# I Confused by nonlocal models and relativity

#### kurt101

Yes, 1 & 4 are fully entangled on the polarization basis (also a couple of other bases). This is demonstrated by violation of a Bell Inequality. Think of it like this: if you were to check the polarization of 1 & 4 at ANY specific angle, the outcome can be predicted. That can't happen UNLESS they are entangled.
A full correlation is exactly what I would expect in the causal scenario I outlined. If you don’t believe me, I can go through the actual calculations or even provide a simulation if I have to.

In other variations, 1 & 4 are measured AFTER they are cast into the entangled state. So here are the key variations to consider:

a. 1 & 4 measured after they are cast into an entangled state.
b. 1 measured before 4 created, and before they are cast into an entangled state.
c. 1 & 4 both measured before they are cast into an entangled state.

An important thing to take away from these variations: the statistics for 1 & 4 do NOT change as you switch from a to b to c. Time ordering is not relevant, which is of course confusing if you attempt to assign causality. Which is what the OP's question relates to.
It is not confusing at all if you use causality. The causal algorithm is very simple and will work for all the scenarios you mentioned and give the same probability.

#### PeterDonis

Mentor
there is disagreement between QFT and the cited experiment
There is? I was not aware that there was any experiment that disagreed with QFT.

#### DrChinese

Gold Member
There is? I was not aware that there was any experiment that disagreed with QFT.
Oops!!! NO disagreement. I went ahead and edited to fix that.

#### DrChinese

Gold Member
A full correlation is exactly what I would expect in the causal scenario I outlined. If you don’t believe me, I can go through the actual calculations or even provide a simulation if I have to.

It is not confusing at all if you use causality. The causal algorithm is very simple and will work for all the scenarios you mentioned and give the same probability.
I don't follow your thinking. Are you a) saying 1 & 4 are entangled, and b) it is due to an effect that both flows from past to future AND is local? Because your example features non-locality, I quote: "1 is measured and non-locally gives the result of this measurement to 2. " I have no problem with a Bohmian type interpretation of entanglement swapping, which is deterministic but nonlocal. Bell rules!

#### kurt101

I don't follow your thinking. Are you a) saying 1 & 4 are entangled, and b) it is due to an effect that both flows from past to future AND is local? Because your example features non-locality, I quote: "1 is measured and non-locally gives the result of this measurement to 2. " I have no problem with a Bohmian type interpretation of entanglement swapping, which is deterministic but nonlocal. Bell rules!
Great that you have no problem with the "Bohmian type interpretation", I was still trying to make a defense of it.

I will assume your definition of entanglement is the accepted one, but I find the statement "photons are entangled that never interacted" confusing/misleading and without careful explanation it makes the universe seem strange and mysterious when it is not necessarily so. Also it is not an accurate description in the causal model I outlined where it would make more sense to define entanglement as a shared state that is created and destroyed by local interaction.

#### DrChinese

Gold Member
1. Great that you have no problem with the "Bohmian type interpretation", I was still trying to make a defense of it.

2. I will assume your definition of entanglement is the accepted one, but I find the statement "photons are entangled that never interacted" confusing/misleading and without careful explanation it makes the universe seem strange and mysterious when it is not necessarily so. Also it is not an accurate description in the causal model I outlined where it would make more sense to define entanglement as a shared state that is created and destroyed by local interaction.
1. No need for me. Bell specifically mentions that as viable in his groundbreaking paper.

2. ...I find the statement "photons are entangled that never interacted" confusing/misleading and without careful explanation it makes the universe seem strange and mysterious when it is not necessarily so...

Well, the title of the cited paper is: "Entanglement Between Photons That Have Never Co-existed". So they didn't interact. Below is another citation (although it is behind a paywall), and if that doesn't say it, I don't know what will. To be fair, I was not intending to make a big deal of how strange and mysterious it is.

Experimental Entanglement Swapping: Entangling Photons That Never Interacted

On the other hand, it is a bit strange and mysterious to me.

#### Demystifier

2018 Award
Entanglement describes correlations which have been prepared at the moment where the photons were created
What does it mean "to prepare correlations"? Correlations of what? One cannot prepare correlations themselves. One can only prepare the objective properties. But you seem to deny the existence of objective properties themselves. This is what Mermin calls "correlations without correlata" https://arxiv.org/pdf/quant-ph/9801057.pdf .

