission and absorption events, rather than "entangled" entities with imprecise undefined properties. Moreover, these photons are identical: if you have one photon $A \to B$ and another one $C \to D$, the Feynman rules say that you also have to add the amplitudes $A \to D$ and $C \to B$. There aren't any facts of the matter "which" photon interacted with "which" electron. For this reason I prefer to think of distributed point-like events rather than some continuous "stuff" connecting them. After eons of evolution we have no difficulties detecting correlations between events, discerning patterns, or words in what are in fact only separate pixels on a computer screen. So my view of quantum theory is decidedly non-local!

If you mean "travelling" in the sense of "propagation of the em. field", it's all fine. You only must not think of photons in terms of little bullets moving along a trajectory. Photons cannot be localized, i.e., there's no position observable for them. All this is properly implemented in the field operators and thus the Feynman diagrams describing the propagation of the photon, including to your statements about the amplitudes.

For most physicists Wheeler-Feynman absorber theory has little appeal. But its mere existence shows that locality is not a strict conditio sine qua non for physics. Just like the gravitational potential can give Newtonian action at a distance a local flavour, we can introduce fields as a convenient book-keeping device. John Cramer created the Transactional Interpretation featuring forward running (in time) "offer waves" and backward running "confirmation waves". This is similar to what I described in my first post, but I cannot accept these waves as physically real. With more than one particle present they can only propagate in an abstract high-dimensional configuration space. I've never understood how exactly Cramer's transactions come about. My view is thus not only non-local but also non-realist, if you insist that continuous fields must exist. What I think of as real are only points in spacetime. Particles and fields are just names we give to special patterns of events.

Wheeler-Feynman absorber theory has never lead to a quantum formulation. AFAIK there's no non-local formulation of relativistic QT, satisfying Einstein causality. It's very hard to imagine how such a theory would look like, i.e., not using the pretty intuitive idea of locality to explicitly implement the causality constraints due to relativistic spacetime structure.

 

[WernerQH]

It's very hard to imagine how such a theory would look like, i.e., not using the pretty intuitive idea of locality to explicitly implement the causality constraints due to relativistic spacetime structure.

Obviously we have radically different views on which "constraints" (like locality and causality) are indispensable and "pretty intuitive".

 

[Delta Kilo]

For me, quantum (field) theory is a microscopic theory, and there is no place for a concept like "measurement" in a
fundamental theory.

Well it has to fit somewhere. Sweeping measurements under the rug sort of works as long as all your measurements are asymptotically far away in the past or in the future and you don't care what happens before initial preparation or after final measurement. Granted, most applications of QM and QFT are like that. But not all. Whenever there is a measurement in the middle and we are interested in states both before and after the measurement, measurement problem cannot be avoided.

The point is that the photon propagator also extends into the backward light cone, something you might interpret as backward causation. But it is misleading to think of one event "causing" another. The formalism just ensures that the pattern of events is always consistent, that conservation laws are satisfied (e.g. that a single photon emitted by one atom can be detected by at most one detector).

Yes, retro-causation is one possible way out. QM is all about standing waves and modes and it is not a big stretch to consider standing wave between two timelike events. Not everyone is ready to accept it as an interpretation though. The distinction between "the formalism ensures" and "one thing causes another" is not at all clear.

Since QM is just the non-relativistic limit of QFT, a QM explanation of an experiment where relativistic effects are negligible (and you have already agreed that this is the case for the experiments we are discussing here) is a QFT explanation. The lack of papers that explicitly use QFT to analyze such experiments is simply because nobody has the copious free time to go and re-derive QM as the non-relativistic limit of QFT again and again in order to explain each new experiment.

And this I simply don't understand. I see the term "spacelike separated" been used all the time when discussing Bell's tests and people going into great length to close locality loophole in their experiments. Yet none of it makes any sense in NRQM because there is a global time order for all events and wavefunction reduction is instantaneous according to postulate. And situation in QFT is clearly different and the claim that we are operating in non-relativistic limit here does not hold water. Like if we have 2 detectors separated by 1 meter and synchronously detecting photons, there is a whole 3ns of dead time during which each detector is guaranteed to be free from causal influence of other detector's measurement. And one can do a lot in 3ns, it's enough time to perform the measurement and register the results.

And yet: what's an example of something in which the statement "spacelike separated measurements commute" is relevant? AFAIK, any pair of spacelike measurements commute (or don't commute) equally in QM or QFT. Lorenz invariance is not a factor in the expectation value. Locality is not an issue.

There are no spacelike measurements in NRQM period. The term does not make sense in context of NRQM.

