A Barandes's Unistochastic Refomulation Applied to Entanglement Swapping

[Morbert]

TL;DR Summary

A sketch of the unistochastic reformulation of quantum mechanics applied to a basic entanglement swapping scenario, with a focus on causal relations implied by the principle of causal locality.

Consider four particles $Q,R,S,T$ ($Q,R$ are entangled, as are $S, T$) and three observer systems $A,B,C$. At time $t'$, $A$ makes a spin measurement of her choice on $Q$, and $B$ makes a spin measurement of her choice on $T$. Then, at time $t''$, $C$ makes Bell-state measurement (BSM) or separable-state measurement (SSM) on $R,S$.

I.e. In a conventional entanglement swapping experiment, we have initially have a tetraparticle system $\psi^-_{QR}\psi^-_{ST}$. We also have Alice and Bob making measurements on particles $Q$ and $T$ while Charles makes a BSM or SSM on $R,S$.

Barandes discusses divisible events in section F here. $t'$ and $t''$ correspond to divisible events, and so the unistochastic process $\Gamma(t)$ is\begin{eqnarray*}
\Gamma(t) = \Gamma(t\leftarrow t'')\Gamma(t'' \leftarrow t')\Gamma(t')
\end{eqnarray*}where
\begin{eqnarray*}
\Gamma(t') &=& \Gamma_{QR}(t')\otimes\Gamma_{ST}(t')\otimes\Gamma_A(t')\otimes\Gamma_B(t')\otimes\Gamma_C(t')\\
\Gamma(t''\leftarrow t') &=& \Gamma_{AQ}(t''\leftarrow t')\otimes\Gamma_{BT}(t''\leftarrow t')\otimes\Gamma_{R}(t''\leftarrow t')\otimes\Gamma_{S}(t''\leftarrow t')\otimes\Gamma_C(t''\leftarrow t')\\
\Gamma(t\leftarrow t'') &=& \Gamma_{AQ}(t\leftarrow t'')\otimes\Gamma_{BT}(t\leftarrow t'')\otimes\Gamma_{CRS}(t\leftarrow t'')\\
\end{eqnarray*}After the measurements conclude, we have the final distribution $p(t) = \Gamma(t)p(0)$. We can identify the Bell-inequality-violating correlations between $A$ and $B$ concurrent with $C$'s relevant BSM outcomes by computing conditional probabilities of interest $p((a_t, b_t), t | c_t, t)$.

Similarly, we can identify causal relations with Barandes's principle of causal locality.

A theory with microphysical directed conditional probabilities is causally local if any pair of localized systems Q and R that remain at spacelike separation for the duration of a given physical process do not exert causal influences on each other during that process, in the sense that the directed conditional probabilities for Q are independent of R, and vice versa.

In particular, causal separation follows from relations like equation (54) here.

We can see that $A$ is free of causal influences by $B, C, S, T$ if\begin{eqnarray*}
p(a_t, t | (q_0,r_0,s_0,t_0,a_0,b_0,c_0), 0) = p(a_t, t | (q_0,r_0,a_0), 0)
\end{eqnarray*}Similarly, $A, C, Q, R$ don't exert causal influences on $B$ if\begin{eqnarray*}
p(b_t, t | (q_0,r_0,s_0,t_0,a_0,b_0,c_0), 0) = p(b_t, t | (s_0,t_0,b_0), 0)
\end{eqnarray*}I suspect these relations do hold, though proving them would be quite involved. For the purposes of this thread I will merely remark that these relations are what reveal causal relations according to Barandes's understanding of causality.

 

[DrChinese]

OK, great example. I would like to make it a bit more concrete, starting with your description of the experiment. By "more concrete", I mean some specific examples that should point out where I think there is a fork in our understanding. By "our", I mean: between myself, you, Barandes or anyone else reading here. But of course, I'd like to learn as much as is possible about the Barandes' view. I dislike formulae that are overly generic and tend to fall into the hand-waving side of things, recognizing that "hand-waving" is definitely in the eye of the beholder...

If you are sufficiently familiar with the details of the usual Entanglement Swapping experiments we have been discussing in this Subforum, you might be able to skip the remainder of this post and do directly to my specific questions in my next post, #3.