#### vanhees71

Gold Member
There are no sources that back up your position on entanglement swapping, and I can cite as many more as you like. I realize you feel strongly about local micro-causality, but Bell prohibits that anyway so I don't see what your sticking point is. QFT is not local deterministic, and of course I agree that there is no disagreement between QFT and the cited experiment. So:

Photons 1 & 4 are entangled, period. That's what entanglement is, and it is certified by correlations that exceed the Bell boundary. Those photons never interacted. If they are NOT cast into an entangled state by a suitable manipulation of photons 2 & 3, then they will NOT be correlated (i.e. entangled). If the manipulation of 2 & 3 is modified only so that 2 & 3 are distinguishable (say by adding a sufficient time delay to 2), then they will NOT be correlated*. That's because the cast of photons 1 & 4 into an entangled state is dependent on the action at 2 & 3 being successful. Photons 1, 2&3, and 4 can be measured in places non-local to each other and the entanglement still occurs. This completely flies in the face of your attempted description.

*If you were correct, then inserting a time delay for photon 2 would not make any difference to the outcome for the 1 & 4 entanglement correlations. You would still select the same 1 & 4 pairs either way (from the detector results at 2 & 3). But the indistinguishable nature of 2 & 3 is an absolute requirement for entanglement of 1 & 4, which are otherwise far away.
I still not understand what you consider wrong with microcausality and what you think is proven wrong with it by entanglement swapping. This would mean nothing less than claiming that QED, one of the best tested theories ever, is wrong, and this I think one would have heard about very clearly, if this were true.

As I always emphasized you have to be concrete in which experiment you want to do. Which time delay do you want to introduce and how?

No matter how, what's very sure from the very foundations of relativistic QFT (microcausality) no space-like separated events can be causally connected in any way, and thus the time order in the sense of any coordinate time in a fixed inertial reference frame is irrelevant for whether your partial ensemble of photon pairs consisting of photons 1&4 is entangled or not. In the experiment described in the quoted paper they are entangled. It's also irrelevant that they have never directly interacted (that's of course true here by the setup of the experiment) but they are entangled through their selection by local measurements on one of the photons of the pair 1&2 and on one of the photons of pair 3&4. Then entanglement of the selected set of pairs 1&4 is due to the entanglement of the pairs 1&2 and 3&4 respectively, and this entanglement is due to the preparation of each of these pairs before (in the invariant sense, i.e., the preparation process of these pairs is at timelike distance to the measurement events leading to entanglement of the partial ensemble of 1&4 pairs after the described selection process).

Again, I do not understand what's wrong with this simple and logical interpretation based on solely on the mathematical formalism of relativistic QFT.

#### vanhees71

Gold Member
1. No need for me. Bell specifically mentions that as viable in his groundbreaking paper.

2. ...I find the statement "photons are entangled that never interacted" confusing/misleading and without careful explanation it makes the universe seem strange and mysterious when it is not necessarily so...

Well, the title of the cited paper is: "Entanglement Between Photons That Have Never Co-existed". So they didn't interact. Below is another citation (although it is behind a paywall), and if that doesn't say it, I don't know what will. To be fair, I was not intending to make a big deal of how strange and mysterious it is.

Experimental Entanglement Swapping: Entangling Photons That Never Interacted

On the other hand, it is a bit strange and mysterious to me.
This paper is very clear in what's done, and there's indeed nothing strange and mysterious but it's all in full accordance with QED again. My main point is even explicitly stated and emphasized by the experimenters

Note that the Bell-state analysis relies on the interfer-
ence of two independently created photons. One, there-
fore, has to guarantee good spatial and temporal overlap at
the beam splitter and, above all, one has to erase all kinds
of path information for photon 2 and for photon 3.
The key issue indeed is, as the authors also very clearly demonstrate in the entire introductory passage above: The key of this experiment is to project the pair 2&3 (which was NOT entangled before) by a Bell measurement to one of the Bell states given in Eq. (2) to select an ensemble of entangled pairs 1&4. This selection process consists of local manipulations on the photons 2&3 (see the quoted passage).

#### DrChinese

Gold Member
1. I still not understand what you consider wrong with microcausality ...

2. As I always emphasized you have to be concrete in which experiment you want to do. Which time delay do you want to introduce and how?
1. There cannot be both causality [deterministic effects flowing from past to future] and locality (per Bell). I am guessing that you are pushing some special meaning of "microcausality" that purports to avoid Bell, but I don't know what that would be. If that is the case, perhaps you can explain relative to the example below.

