Graduate Hidden Assumptions in Bell's Theorem?

[kurt101]

Consider billiard balls without friction. If you know the positions and velocities of the balls in the future, you can determine their positions and velocities in the past.

Are you saying that is the essence of your Relativistic Bohmian / QFT Interpretation?

It sounds superdeterminstic to me, like every object has to know what the end state of the universe is and collaborate in just the right way so they don't violate any of the rules as they arrive at that end state (assuming there is even an end state!). Or do you have some characteristic that cuts off future knowledge, like it only has to know the future to a certain point? Or maybe you are just going to say the future knowledge is emergent, but not provide any deterministic explanation on how that emergence actually works.

And I did read a bit of your latest paper and I feel I made a mistake in bringing you into my disagreement with @DrChinese (at least I think we disagree). I thought you held a Bohmian interpretation that had definite paths for photons. My argument requires an interpretation with the characteristics of reality, cause and effect, and non-locality. And now I don't think your interpretation fits those charateristics.

I still think it would be interesting to hear some high level description of how your Bohmian interpretation explains the entanglement swapping experiment or even the simpler EPR experiment like Alain Aspect first executed where the measuring device is modified at the last moment, but maybe that is a large undertaking or low value for whatever reason.

 

[Demystifier]

Are you saying that is the essence of your Relativistic Bohmian / QFT Interpretation?

Yes.

It sounds superdeterminstic to me,

But it's not, as I explained in one of the posts above.

like every object has to know what the end state of the universe is and collaborate in just the right way so they don't violate any of the rules as they arrive at that end state (assuming there is even an end state!).

This does not involve fine tuning of initial conditions, so it's not superdeterminism. After you hit the billiard ball, the classical system of the billiard table and balls "knows" that the ball will fall into the hole before it actually falls into it.

I still think it would be interesting to hear some high level description of how your Bohmian interpretation explains the entanglement swapping experiment or even the simpler EPR experiment like Alain Aspect first executed where the measuring device is modified at the last moment, but maybe that is a large undertaking or low value for whatever reason.

The latter is simpler to describe. Let $x=\{x_1,x_2\}$ be positions of the two entangled EPR particles and let $y=\{y_1,y_2,...\}$ be positions of particles of the measuring apparatuses. Their interaction is described by some potential $V(x,y,t)$. The total wave function $\psi(x,y,t)$ satisfies the Schrodinger equation with this potential. Changing measuring device at the last moment means that $V(x,y,t)$ depends on $t$ such that $V$ changes at the last moment. Whenever $V(x,y,t)$ changes, the $\psi(x,y,t)$ changes accordingly as well, that's what the Schrodinger equation tells us. The Bohmian trajectories are deterministically guided by this $\psi(x,y,t)$, so whenever $V(x,y,t)$ changes, the particle trajectories change as well. That's how Bohmian mechanics explains EPR experiments with the modification of measuring device at the last moment. Does it help?

 

[kurt101]

But it's not, as I explained in one of the posts above.

I reread your previous posts and I think I am understanding better, but I am definitely not there yet. I will keep reading and I may have further questions for you in the future. And thanks for the EPR explanation. It does help a lot.

 

[lodbrok]

How do you define "causation"?

"Causation" derives from "cause" which means ... to be wholly or partially responsible for the occurrence of ... "Event B" is said to be caused by "Event A" if "Event A" is wholly or partially responsible for the occurrence of "Event B".

This is the standard understanding of "causation" in classical physics, special relativity, QFT, etc with the additional implication that "Event B" would not have occurred without "Event A" happening in the past of the light cone of "Event B".

Causation is a physical process (ontic), whereas using information about the current state of a system to "determine" the state in the past or using information about the state of the past to determine the state of the future is anthropomorphic information processing (epistemic). Otherwise, you obtain an absurd situation in which different agents can choose to "cause" or not "cause" the past/future by choosing whether to perform or not perform a mathematical calculation.

Do you define it differently?

 

[Demystifier]

Do you define it differently?

Yes. In your definition it's not clear what "responsible" means. Intuitively I understand what you mean, but this concept is not precisely defined in physical terms. Therefore I don't think that "responsibility" and causality are ontic. I think they are emergent concepts, making sense only at the effective macroscopic level. It only looks like something is responsible for something else, while in reality, on the fundamental microscopic ontic level, there is no responsibility and no causality in this sense.