So let's start with your excellent Entanglement Swapping setup: Photons Q/R/S/T starting as pairs Q/R and S/T in the ψ- Bell state (anti-correlated). Observers/observer systems A(lice)/B(ob)/C(harlie) just as you have them, and we will perform suitable (4-fold) coincidence counting to obtain statistics - all others (1, 2 or 3 clicks) will be discarded. We want to compare some particular series of runs which I will refer to as f(BSM) vs. f(SSM) and determine if there is violation of Barandes' "principle of causal locality". BSM (Bell State Measurement) meaning "swap", and SSM (Separable State Measurement) meaning "no swap". And we will of course assume that the observers are sufficiently distant to each other at the time the decision is made to have the BSM or the SSM that there is a violation of causal locality (CL) if we agree: The f(BSM) should equal f(SSM), but does not. So it is possible that we could agree that f(BSM)<>f(SSM), but disagree that it led to a violation of CL. Hopefully this makes sense...

---

Specifics of Setup:

But I want to drill into the setup and limit it to a very particular subset of setting and outcomes. Here are the particulars:

1. The A setting ONLY clicks if the Q photon is 0>. So a polarizer (set at 45 degrees) is placed in front of a single detector on the A side. We know that the R photon, were it to be measured on the 0>/1> basis before getting to observer C, would certainly register as 1> (i.e. opposite to Q) since the Q and R photons were initially in the ψ- Bell state (therefore having opposite polarizations). (By convention, 0> and 1> outcomes means they are either being recorded as +45 degrees or -45 degrees.)

2. The B setting has a Polarizing Beam Splitter (PBS) set in front of detectors such that they can click as either 0> or 1> when each T photon arrives, depending on PBS output port.

3. The C observer will set their detectors (there are usually 4 total) to indicate a H> or a V> - which by convention means they are either being recorded as +45 degrees or -45 degrees. That being a mutually unbiased setting relative to the 0> or 1> settings of observers A and B. In the diagram below, the 4 detectors are labeled DQ_1H, DQ_1V, DQ_2H and DQ_2V. Whenever DQ_1H and DQ_2V click at the same time, or DQ_1V and DQ_2H click at the same time: This can lead to a successful BSM to the Bell State ψ-, but can also indicate an SSM if the input photons R and S weren't suitably previous entangled from eligible sources (Q/R and S/T).

Per diagram source Kaltenbaek et al: "A two-fold coincidence detection event between either DQ1H and DQ2V or DQ1V and DQ2H indicates a projection on ψ−."

4. We will ONLY consider outcomes in which this signature 4-fold outcome occurs, the ψ- state. In this state, if a successful BSM on R and S were to occur, the Q and T photons should be physically* and remotely* cast also into the ψ- state. If measured on the 0>/1> basis, they will always be opposite (ideal case of course). Since we are only looking at Q photons registering as 0>, we would expect to see the matching T photons show up as 1> if there is a successful BSM as I have specified.

So we will say that all variables together, the function f() is defined as the percentage of total 4-fold outcomes in which we have observed the T photon as 1>, less those where outcomes for the T photon is observed as 0>:

f(BSM) would be expected to be >0, approaching 100% in the ideal case.
f(SSM) would be expected to be =0, approaching 0% in the ideal case.

All of the above is standard experimental physics, and follows the usual theory, and in no way should be considered controversial. In addition to the Kaltenbaek reference, you might also consult Ma et al.

---

Theory:

i) For a successful swap (BSM) to occur, the R and S photons must be in an indistinguishable state. When the detectors fire upon registration of the R and S photons, you must not be able to determine - even in principle - which was the source for each click. If they are distinguishable, the swap fails and you get SSM outcomes. This is fundamental.

ii) Note that regardless of whether any one of a polarization entangled photon pair (such as Q and R) are found to be have a particular eigenvalue on some basis (say 0> on the 0>/1> basis), the other will never have any correlation on one of the biased bases (such as H>/V> or L>/R>). This too is fundamental in QM.

iii) Similarly: There can be no initial correlation between any 2 maximally polarization entangled pairs, such as Q/R and S/T. Per Kaltenbaek: "These [are] strong non-classical correlations between particles that do not share any common past..." And: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons [Q and T]." The point being: there should be no "hidden" correlation between the independently produced initial pairs. That would violate Monogamy of Entanglement. However, this particular assumption can in fact be tested using the method I will describe later.