2. Sure, and the reference diagram is from here.

a) In the various swapping experiments cited, entanglement of photons 1 & 4 occurs when photons 2 & 3 are cast via a Bell State Analyzer (the BSA is to be set at 0 degrees). The BSA is in the upper middle balloon of the diagram. The 1 & 4 pairs are spacetime separated, post selected, and the setup calls for the 1 & 4 to arrive at their beamsplitters near simultaneously (within a suitable coincidence window - so note that this is NOT the variation where the photons never coexisted). For simplicity, let's say we post select only those pairs that are psi+ entangled (same polarization when both measured at 45 degrees or any angle). By selecting 0 degrees for the BSA, and 45 degrees for the 1 & 4 pair, you can't learn anything about polarization of 1 & 4 when you perform the BSA on 2 & 3. The BSA on 2 & 3 rings either HH or VV for psi+, and again, the coincidence window is suitably small so that 2 & 3 are indistinguishable.

The 1 & 4 pairs will be matched in polarization about 100% assuming an ideal setup for the group we post select.

b) Now, we insert a 100 picosecond delay into the path of photon 2 (but nothing done to any of the other paths). The 1 & 4 pairs we want will still arrive within the requisite time window (relative to each other). But the 2 & 3 pairs will be easily distinguished as photon 2 will arrive about 100 ps later than photon 3. Importantly, we can still identify the 2 & 3 pairs as being either HH or VV as before, so that we can still post-select the proper 1 & 4 pairs. If there is local microcausality, as you claim, this modification should NOT affect the results at 1 & 4. (There is no causal connection between events at the BSA and detections at 1 & 4.)

But that is not the case. Instead, the 1 & 4 polarization matching will be about 50%, no correlation*. How is it that the same pairs arriving at 1 & 4 - which are spacelike separated - are suddenly giving Product state statistics rather than the Entangled state statistics? The only change was to the path length of photon 2, which is spacelike separated from photon 1 (and 4)? Because of the separation, there cannot be any causal connection between the decision to add the 100 picosecond delay and the matching between photons 1 and 4.

And yet this is all standard QFT. Which of course follows Bell, which rejects local determinism (a/k/a local realism). In case anyone is wondering if my version of this setup has ever been tested: EVERY entanglement swapping experiment demonstrates this! They always start with the 2 & 3 photons being distinguishable and then attempt to tune it to the indistinguishable version. When the 1 & 4 stats move from being Product state stats to Entangled state stats, they know they have succeeded. QED.

*The stats would be as follows: The matches between entangled photons 1 & 2 will be 50% (i.e. random) due to the 45 degree separation in polarization angles being measured (cos^2 theta). Ditto for entangled photons 3 & 4. 1 & 4 are not entangled, and so their match rate will likewise be random. Of course, we are still only post selecting the portion that are denoted by HH or VV at the BSA.

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Instead, the 1 & 4 polarization matching will be about 50%, no correlation*. How is it that the same pairs arriving at 1 & 4 - which are spacelike separated - are suddenly giving Product state statistics rather than the Entangled state statistics? The only change was to the path length of photon 2, which is spacelike separated from photon 1 (and 4)? Because of the separation, there cannot be any causal connection between the decision to add the 100 picosecond delay and the matching between photons 1 and 4.
Because when you add the delay, you are post-selecting different pairs of photons 1+4. Before you decide to add the delay or not, you can have the results of all the 1+4 measurements on a sheet of paper by your side (with randomly chosen HH or VV results). If the selections would be equal, what you are suggesting is that either the contents of the paper change based on your choice to delay or that your choice to delay is already determined based on the contents.

Or maybe I'm missing something - can you show that the same pairs are chosen in either case?

#### DrChinese

Gold Member
Because when you add the delay, you are post-selecting different pairs of photons 1+4.
The pair selection is the same. When any photons at the BSA hit a detector, a time stamp is recorded. Normally you would pick pairs that arrived within a 10 ps time window (or whatever). There won't be much outside that window as suitable 2 & 3 pairs (actually 4 fold coincidences) only come along every few seconds (perhaps 1500 in a 9000 second run). That makes the average time distance between pairs on the magnitude of a billion times the size of the window. It's practically a desert for coincidences between suitable pairs.

Now, if I add 100 ps to the photon 2 path, everything will else remain the same in terms of the relative ordering except that 1 of the BSA clicks will be marked as being between 95 and 105 ps later than the other. We would label that one as photon 2 - now clearly distinguished from photon 3. They would still be recorded as both H or both V. But if the one labeled photon 2 arrives that much later, we know it arrived still entangled with photon 1. Accordingly, no swap occurred, and it was not entangled with photon 4. Therefore, 3 & 4 were still entangled. You can work out the stats yourself, but the upshot is that 1 & 4 arrive at their respective 45 degree detectors with the same polarization HH or VV. Since they are not entangled though, we see Product state statistics for their matching rather than entangled state.