 

[Demystifier]

I reread your previous posts and I think I am understanding better, but I am definitely not there yet. I will keep reading and I may have further questions for you in the future. And thanks for the EPR explanation. It does help a lot.

Let me also explain what superdeterminism would be in a billiard context. Suppose that Alice and Bob are spatially separated and each plays billiard on her/his table. And suppose that their playing is correlated: whenever Alice hits the ball in the right hole, Bob hits the ball in the left hole, and vice versa. How to explain this correlation? A nonlocal "Bohmian" explanation would be that Alice and Bob have a secret communication faster than light, that's deterministic but not superdeterministic. A superdeterministic explanation would be that there is no secret communication, but initial conditions of the Universe are fine tuned so that the processes in the Alice's and Bob's brain evolve such that they always make the opposite decisions on hitting the balls.

 

[Fra]

Causation is a physical process (ontic), whereas using information about the current state of a system to "determine" the state in the past or using information about the state of the past to determine the state of the future is anthropomorphic information processing (epistemic).

Otherwise, you obtain an absurd situation in which different agents can choose to "cause" or not "cause" the past/future by choosing whether to perform or not perform a mathematical calculation.

What seems absurd is I think interpretation dependent. For me it is not absurd at all:

The logic is simple:

For me I take as one guiding principles of is that the abstractions information processing and representation of states of information should loosely speaking be corresponding to physical internal processes and internal states of an agent/observer.

Then the "causation" is that the agents inference of the probable[information processing=computation] future from its subjective obsevations (which btw are possibly different from what obe calls "observable" in QM), causally influences the agents actions. So in the qbist vieq i would say the causaliy is internal as in my processing of input causally influences my decided actions.

From this follows a "game of expectations"
This is also why one says that the probability in qbism is normative or guiding, not descriptive. Beacause you can only describe the past, and you at best "expect" a certain future.

This is the dark side and apparently not for everyone but I think once you get in, its not absurd at all.

/Fredrik

 

[kurt101]

Let me also explain what superdeterminism would be in a billiard context. Suppose that Alice and Bob are spatially separated and each plays billiard on her/his table. And suppose that their playing is correlated: whenever Alice hits the ball in the right hole, Bob hits the ball in the left hole, and vice versa. How to explain this correlation? A nonlocal "Bohmian" explanation would be that Alice and Bob have a secret communication faster than light, that's deterministic but not superdeterministic. A superdeterministic explanation would be that there is no secret communication, but initial conditions of the Universe are fine tuned so that the processes in the Alice's and Bob's brain evolve such that they always make the opposite decisions on hitting the balls.

This is what I still don't understand about your interpretation. You say that measuring Alice instantly changes the potential which changes Bob's wave function and the state of the apparatus Bob will be measured by, even though Bob's future measurement apparatus is outside of the light cone of Bob at that point and its future configuration is not yet known (actually this later part I am not sure if it is what you are saying). I just don't see the causal connection between Alice's measurement and Bob's future measurement apparatus. I can change lots of other things near Bob's future measurement apparatus; do those things affect the measurement of Bob? Not really, so what is so special about Alice's measurement that can change Bob's future measurement apparatus.

Basically if you said that Alice's measurement changed the wave function of Bob and left it at that, I would be perfectly satisfied with the explanation. I am just confused if you are also implying that Alice's measurement changes the potential and the configuration around Bob's future measurement apparatus which is outside of the light cone of Alice and Bob.

 

[lodbrok]

Yes. In your definition it's not clear what "responsible" means. Intuitively I understand what you mean, but this concept is not precisely defined in physical terms. Therefore I don't think that "responsibility" and causality are ontic. I think they are emergent concepts, making sense only at the effective macroscopic level. It only looks like something is responsible for something else, while in reality, on the fundamental microscopic ontic level, there is no responsibility and no causality in this sense.

It is very clear. An event is responsible for another event if the other event would not have happened without the first event happening in its past light cone.

So what is your definition then?

 

[mattt]

It is very clear. An event is responsible for another event if the other event would not have happened without the first event happening in its past light cone.

So what is your definition then?

Given that in Classical Mechanics and in Bohmiam Mechanics, for an isolated system (take the whole universe) any two world-curves are disjoint in Phase-Space, your definition of causality gives rise to:

A is cause of B iff A and B belong to the same world-curve of the system and the time parameter for A is lower than the time parameter for B.