Again, the above concepts are uncontroversial and conventional. In my thought experiment, we will measure f(BSM) as described above and actually performed in the cited experiments and others. In the Ma experiment, this correlation value was about -61.1% (theoretical would be 100% anti-correlated). Their comparable f(SSM) value was -4.5% (theoretical would be aforementioned 0%).

To obtain their SSM dataset results (for comparison to the BSM results), Kaltenbaek and Ma each use a different technique for achieving SSM results. There have been some criticism of these techniques by posters here in earlier threads. The essence of the criticisms is: The f(SSM) results are not directly comparable to the f(BSM) results. They say that in some way, the conditions being measured when there is no swap (SSM) is fundamentally different that when the swap is successful (BSM). In one of the experiments (Ma), the number of recorded 4-fold events is about twice what it is in for one function versus the other. Also, there are alterations to the beam path resulting in questions as to whether the results are directly comparable. [Note that I believe these criticisms are not well founded, but that is immaterial here.]

I will use a different technique to achieve Separable State Measurement (SSM) results. There is only a single simple difference in the achievement of the SSM outcomes versus the BSM outcomes. Importantly, that kink (difference) used does NOT allow for the distinguishability of the sources - at least not as exploited here. But it does distinguish them in principle since a basis measurement is performed - if you consider this reduncant measurement "physical". In the cited Kaltenbaek and Ma experiments, it IS possible to determine in each and every 4-fold event which detector is clicking due to the R photon, and which is clicking due to the S photon. In in the technique I present, all of the the observable properties are otherwise unaffected and the count rates** should be about the same.

On my following post: I will explain the details of my "kink" so as to separate discussion of that from discussion of Morbert's setup with my minor modifications - since everything so far is generally accepted.


*Of course, what we seek to understand is IF the BSM is physical and remote. As best as I understand Barandes, he asserts a BSM is not physical and therefore cannot have a remote component. But this is precisely what I want to understand. As Morbert properly notes, he definitely asserts "causal locality". So does he allow any remote action, perhaps one that is non-causal?

**Typical count rates for these experiments are on the order of about 1 per 10 seconds to 10 per second. The low rate is because near-simultaneous emission times for 2 independent pairs occurs completely randomly. They must occur within a very narrow time window (a few ns) in order to qualify as eligible 4-fold events.

 

[DrChinese]

Follow-on to my previous post, which is a referenced and slimmed down version (fewer qualifying events) than as described by @Morbert. If you are familiar enough with those references, you can skip to here.

The Kink: To achieve an SSM result, we place a polarizer (let's call it K) in the R photon path at a point (i) AFTER the time [let's ignore relativistic considerations due to frame] which the Q photon has registered as 0>, and BEFORE R arrives at the Beam Splitter of the Swap portion of the setup (per the diagram). That K polarizer will be oriented to allow only 1> polarized R photons through.

We presumably "knew" that these same R photons would be polarized as 1> when we observed its partner photon Q as being 0> polarized (since Q and R are anti-correlated). So if R is indeed polarized as 1>, inserting the K polarizer allowing that polarization to pass does not yield any new information whatsoever. It's redundant. So if those R photons were coincidentally matched somehow to the S photon stream, the K polarizer should do nothing subsequently when the R and S photons physically overlap.

To summarize: If there is "causal locality", then why would inserting the K polarizer - revealing no new information of any kind, or otherwise altering the dataset collection - produce a situation where f(BSM) is not equal to f(SSM)? After all, there is no known correlation between a 1> measurement outcome on any photon and a subsequent measurement on the H>/V> basis.

---

Questions:

a) How does the word "stochastic" (as used by Barandes or anyone) have any application to this experiment as I have presented it?

One definition of stochastic: "Stochastic theories are those that model systems or phenomena with random or probabilistic elements, meaning their outcomes are not fully predictable but rather influenced by chance." Of course, which specific events qualify for our f() functions is itself random, that part fits. But why would independently evolving elements (pairs Q/R and S/T) be perfectly correlated in some cases - but not others - when all observables are identical? That part doesn't seem to fit.