Considering that the decision to delay any particular photon 2 can be made before, after, or (near) simultaneously to the detections of photons 1, 3 and 4, it would require you to accept my central premise in the first place to believe that different 1 & 4 pairs are now selected. My premise being exactly that the entire context - which is clearly NOT locally causal (as there is no way to trace and/or otherwise assign causes and effects ) - must be considered to make a correct statistical prediction. Which is exactly what QFT says.

#### vanhees71

Gold Member
1. There cannot be both causality [deterministic effects flowing from past to future] and locality (per Bell). I am guessing that you are pushing some special meaning of "microcausality" that purports to avoid Bell, but I don't know what that would be. If that is the case, perhaps you can explain relative to the example below.

2. Sure, and the reference diagram is from here.

View attachment 245955

a) In the various swapping experiments cited, entanglement of photons 1 & 4 occurs when photons 2 & 3 are cast via a Bell State Analyzer (the BSA is to be set at 0 degrees). The BSA is in the upper middle balloon of the diagram. The 1 & 4 pairs are spacetime separated, post selected, and the setup calls for the 1 & 4 to arrive at their beamsplitters near simultaneously (within a suitable coincidence window - so note that this is NOT the variation where the photons never coexisted). For simplicity, let's say we post select only those pairs that are psi+ entangled (same polarization when both measured at 45 degrees or any angle). By selecting 0 degrees for the BSA, and 45 degrees for the 1 & 4 pair, you can't learn anything about polarization of 1 & 4 when you perform the BSA on 2 & 3. The BSA on 2 & 3 rings either HH or VV for psi+, and again, the coincidence window is suitably small so that 2 & 3 are indistinguishable.

The 1 & 4 pairs will be matched in polarization about 100% assuming an ideal setup for the group we post select.

b) Now, we insert a 100 picosecond delay into the path of photon 2 (but nothing done to any of the other paths). The 1 & 4 pairs we want will still arrive within the requisite time window (relative to each other). But the 2 & 3 pairs will be easily distinguished as photon 2 will arrive about 100 ps later than photon 3. Importantly, we can still identify the 2 & 3 pairs as being either HH or VV as before, so that we can still post-select the proper 1 & 4 pairs. If there is local microcausality, as you claim, this modification should NOT affect the results at 1 & 4. (There is no causal connection between events at the BSA and detections at 1 & 4.)

But that is not the case. Instead, the 1 & 4 polarization matching will be about 50%, no correlation*. How is it that the same pairs arriving at 1 & 4 - which are spacelike separated - are suddenly giving Product state statistics rather than the Entangled state statistics? The only change was to the path length of photon 2, which is spacelike separated from photon 1 (and 4)? Because of the separation, there cannot be any causal connection between the decision to add the 100 picosecond delay and the matching between photons 1 and 4.

And yet this is all standard QFT. Which of course follows Bell, which rejects local determinism (a/k/a local realism). In case anyone is wondering if my version of this setup has ever been tested: EVERY entanglement swapping experiment demonstrates this! They always start with the 2 & 3 photons being distinguishable and then attempt to tune it to the indistinguishable version. When the 1 & 4 stats move from being Product state stats to Entangled state stats, they know they have succeeded. QED.

*The stats would be as follows: The matches between entangled photons 1 & 2 will be 50% (i.e. random) due to the 45 degree separation in polarization angles being measured (cos^2 theta). Ditto for entangled photons 3 & 4. 1 & 4 are not entangled, and so their match rate will likewise be random. Of course, we are still only post selecting the portion that are denoted by HH or VV at the BSA.
1. Relativistic QFT clearly shows that there are both locality of interactions and "non-locality" of correlations, and that's not a contradiction. To the contrary it is precisely what's needed to be (a) consistent with the relativistic space-time structure and the corresponding causality structure and (b) consistent with the observered violation of Bell's inequality as predicted by any QT in general and particularly by local, microcausal, relativistic QFT. There's no "special meaning" of microcausality but the usual one used in any QFT textbook: The Hamilton density commutes with local observables at space-like distances,
$$[\mathca{H}(x),\mathcal{O}(y)]=0 \; \quad \text{if} \quad (x-y)^2<0,$$
where I use the west-coast convention, $\eta_{\mu \nu}=\mathrm{diag}(1,-1,-1,-1)$.