That's what your definition of causality looks like if you try to apply it to the fundamental, microscopic level (in Classical Mechanics or Bohmiam Mechanics).

Your definition have some utility if you apply it at the macroscale, where a huge number of microstates correspond to the same macrostate ( and a huge number of different microscopic world-curves can pass through different microstates that all corresponde to the same macrostate).

In this context, a macrostate A can be thought of as the cause of macrostate B in the way you described.

 

[DrChinese]

"Causation" derives from "cause" which means ... to be wholly or partially responsible for the occurrence of ... "Event B" is said to be caused by "Event A" if "Event A" is wholly or partially responsible for the occurrence of "Event B".

...
Otherwise, you obtain an absurd situation in which different agents can choose to "cause" or not "cause" the past/future by choosing whether to perform or not perform a mathematical calculation.

The decision to swap - or not - can be made in the future. It is partially responsible for the entanglement effect. Then by your own definition, the future causes the past, which is your "absurd" ("paradoxical" to others). Of course, it's actually the full context - with past and future elements - that "causes" the ultimate outcome. It can't be Einsteinian causality, because time order and distance are not factors, and the outcome is not uniquely determined (a la Born Rule). So there really isn't a good word to encompass what role the BSM takes on in these swaps. "Quantum" cause?

Let's see if I understand your alternative idea correctly.

You say that a) the maximally entangled [1 & 2] pairs - which cannot be entangled with anything else; and b) the maximally entangled [3 & 4] pairs - which also cannot be entangled with anything else; contain c) a subset in which the [1 & 4] pairs are also maximally entangled; and d) there's a subset in which the [2 & 3] pairs are maximally entangled (in the same Bell State as the matching [1 & 4] pairs per c). So you imagine that the revelation of specific [2 & 3] entangled pairs as being in an entangled state (such as Psi-) via the BSM will identify a matching [1 & 4] subset that will violate a Bell inequality. At no time, in your view, does the successful BSM on the [2 & 3] pairs CHANGE anything in the identified [1 & 4] subset, much less change anything in the past (which you consider "absurd").

Do I have this about right?

Because... I have already explained multiple times that your idea is falsified by Monogamy of Entanglement (reference and proof previously provided). [1] can never be maximally entangled with [2] and also maximally entangled with [4]. Or maybe you deny Monogamy of Entanglement?

 

[lodbrok]

For me I take as one guiding principles of is that the abstractions information processing and representation of states of information should loosely speaking be corresponding to physical internal processes and internal states of an agent/observer.

I agree all agents are governed by the same physical laws and processes as other systems.

Then the "causation" is that the agents inference of the probable[information processing=computation] future from its subjective obsevations (which btw are possibly different from what obe calls "observable" in QM), causally influences the agents actions.

Yes, causation within the agent, not the systems being observed or about which information is being processed. Demystifier appears to suggest in post #172 that being able to calculate the past state of a non-dissipative system from the present state is retrocausality. It may be causality in the internal state of the observer but has nothing to do with the causality of the system under observation.
Alice and Bob's analysis of the 1&4 data happens in the future light cone of Victor's measurement. Victor's results are transmitted to Alice and Bob through classical channels. The use of Victor's data to filter [1&4] causes the selection of a sub-ensemble which shows entanglement. Here we have causation within the agents while processing information obtained at sub-light speeds in the proper time ordering consistent with the definition of causation. None of this has anything to do with the actual physical systems of the particle streams [1, 2, 3, 4].

I would be curious to hear a definition of "causality" that suggests otherwise.

This is the dark side and apparently not for everyone but I think once you get in, its not absurd at all.

I'll conjecture that the dark side definition of causality can't distinguish "A retro-causes B" from "B causes A".

 

[Demystifier]

It is very clear. An event is responsible for another event if the other event would not have happened without the first event happening in its past light cone.

Not applicable in Bohmian mechanics because it's nonlocal so light cones don't play such a role.

 

[Demystifier]

which changes Bob's wave function

There is no such thing as Bob's wave function. In the case of entanglement, there is only one wave function describing, Bob, Alice, their apparatuses, etc.

 

[Demystifier]

I am just confused if you are also implying that Alice's measurement changes the potential and the configuration around Bob's future measurement apparatus which is outside of the light cone of Alice and Bob.

The change of Alice's potential does not affect the Bob's potential. But Alice and Bob share the same wave function, so when the wave function is changed due to the Alice's potential, it has consequences for Bob as well.