(I say "ordinary causality" to avoid taking any position here on whether whatever kind of connection there is between entangled particles that enforces correlations that violate the Bell inequalities is a "causal" connection.

Yes that's another thing that I don't get, people making this distinction between "causal influence" and "non-local acasual connection" which purportedly spreads faster than light but does not carry classical information so that makes it ok. Lets say there is such an acausal connection, then it must be expressed by some mathematical entity, let's call it X. So, how does X transform under Lorentz group and where does it come from in an otherwise manifestly covariant theory?

 

[PeterDonis]

that's obviously not true, because relativistic QFT is a locally causal theory

@vanhees71, I am tired of having to repeat to you why comments like this from you are not warranted. I am particularly tired of having to do it in a thread where I have already explicitly stated that you and @DrChinese use the term "local" to mean different things, and therefore you are not disagreeing with him and saying that his claims are "not true" is obviously wrong. So now I am banning you from further posts in this thread.

 

[DrChinese]

1. Using zig-zag lines with pieces going forward and backward in time you can, in principle, construct arbitrarily long spacelike "causal" chains.

2. You are right. Of course it's an absolutely compelling idea that photons "travel" from the source to the detector. As compelling as the idea that light waves cannot exist without an aether carrying them was for Maxwell. Like the aether, traveling photons have conflicting attributes: polarization is one of their fundamental features, but while the photons in the Bell-type experiment are on the way to the detectors, they are (according to @vanhees71) "completely unpolarized". I think it's more economical to define photons simply as pairs of emission and absorption events, rather than "entangled" entities with imprecise undefined properties. ... So my view of quantum theory is decidedly non-local!

3. For most physicists Wheeler-Feynman absorber theory has little appeal. But its mere existence shows that locality is not a strict conditio sine qua non for physics.

1. Agreed. Huw Price and Ken Wharton have written on this point, including in Entanglement Swapping and Action at a Distance. They refer to your "zigzag" (which is as good as any) as "cross-W". But they don't cast it in QFT terms specifically.

2. Then I don't see how entangled photons with "undefined" spin properties would then be qualitatively any different from entangled electrons or other entangled systems. I have no issue with your view of QT as non-local.

3. Time symmetry in physics might accommodate effects in QM that appear non-local from our forward-in-time perspective.

 

[PeterDonis]

Using zig-zag lines with pieces going forward and backward in time you can, in principle, construct arbitrarily long spacelike "causal" chains.

Not with the ordinary meaning of "causality", because that requires the "cause" to come before the "effect", and the "backward in time" legs of your zig-zag lines will reverse that.

The transactional interpretation of QM does work something like what you describe, but it does not claim that the connections formed that way are ordinary causal connections.

 

[Delta Kilo]

Looking at the section 4.3 in the paper I linked at the start of the thread. I'm still trying to figure out exactly what is going on there but looks like they are trying to reduce QFT problem to "already solved" QM. In case of multiple measurements they choose (random) causal ordering of measuring devices' "coupling zones" and then pretend it is a normal QM. Then if there are different causal orderings possible (for spacelike separated regions) then they prove the observable effect and the final state is the same (although intermediate states depend on the order). I don't really like it, it sort of works but does not explain anything and it just does not feel properly relativisticslly covariant.

 

[DrChinese]

Timelike or null separated measurements can be causally connected in the ordinary way, in which case they certainly will not commute. "Spacelike separated measurements commute" is basically a way of ruling out ordinary causal connections between those events, so that ordinary causality respects the light cone structure of spacetime. ...

Huh? All spacelike separated measurements commute in QFT, by construction. In non-relativistic QM, you can take a pair of measurements that don't commute, and make them spacelike separated, and they still won't commute. Non-relativistic QM has no way of ruling that out unless you add auxiliary assumptions.

A better question might be whether there are any meaningful cases in QFT where the non-commuting measurements aren't on the same particle, since in QFT two measurements made on the same particle cannot be spacelike separated, since the particle has to travel between them and it can't travel faster than light. In non-relativistic QM there is no such restriction, so we could conceive, for example, of measuring spin-z and spin-x on the same spin-1/2 particle at spacelike separated events, and those measurements would not commute.

I said: AFAIK, any pair of spacelike measurements commute (or don't commute) equally in QM or QFT. And there just aren't any examples where this point isn't true.

Let's be clear to start with: Statistical measurements on entangled systems NEVER show any difference due to order of measurements, and therefore they commute in that sense. It matters not whether the measurements are local or nonlocal to each other. Further, there is no difference I am aware of in which statistical predictions on entangled systems are different in QM as compared to QFT. So I am flat out asking: what is the significance of saying "spacelike separated measurements commute" in QFT unless there is a concrete example to contrast against the predictions of non-relativistic QM?