2. also in this experimental setup I see nothing which contradicts the standard interpretation I follow. The selection of the pairs 1&4 is based on a selection of 2&3 with measurements/manipulations all explainable by local interactions with the various apparati used in the experiment, including the coherence arguments you quote. Of course, if you make the photons in the pair 2&3 distinguishable you loose this coherence (that's what Bohr called "complementarity") you choose a different subensemble than before and you loose the 100% correlations. What's imho wrong with your argument thus simply is that you do NOT post-select the same ensemble with and without the delay you mention. To get 100% correlation for 1&4 you MUST not make 2&3 distinguishable. If you make the dinstinguishable you necessarily choose another sub-ensemble which necessarily doesn't show the correlations. In other words in this case you have not "swaped the entanglement".

Again there's nothing non-locally interacting here. It's just which subensemble you "post-select" to observe for the photons in the pair 1&4 based on what you observe (by local measurements) on the photons in the pair 2&3. Of course, the photons in 1&4 have never (or at least need not) locally interacted themselves at any point in the experiment. To describe the experimental outcomes it's sufficient to have the pairs 1&2 entangled and the pair 3^4 entangled as described. You thus have long-range correlations which can be "swapped" to the pair 1&4 by local manipulations on the pair 2&3 without necessarily enforcing ever a local interaction of pair 1&4. There's no contradiction between the locality/microcausality of interactions in relativistic QFT with the long-ranged correlations described by entanglement.

Then for clarification: Bell has shown that any local deterministic hidden-variable theory is INCOMPATIBLE with QT (and particularly thus also QFT), i.e., he derived his famous inequalities contradicting QT and thus made this type of theories testable against QT. The result is well-known today: The local deterministic HV theories are wrong but QT so far has been in accord with observations in all cases, sometimes with astonishing significance.

#### DrChinese

Gold Member
1. Relativistic QFT clearly shows that there are both locality of interactions and "non-locality" of correlations, and that's not a contradiction. ..

2. What's imho wrong with your argument thus simply is that you do NOT post-select the same ensemble with and without the delay you mention. To get 100% correlation for 1&4 you MUST not make 2&3 distinguishable. If you make the distinguishable you necessarily choose another sub-ensemble which necessarily doesn't show the correlations. In other words in this case you have not "swapped the entanglement".

Again there's nothing non-locally interacting here. It's just which subensemble you "post-select" to observe for the photons in the pair 1&4 based on what you observe (by local measurements) on the photons in the pair 2&3.
1. It's a contradiction. Established science is: Local determinism is excluded. As Demystifier says: "What does it mean "to prepare correlations"? Correlations of what? One cannot prepare correlations themselves. " You are going to have to provide a reference if you think QFT is local.

The entire point of this discussion is to clarify that with entanglement swapping variations - experiments that have been executed over the past 20 years by top research teams - there is no way to get back to a local description of what occurs. From the Zeilinger et al reference: "This shows that the independent photons [particles that do not share any common past ] in modes 1 and 4 clearly are entangled and can asymptotically be distilled into the maximally entangled singlet state...". They are in the singlet state, not just "correlated".

2. If the decision to entangle photons 1 & 4 is made at the last minute: please explain how that causes different 1 & 4 pairs to be selected. According to you, nothing changes there. ("there's nothing non-locally interacting here.") And presumably, 2 photons from independent sources (2 & 3) don't interact in your view either (regardless of whether they arrive at a beamsplitter simultaneously or not) . How could they? So how would different ensembles be selected?

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#### PeterDonis

Mentor
You are going to have to provide a reference if you think QFT is local.
I think first there needs to be a precise definition of what "local" means. Bell gave a definition of "locality" in his paper which any theory that matches the predictions of QM must violate; that's what his paper proved. But his definition is not the only possible one.

#### DrChinese

Gold Member
Then for clarification: Bell has shown that any local deterministic hidden-variable theory is INCOMPATIBLE with QT (and particularly thus also QFT), i.e., he derived his famous inequalities contradicting QT and thus made this type of theories testable against QT. The result is well-known today: The local deterministic HV theories are wrong but QT so far has been in accord with observations in all cases, sometimes with astonishing significance.
I quite agree. So why are you pushing QFT as locally causal? Your words below seem quite clear.

"The interactions are, according to the very fundamental construction of relativistic QFTs of which QED is the paradigmatic example, local and also only those QFTs are successful which obey the microcausality principle..."