 

[kurt101]

There is no such thing as Bob's wave function. In the case of entanglement, there is only one wave function describing, Bob, Alice, their apparatuses, etc.

Does the entire universe share the same wave function in your interpretation?

The change of Alice's potential does not affect the Bob's potential. But Alice and Bob share the same wave function, so when the wave function is changed due to the Alice's potential, it has consequences for Bob as well.

Why does the change in the wave function from Alice's measurement affect Bob? And why does it not effect some other pair of locally prepared entangled photons. I assume the answer is preparation like @vanhees71 might tell me, but what is the answer in your interpretation? And again, why is the wave function of Bob's future measuring apparatus affected or is is only affected once the light cone from Bob reaches it?

 

[lodbrok]

The decision to swap - or not - can be made in the future. It is partially responsible for the entanglement effect. Then by your own definition, the future causes the past, which is your "absurd" ("paradoxical" to others).

The past can't be in the future light cone of the future so that's not my definition at all. The entangled subset is generated by Alice and Bob, in the future relative to Victor's measurements. Victor's data are transmitted to Alice and Bob through classical sub-light speed channels. Therefore the selection of the subset is from information obtained from the past relative to the moment the selection happens.

The rest of your post does not accurately represent what I stated.

 

[kurt101]

Because... I have already explained multiple times that your idea is falsified by Monogamy of Entanglement (reference and proof previously provided). [1] can never be maximally entangled with [2] and also maximally entangled with [4]. Or maybe you deny Monogamy of Entanglement?

I just want to point out that your monogamy argument only works in the case where the BSM test is done before the measurement of 1 & 4. It does not apply to when the BSM test is done after the measurement of 1 & 4 because 1 & 4 no longer exist when the BSM test is done between 2 & 3. In other words, in the case where the BSM test is done after measurement of 1 & 4 you are just reporting what used to be true of 1 & 4, not what is currently true of 1 & 4 and so the monogamy rule is not violated.

 

[Fra]

I agree all agents are governed by the same physical laws and processes as other systems.

Good start :)

Yes, causation within the agent, not the systems being observed or about which information is being processed. Demystifier appears to suggest in post #172 that being able to calculate the past state of a non-dissipative system from the present state is retrocausality. It may be causality in the internal state of the observer but has nothing to do with the causality of the system under observation.
Alice and Bob's analysis of the 1&4 data happens in the future light cone of Victor's measurement. Victor's results are transmitted to Alice and Bob through classical channels. The use of Victor's data to filter [1&4] causes the selection of a sub-ensemble which shows entanglement. Here we have causation within the agents while processing information obtained at sub-light speeds in the proper time ordering consistent with the definition of causation. None of this has anything to do with the actual physical systems of the particle streams [1, 2, 3, 4].

I would be curious to hear a definition of "causality" that suggests otherwise.

I'll conjecture that the dark side definition of causality can't distinguish "A retro-causes B" from "B causes A".

My main point was to just argue against "absurd situation in which different agents can choose to "cause" or not "cause" the past/future by choosing whether to perform or not perform a mathematical calculation".

I see your reseponse but I realize that to try to explain more I need to get into deep water as it goes much beyond the basic concepts of information processing agents, and that we can't talke about. So perhaps I should leave it here or mentors will bash me. But the idea would be in short that a real agent, has limited freedom of choosing which operations to perform or not. Just like there is only so many "actions" a molecule can take, and the ones actually take are not entirely condicidental. But I will stop there.

A paper that is not really all the way to where I aim, but in the right direction is this one, but not sure if you see the connection...
Precedence and freedom in quantum physics
-- https://arxiv.org/abs/1205.3707

/Fredrik

 

[mattt]

This is what I still don't understand about your interpretation. You say that measuring Alice instantly changes the potential which changes Bob's wave function and the state of the apparatus Bob will be measured by, even though Bob's future measurement apparatus is outside of the light cone of Bob at that point and its future configuration is not yet known (actually this later part I am not sure if it is what you are saying). I just don't see the causal connection between Alice's measurement and Bob's future measurement apparatus. I can change lots of other things near Bob's future measurement apparatus; do those things affect the measurement of Bob? Not really, so what is so special about Alice's measurement that can change Bob's future measurement apparatus.