Otherwise: I am denying there is any practical meaning - and certainly none related to "forward in time local causality" - to the QFT idea that "spacelike separated measurements commute" as it applies to entanglement experiments. You, @gentzen, @Delta Kilo and @vanhees71 had no examples to help me out on that point. At least @Delta Kilo stated what I think should be obvious: there are no such examples (essentially by definition). Which is why I say it is a meaningless phrase (if it has no application whatsoever). Precisely because there are no "causal" outcomes in entanglement experiments, naturally they all (appear to) commute. You don't need to "construct" them that way. It is an empirical requirement that was evident since pre-Bell*.

And as always, I agree that there is no nonlocal signaling in nature. And I also agree that there are no "causal" actions that can result from entanglement, other than those that could be labeled "indeterministic" or random.* In EPR, they concluded that QM was incomplete because they thought that measurements on position and momentum on a pair of entangled particles would violate the Heisenberg Uncertainty Principle - by yielding precise values for what should be non-commuting observables.

 

[PeterDonis]

I am denying there is any practical meaning - and certainly none related to "forward in time local causality" - to the QFT idea that "spacelike separated measurements commute" as it applies to entanglement experiments.

As it applies to entanglement experiments, i.e., the kinds of experiments we are discussing, I believe I have already said that I think this is true. But entanglement experiments are hardly the only kind of experiments that can be done.

 

[WernerQH]

Then I don't see how entangled photons with "undefined" spin properties would then be qualitatively any different from entangled electrons or other entangled systems.

Right. What I said about photons should apply to electrons too. Because we assume these "systems" to have an existence continuous in time, we use contorted language to talk about "entanglement" and "properties" of these systems ("observables") that are not permanent, but become manifest only at instants of time. I prefer also a minimal ontology, and propose to dispense with electrons and photons altogether, considering only interactions between them as "real". Incidentally, "system" was another word that John Bell sought to ban from discussions about the foundations of quantum theory.

Time symmetry in physics might accommodate effects in QM that appear non-local from our forward-in-time perspective.

Yes!

 

[WernerQH]

Well it has to fit somewhere. Sweeping measurements under the rug sort of works as long as all your measurements are asymptotically far away in the past or in the future and you don't care what happens before initial preparation or after final measurement. Granted, most applications of QM and QFT are like that. But not all. Whenever there is a measurement in the middle and we are interested in states both before and after the measurement, measurement problem cannot be avoided.

I don't think there is a measurement problem. Q(F)T works beautifully.
How do you define what constitutes a "measurement"?

Yes, retro-causation is one possible way out. QM is all about standing waves and modes and it is not a big stretch to consider standing wave between two timelike events. Not everyone is ready to accept it as an interpretation though. The distinction between "the formalism ensures" and "one thing causes another" is not at all clear.

Our "forward-in-time perspective" (to borrow @DrChinese's phrase) is firmly based in the macroscopic world. There absorption and emission of light are considered irreversible processes. In the microworld they are symmetric, and it's not clear to me that cause and effect are useful terms for characterizing microscopic events.

 

[Delta Kilo]

I don't think there is a measurement problem. Q(F)T works beautifully.
How do you define what constitutes a "measurement"?

For the QM it is defined in a usual way, as per postulates, as the "R" process of wavefunction reduction whereupon wavefunction collapses into one of the eigenstates of observable operator, as opposed to "U" process of unitary evolution. For example this is from Griffiths:

We say that the wave function collapses upon measurement <...> There are, then, two entirely distinct kinds of physical processes: "ordinary" ones, in which the wave function evolves in a leisurely fashion under the Schrodinger equation, and "measurements", in which $\Psi$ suddenly and discontinuously collapses.

Other people like Ballentine sidestep the issue by refusing to deal with individual systems but only with ensembles of identically prepared systems. Yet others say nothing except macroscopic results is real but just some math tricks that just happen to work and give right predictions.

It's actually hard to define exactly what the measurement problem is because it is manyfold and different interpretations tend to solve some parts while glossing over the others. Some examples:
* Criteria for choosing R process over U process (why some interactions are measurements while others are not).
* Measurement apparatus not fully described by QM, need for quantum/classical cut
* Explaining the apparent single outcome when measuring superposition.
* Explaining/deriving Born rule

I know there's been a great deal of progress in decoherence, einselection etc. and it does answer some questions but apparently not all of them.