"My conviction is so strong, because I think that locality of interaction/micro-causality is [one of] the very fundamental assumptions put into the construction of relativistic QFTs and particularly the Standard Model/QED. "

#### vanhees71

Gold Member
1. It's a contradiction. Established science is: Local determinism is excluded. As Demystifier says: "What does it mean "to prepare correlations"? Correlations of what? One cannot prepare correlations themselves. " You are going to have to provide a reference if you think QFT is local.

The entire point of this discussion is to clarify that with entanglement swapping variations - experiments that have been executed over the past 20 years by top research teams - there is no way to get back to a local description of what occurs. From the Zeilinger et al reference: "This shows that the independent photons [particles that do not share any common past ] in modes 1 and 4 clearly are entangled and can asymptotically be distilled into the maximally entangled singlet state...". They are in the singlet state, not just "correlated".

2. If the decision to entangle photons 1 & 4 is made at the last minute: please explain how that causes different 1 & 4 pairs to be selected. According to you, nothing changes there.
Ad 1) How then can relativistic QFT be the best model of relativistic QT on the market, and it's not contradicting also the quoted Bell experiments, including entanglement swaping, teleportation, quantum erasures etc.

It's very clear what's correlated given the states your photons are prepared in. The photons from parametric down conversion are both correlated in momenta and in polarization. That's the very basis of all these experiments.

As I tried to explain for several times. The very quote by Zeilinger is fully consistent with standard QED. The partial ensemble of 1&4 pairs selected (or post-selected!) depending on local measurements on pairs 2&3 must be entangled, though the 1&4 never interacted. To be sure that they have never interacted you even need the microcausality argument since you can be sure about this only within the standard relativistic microcausal QFT according to which there are no actions a distance (i.e., causal connections between space-like separated events). Indeed they are not "just correlated" but even entangled, leading to stronger correlations than possible in deterministic local hidden-variable theories.

All your arguments thus rather confirm my arguments than disprove them!

Ad 2) It's said in the paper you quoted in the posting I was answering to: You must be sure to measure photons 2&3 within the coherence times/lengths of the photons to get the entanglement. If you make a time delay such that the "photons are getting dinstinguishable", then you don't exploit the correlations due to the initial entanglement of the pairs 1&2 and 3&4 anymore, because you are beyond the coherence "space-time inverval", and then the chosen subensemble of 2&3 doesn't select the same subensemble of 1&4 as before. As you say yourself, in this case one expects simply uncorrelated photons in 1&4 in this subsensemble. This is what I said in my previous answer too. Why you are claiming the opposite, I don't know ;-).

#### PeterDonis

Mentor
local, microcausal, relativistic QFT
You gave a precise mathematical definition for what "microcausal" means here (basically that operators at spacelike separated events commute). What is the precise mathematical definition for what "local" means here?

#### vanhees71

Gold Member
I quite agree. So why are you pushing QFT as locally causal? Your words below seem quite clear.

"The interactions are, according to the very fundamental construction of relativistic QFTs of which QED is the paradigmatic example, local and also only those QFTs are successful which obey the microcausality principle..."

"My conviction is so strong, because I think that locality of interaction/micro-causality is [one of] the very fundamental assumptions put into the construction of relativistic QFTs and particularly the Standard Model/QED. "
What do you mean by "locally causal"? By construction we build QFTs fulfilling the microcausality condition, because that's sufficient to define unitary S-matrix elements fulfilling the linked-cluster theorem. It's of course NOT a local deterministic theory, but a quantum theory implementing the locality of interactions. This, of course does NOT imply something deterministic in the sense of HV theories.

E.g., if you prepare two photons in a singlet-polarization state the single-photon polarization states are "really" completely undetermined but still the outcomes of measurements in the same polarization direction are 100% correlated. Since in the described experiments the photons are also 100% correlated in their momenta (in Quantum Optics slang called the "phase-matching condition" in parametric downconversion) the 100% polarization correlation can be measured by making coincidence measurements at far-distant places such that you still can be sure to really measure the very two photons that are entangled. The measurements are localized at the places where the measurement apparatus (here in the simplest case simply consisting of a polarization filter and a subsequent photodetectro) is located. This locality of the measurement is of course assumed due to the underlying microcausality of QED. From reading many papers about such experiments, it seems to be usually accepted in the quantum-optics community that, space-like separated measurements cannot mutually cause each other in any way.