Basically if you said that Alice's measurement changed the wave function of Bob and left it at that, I would be perfectly satisfied with the explanation. I am just confused if you are also implying that Alice's measurement changes the potential and the configuration around Bob's future measurement apparatus which is outside of the light cone of Alice and Bob.

In Bohmian mechanics, the change in disposition of one piece of apparatus can affect the results obtained elsewhere with a distant apparatus (even if the statistical distribution of those distant measurements, taken alone, does not change, so a person there cannot know if a person here has changed orientation of the apparatus or not).

Exactly the same as standard quantum mechanics.

Take into account that the global wave function satisfy the same Schrodinger equation as always, so it's exactly the same as in standard quantum mechanics.

The only addition is the guiding equation, that gives you the velocities of the bohmian particles determined by the wave function, and the equilibrium condition.

A little bit more involved is the treatment of subsystems and their version of what a measurement is.

 

[DrChinese]

1. The past can't be in the future light cone of the future so that's not my definition at all. The entangled subset is generated by Alice and Bob, in the future relative to Victor's measurements. Victor's data are transmitted to Alice and Bob through classical sub-light speed channels. Therefore the selection of the subset is from information obtained from the past relative to the moment the selection happens.

2. The rest of your post does not accurately represent what I stated.

1. You exclude by future to past action by assumption only. Facts contradict you, because changing the ordering does not change the statistical outcome. The subset can be selected at any time. And in fact there is no particular need for any of Alice, Bob and Victor to be separated; they could be in the same place (in which case no sub-light signal is needed). The successful BSM can be performed as arbitrarily close in time as desired to the Bell test.

2. So... what are you saying? I read above: "The use of Victor's [2 & 3] data to filter [1&4] causes the selection of a sub-ensemble which shows entanglement."

a) Does the BSM on [2 & 3] "quantum cause" the entanglement swap to [1 & 4] or not? Or is it a after-the-fact filter?
b) If not, how do the [1 & 4] sub-ensemble pairs become entangled (since none start out that way, as [1] and [4] are monogamously bound to other photons initially)? Again, do you deny Monogamy of Entanglement?

----------------------

Interpretations claiming one or more classical features (in this case Einsteinian causality), but which are unable to explain swapping satisfactorily, are a disappointment. You can't just say "my interpretation is equivalent to QM in all respects" and then deny Monogamy of Entanglement - which is a deduction from that same QM.

 

[PeterDonis]

if you said that Alice's measurement changed the wave function of Bob and left it at that, I would be perfectly satisfied with the explanation

That is what he's saying. In Bohmian mechanics, "the wave function" is not local: Alice's measurement changes the wave function throughout the entire universe.

 

[kurt101]

Exactly the same as standard quantum mechanics.

Take into account that the global wave function satisfy the same Schrodinger equation as always, so it's exactly the same as in standard quantum mechanics.

I have had this question about relativistic QFT for a long time now and I still don't have a clear answer, but I think it should be easy for someone who understands relativistic QFT math well to answer. The question is if there is a change outside of the light cone of the experiment being considered. How long does it take before that change makes a contribution (mathematically) to the experiment? Does it instantly make a mathematical contribution or does its contribution have to respect the speed of light?

To me it sounds like a simple question. One should be able to come up with a simple case and understand when the contribution of the change outside of the light cone of the experiment being considered makes any kind of contribution. Again: is the contribution instant or does it respect the speed of light? And I am looking for the relativistic QFT answer here.

 

[vanhees71]

I have had this question about relativistic QFT for a long time now and I still don't have a clear answer, but I think it should be easy for someone who understands relativistic QFT math well to answer. The question is if there is a change outside of the light cone of the experiment being considered. How long does it take before that change makes a contribution (mathematically) to the experiment? Does it instantly make a mathematical contribution or does its contribution have to respect the speed of light?

No! By construction there cannot be any causal influence between space-like separated events. In other words there's no faster-than-light signalling possible by definition within local relativistic QFT. It's called the microcausality principle and together with the assumption of the existence of a stable ground state predicts the CPT theorem, the spin-statistics theorem and makes the S-matrix unitary.

I don't know, why again and again it's claimed that the violation of Bell's inequality would imply non-locality (i.e., faster-than-light signalling) although it's clearly excluded by the math of relativistic QFT, which nevertheless predicts at the highest precision and statistical significance successfully the outcome of these very experiments ("Bell tests").