I did not include any of the Bell test / spooky-action-at-a-distance issues because I feel a lot of them are due to limitations of QM being non-relativistic and non-local by design. Like a perfectly rigid rod in Minkowsi space. It is my hope that QFT can do better in this regard.

 

[A. Neumaier]

Photons are exactly what travel from a source to a detector. They are "real" in any sense I can think of, and are not merely mathematical abstractions. Whether or not they follow a single specific path is a different question.

A single photon ( an object in an eigenstate of the photon number operator with eigenvalue 1) may be considered to be real in any sense. But in the entangled case, it is not two photons that travel but a single two-photon object (an object in an eigenstate of the photon number operator with eigenvalue 2) travels. This is clear from the way quantum mechanics is argued to violate Bell inequalities.

One cannot separate the two-photon object into two photons. Therefore the photons in entangled photons are quite unreal. What is real is just the detector clicks that are interpreted of having recorded a corresponding number of photons.

 

[Lord Jestocost]

It's actually hard to define exactly what the measurement problem is because it is manyfold and different interpretations tend to solve some parts while glossing over the others.

A so-called measurement problem exists only for those who cling with ferocity to the assumption that the "state vector" is a representation of some reality behind the phenomena.

 

[A. Neumaier]

A so-called measurement problem exists only for those who cling with ferocity to the assumption that the "state vector" is a representation of some reality behind the phenomena.

For those who don't cling to this assumption, a much more severe problem is that of connecting in an objective way the subjective probabilities associated with the vague psychological concept of knowledge to physical reality.

Unless they regard physics as a subdiscipline of psychology, they need to define precisely how and under which objective conditions this subjective knowledge changes.

 

[Delta Kilo]

Thinking about measurements in context of QFT and MWI, I believe there is a way to consistently handle entangled measurements with no spooky actions. Consider typical Bell test. There is a diamond arrangement OABC with 2 particles (say photons) starting at O, measured at spacelike separated A and B, and the results are sent to C, equidistant from A and B, where they are compared.

Let's assume that in a small vicinity of each of the vertices OABC, QFT can be approximated by ordinary QM, but there is a limit of $c$ on propagating speed of any disturbances. So we do get a wave function locally but it can go somewhat out of sync over large distances. Yes, and each wavefunction is assumed to have $|the\ rest\rangle$ appended, which absorbs all other dimensions we don't care about.

So the two photons start at $O$ in a state:
$$|\phi_O\rangle = \sum_{ij} c_{ij} |p_a^i\rangle p_b^j\rangle$$
Photon $p_a$ flies to $A$ where it interacts with $A$:
$$|\phi_A \rangle= |\phi_O\rangle |A\rangle \rightarrow |\phi_A \rangle=\sum_{ijk} a_{ijk} |p_a^i\rangle p_b^j\rangle|A^k\rangle$$
where we get $a_{ijk}$ by converting $p_a$ to $A$'s measurement basis $|m_a^k\rangle$ and back:
$$a_{ijk} = \sum_n c_{nj} \langle p_a^i|m_a^k\rangle \langle m_a^k|p_a^n\rangle $$
and because $|A^k\rangle$ are macroscopic states involving lots of degrees of freedom, the world is split locally, with probabilities of each branch:
$$P(A^k) = \sum_{ij}\left\|a^{ijk}\right\|^2$$
Ditto for $|\phi_B \rangle$:
$$|\phi_B \rangle=\sum_{ijl} b_{ijl} |p_a^i\rangle p_b^j\rangle|B^l\rangle$$
When both results meet at $C$ the results are combined. We can treat is as measurement of $|\phi_A\rangle$ in basis of $|\phi_B^l\rangle$ or $|\phi_B\rangle$ in basis of $|\phi_A^k\rangle$, the result is the same:
$$|\phi_C\rangle = \sum_{ijkl} a_{ijk} b_{ijl} |p_a^i\rangle p_b^j\rangle|A^k\rangle|B^l\rangle$$
with the world split 4-ways:
$$P(A^kB^l) = \sum_{ij}\left\|a_{ijk} b_{ijl}\right\|^2$$
Eventually the split will propagate outwards from C back to A and B and everyone gets a consistent picture of events. If we set photons to be maximally entangled, for example $c_{ij} = \delta_{ij}$ and the values for $\langle m_a^k|p_a^i\rangle$ and $\langle m_b^l|p_b^j\rangle$ appropriate for Bell test angles, we'll get 50% for $P(A^k)$ and $P(B^l)$ and expected probabilities of coincidences $\sum_n P(A^nB^n)$.