#### vanhees71

Gold Member
You gave a precise mathematical definition for what "microcausal" means here (basically that operators at spacelike separated events commute). What is the precise mathematical definition for what "local" means here?
I think "local" (applied to intereactions) is synonimous with "microcausal". It's a pity that many notions are so unsharp in these discussions that you have to use much more precise formulations, making the entire writing even more complicated than the whole issue really is. The only clear language at the end are mathematical fromulae ;-))).

#### DrChinese

Gold Member
It's very clear what's correlated given the states your photons are prepared in. The photons from parametric down conversion are both correlated in momenta and in polarization. That's the very basis of all these experiments.
You keep saying correlated as if they are not entangled, when they are. Entanglement is a quantum state. Particles can be correlated without being entangled, but not vice versa.

1 & 4 are not entangled into the singlet state UNTIL and UNLESS a swap occurs between system A (photons 1 & 2) and system B (photons 3 & 4). The swap affects both systems (A and B), each which has both temporal and spatial extent. The order of the detection and swap events is not relevant, and the swap itself affects the entirety of each system - violating local causality.

I keep calling for references, and you keep quoting yourself.

#### DrChinese

Gold Member
1. E.g., if you prepare two photons in a singlet-polarization state the single-photon polarization states are "really" completely undetermined but still the outcomes of measurements in the same polarization direction are 100% correlated.

2. Since in the described experiments the photons are also 100% correlated in their momenta (in Quantum Optics slang called the "phase-matching condition" in parametric downconversion) the 100% polarization correlation can be measured by making coincidence measurements at far-distant places such that you still can be sure to really measure the very two photons that are entangled.

3. The measurements are localized at the places where the measurement apparatus (here in the simplest case simply consisting of a polarization filter and a subsequent photodetectro) is located.

4, This locality of the measurement is of course assumed due to the underlying microcausality of QED.

5. From reading many papers about such experiments, it seems to be usually accepted in the quantum-optics community that, space-like separated measurements cannot mutually cause each other in any way.
1. Agree.

2. Agree.

3. This might be true when you are referring to an entangled system PRIOR to the swap. But after the 2 entangled systems (1 & 2, and 3 & 4) interact, both change to a different overall context. Now 1 & 4 are the entangled system.

4. Circular reasoning, my friend.

5. The rest of the community does not share your personal interpretation. I have provided plenty of quotes expressing the opposite view. Post Bell: No local realism, no local hidden variables, no local determinism, no local causality, no local micro-causality (whatever that is) etc. Every generally accepted interpretation denies some/all of these.

I get (and agree) that you deny that a particle in a superposition does not have an objective well-defined value independent of observation. And I get that your "causal" idea works fine for a typical PDC pair. But the whole point of swap experiments is to show that is an incorrect picture in and of itself. It simply doesn't work with swaps because it is not 2 particles interacting locally (2 & 3) as you suppose; it is the 1 & 2 system interacting with the 3 & 4 system, and those systems have spatio-temporal* extent.

*I.e. lacking a spatial point, and lacking a point in time.

#### vanhees71

Gold Member
If there's anything correlated than it's if it's entangled. Entanglement is the strongest correlation you can have. It's even stronger than any correlation possible for a local deterministic HV theory. I think we simply do not use the same language, and I was sloppy here. So let me try again.

(a) The experiment considered here can be described as follows. There are two pairs of polarization-momentum entangled photons prepared, namely 1&2 and 3&4. The four-photon state at the beginning is thus given by the state ket
$$|\psi_{12} \rangle \otimes |\psi_{34} \rangle.$$
In full glory it's pretty lengthy to write. It's usually simplified as in the paper by only writing down the polarization part the experimenters are dealing with. However the full pair states also include the momentum part. If the polarization part is antisymmetric this must also be the case for the momentum part since photons are bosons. To fully discuss the experiment it may be important to once sit down and write this out completely, but it's understood implicitly also in the notation of the paper (which becomes clear by the figure discribing the experiment).

Anyway, due to the direct product, of course the photon pair 1&3, 1&4, 2&3, 2&4 are all NOT entangled.

However, when you make a selection by make a Bell measurement on photons 2&3 in the described way, particularly in a space-time region that is close enough together to be in the coherence lengths of all the photons, you can project (even long after the experiment is done as long as you have a complete measurement protocol with all the time stamps at place) to one of the possible Bell states for the pair 2&3. Here only local interactions of photons 2 and 3 are used, while 1&4 never have interacted in such a close region. Nevertheless due to the selection ensuring the entanglement of 2&3 due to being measured as being in one of the Bell states (the authors choose the polarization singlet state, but you can as well use any other of the four possible Bell states) for this subensemble 1&4 are now entangled.