To me it sounds like a simple question. One should be able to come up with a simple case and understand when the contribution of the change outside of the light cone of the experiment being considered makes any kind of contribution. Again: is the contribution instant or does it respect the speed of light? And I am looking for the relativistic QFT answer here.

Of course, I cannot write an quantum-field theory textbook in terms of forum postings. Have a look here:

S. Coleman, Lectures of Sidney Coleman on Quantum Field
Theory, World Scientific Publishing Co. Pte. Ltd., Hackensack
(2018), https://doi.org/10.1142/9371

or, in more generality and detail

S. Weinberg, The Quantum Theory of Fields, vol. 1,
Cambridge University Press (1995).

 

[PeterDonis]

The question is if there is a change outside of the light cone of the experiment being considered. How long does it take before that change makes a contribution (mathematically) to the experiment? Does it instantly make a mathematical contribution or does its contribution have to respect the speed of light?

These questions are not well posed in relativistic QFT because the idea of "change" doesn't make sense in a relativistic theory the way you are using it. The relativistic model includes all of spacetime; it doesn't "change", it just is. Only one thing can happen at each event in spacetime, so the idea of something "changing" doesn't even make sense.

What you can ask about in relativistic QFT is whether operators representing measurements made at different spacetime events commute. In a relativistic QFT, operators representing measurements at spacelike separated events will always commute--meaning their results cannot depend on the order in which they are made. Operators representing measurements at lightlike or timelike separated events do not have to commute in relativistic QFT, but they can; and it turns out that, in the particular experiments under discussion here, they do: the measurements commute regardless of the spacetime relationship between the events at which they take place.

 

[PeterDonis]

By construction there cannot be any causal influence between space-like separated events.

The reason for this is that in relativistic QFT operators representing measurements at spacelike separated events commute.

But, as I just pointed out in post #205, in the particular experiments under discussion, the measurement operators commute regardless of the spacetime relationship between the events: they commute whether the measurements are spacelike, lightlike, or timelike separated.

By your logic, this would rule out causal influences between the measurements altogether; but that would in turn leave you with the problem of how to explain the Bell inequality violations and the swapping of entanglements. @DrChinese has accounted for that by drawing a distinction between ordinary causality, the kind that measurement operators commuting rules out, and "quantum causality", the kind that can account for things like Bell inequality violations and entanglement swapping even though the measurement operators commute.

 

[PeterDonis]

non-locality (i.e., faster-than-light signalling)

Please stop misrepresenting what the term "non-locality" means in the literature in this area. It doesn't mean FTl signaling. It means violation of the Bell inequalities. Nobody is claiming that any of these experiments can be used for FTL signaling.

 

[vanhees71]

Why do you call it "non-locality" when you want simply to say "violation of Bell's inequality"? It's misleading!

 

[PeterDonis]

Why do you call it "non-locality" when you want simply to say "violation of Bell's inequality"?

Because that's how the term is used in the literature in this area.

It's misleading!

Perhaps if one has never encountered the terminology before; but you don't have that excuse. We have had this discussion in multiple threads and you are perfectly well aware of what "non-locality" means in the context of discussions of Bell's Theorem and the Bell inequalities. If you don't like the terminology, then convince the community of physicists who are working in this area to change their usage. Continuing to belabor it in PF threads is pointless.

 

[vanhees71]

The reason for this is that in relativistic QFT operators representing measurements at spacelike separated events commute.

But, as I just pointed out in post #205, in the particular experiments under discussion, the measurement operators commute regardless of the spacetime relationship between the events: they commute whether the measurements are spacelike, lightlike, or timelike separated.

Yes, but only if they are spacelike separated you can be sure that the measurements are not causally connected with each other.

By your logic, this would rule out causal influences between the measurements altogether; but that would in turn leave you with the problem of how to explain the Bell inequality violations and the swapping of entanglements. @DrChinese has accounted for that by drawing a distinction between ordinary causality, the kind that measurement operators commuting rules out, and "quantum causality", the kind that can account for things like Bell inequality violations and entanglement swapping even though the measurement operators commute.

I don't understand this question. If the measurement events (i.e., the various registrations of photons in coincidence measurements) are space-like separated within relativistic microcausal QFT, they cannot causally influence each other. The explanation for the correlations described by entanglement is simply that they are simply properties described by the entangled state, which has been prepared in the very beginning by creating the corresponding entangled photon pairs (or more than 2 photons in other experiments). I have explained zillions of times my point of view, how the observed entanglement swapping is explained within this point of view.