Note that it's just the selection that leads to the entanglement. There's no non-local action at a distance at place since the meaurement on photons 2&3 (which must be close enough together in spacetime due to the coherence constraint) can well be space-like separated from the measurments on photons 1&4. You can post-select one of the Bellstates of 2&3 long after the entire experiment ist done and still find that the subensemble of photons 1&4 are correlated as described by their entanglement.

You are right in saying that the two entangled systems interact by just doing a local measurement on 2&3, because indeed 1&2 as well as 3&4 are entangled, i.e., they are "inseparable". That's the clue of the entire experiment! I however don't see why you say that there's anything non-local going on here. The interaction of the photons 2&3 with the measurment devices that enables you to select the wanted Bell state is local (in the sense of microcausality of QED).

I still don't understand your statement ad 5). Since that's precisely what I emphasize the whole time: All the models you quote are contradicting relativistic local (i.a., microcausal) QFT, but all experiments are in accord with QFT rather than any of these models which are constructed such as to contradict QFT.

I don't see anything in Zeilinger's et al's papers contradicting the minimal interpretation. It think it's precisely the interpretation Zeilinger always emphasizes. He's calling it "Copenhagen", but one should be careful to clearly state that it's the flavor of Copenhagen which doesn't assume non-local actions at adistance which is a clear contradiction to the microcausality postulate which you put into the contsruction of relativistic QFTs from the very beginning. I think it's the view widely accepted in the quantum-optics community. So I think I am rather in the main stream here ;-)).

#### PeterDonis

Mentor
I think "local" (applied to intereactions) is synonimous with "microcausal".
Then why put in the extra word "local"? Particularly when it causes interminable arguments in threads like this, because the word "nonlocal" is commonly used to describe correlations that violate the Bell inequalities?

#### DrChinese

Gold Member
1. If there's anything correlated then it's if it's entangled.

2. Anyway, due to the direct product, of course the photon pair 1&3, 1&4, 2&3, 2&4 are all NOT entangled.

3. Here only local interactions of photons 2 and 3 are used, while 1&4 never have interacted in such a close region. Nevertheless due to the selection ensuring the entanglement of 2&3 due to being measured as being in one of the Bell states (the authors choose the polarization singlet state, but you can as well use any other of the four possible Bell states) for this subensemble 1&4 are now entangled.

Note that it's just the selection that leads to the entanglement.

4. I don't see anything in Zeilinger's et al's papers contradicting the minimal interpretation. ... So I think I am rather in the main stream here ;-)).
1. Finally!

2. Agreed.

3. No, and once again, please give a reference other than yourself. I have never seen such a [*] description in any entanglement swapping paper [**]. If the entanglement swap is not executed at 2 & 3, as I indicated above, the far separated 1 & 4 will not be entangled - contradicting your purely local [***] characterization.

Once 1 & 4 are entangled, they are mirrors of each other and have quantum properties that far exceed what 2 otherwise independently created particles could ever have. Of course, they are now part of a quantum system and are no longer separable. You could never construct such a system of 2 particles otherwise as you could never know that many non-commuting observables. Zeilinger says, of the 2 entangled particles that never interact:

"The aim is that the distant experimenter Bob [looking at photon 4] obtains an exact replica of that particle. It is evident that no measurement whatsoever Alice [looking at photon 1] might perform on the particle could reveal all necessary information to enable Bob to reconstruct its state."

That doesn't happen because of post-selection! That should be obvious. There are NO such 2 particles that can be independently created and later post selected (they must be entangled, and cannot be entangled with any other particle). That is strictly forbidden by the HUP. The mirror particles (the ones projected into the singlet state) have the mirroring values for non-commuting p and q, for example. They must be physically connected as part of a single, non-separable, quantum system. It's non-local in spatial extent.

4. The humorous element is that you completely ignore everything Zeilinger actually says, and then recast his viewpoint to match yours. Zeilinger does not claim to have an understanding of the mechanism by which quantum nonlocality operates (and I don't either). But he would never refer to QM as being local causal, and I certainly can't recall a respected paper of the last 20 years using any terminology similar to yours.

And please, despite our going back and forth on the subject, I hope you would not take our discussion as anything other than friendly.

*Let's just say "contrived".
*** Seriously, it's 2019 my friend. Quantum non-locality was generally accepted some time ago.

"Confused by nonlocal models and relativity"

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