There are no stochastic elements that I see. If the R and S photons are not physically interacting at the beam splitter (in the swap mechanism), in fact why do they even need to overlap? Presumably so they are indistinguishable, of course, and we are lacking a single piece (1 bit) of information. That bit is missing either way in my scenario. But how does that relate to stochastics or entanglement swapping?


b) Would anyone disagree that placing a 1> oriented filter ("K") in the path of photon R will prevent a successful swap? I.e. The K filter will force only SSM outcomes, eliminating all (anti)correlation between Q and T...

(Note that if you disagree with what I am saying here, there are clear experimental reasons why this must be so. But I prefer not to detail this here, because it will divert from the main thread.)


c) Assuming you agree with my assessment per b): Would anyone disagree that the decision to place the K filter (forcing SSM instead of a BSM) is the therefore the CAUSE of the outcome statistics as indicating SSM or BSM? (It's the only independent variable.) That being: obtaining f(BSM) vs. f(SSM) is based on a decision to create a discernible physical and statistical difference that should not in any way affect the criteria of which 4-fold events are being recorded and reported.

d) And tying back to Morbert's OP and his representation of causal locality: Aren't his last 2 equations simply a restatement of the idea of signal locality? If those equations DIDN'T hold, we could use that to signal... right?

 

[Fra]

By "our", I mean: between myself, you, Barandes or anyone else reading here. But of course, I'd like to learn as much as is possible about the Barandes' view. I dislike formulae that are overly generic and tend to fall into the hand-waving side of things, recognizing that "hand-waving" is definitely in the eye of the beholder...

I think some hand-waving is because even to me, that likes Barandes view, find it incomplete. So I fill in the gaps with "hand-waving" until we have it explicit.

To keep this comment short i will focus on what i think is the key issue.

But why would independently evolving elements (pairs Q/R and S/T) be perfectly correlated in some cases - but not others - when all observables are identical? That part doesn't seem to fit.

I would say the "answer" in Barandes view is that the time evolution of the transition matrices of two independent subsystems are constrained my the time evolution of the total system. And sometimes this factorizes, sometimes it does not, depending on the particular interaction of course.

But indeed the time dependnent gamma matrix, is implicitly like a sort of global non-local constraint. Barandes does not explain this. But this is like we don't "explain" the hamiltonian in the regular hilber picture; it's given; or model input. It's in here that the apparent "non-locality" is encoded IMO.

What Baranders does is to separate this to the total evolution law, into indepdendent stochastics + constraint on the stochstics matrices as they evolve in time.

Obviously this is not completely answering the mystrey, but it's a step.

And they my I myself personally in my interpretation (fill in this gap) that makes this makes sense for me is to assume that the "constraint" wether global dynamical law, or hamiltonians, or unistochastic gamam matrices are NOT to be understood as fixed constraints - because this is the root of the apparentl non-locality. Both in Barandes picture and in QM picture.

If we instenad understand these as emergent structues, ie. what "looks like a constraint" can very well be just a stead state similar to an equilibrium. This means - that parts are not really "constrained", they are "tuned" by evolution. This is not trivial, but it is similaryly non-trivial to jus say, consider a pair production of an electron and a positron - but what IS an electron - really? That's a mystery itself. we aren't talking about RANDOM subsystem microstroctures in these experiments.

So in my view - the missing parts I fill in for myself in order to coherently "interpret" Barandes picture - is simply that independently acting parts SEEM like tied together by a constraint, while it may instead by that they are "tied together" by a commong history (memory) that hase caused their behaviour to be in tune "or perfect anti-tune as per some respect"

This my "answer" to this. But indeed this is not a explicit answer. It is handwaving, and at least IMO it is conceptually coherent. The Missing part noone can answer yet is the "evolutionary mechanism" that explains the origin of matter, in a way that "at steady state" meets up with the unistochastic matrices of parts, in a way that are co-evolved by other parts. Because in evolution, every subsystem is obviously DEPENDENT by it's environment for survivial. But this is more like a steady state conditions and not a "constraint". This is very similar to the abstraction of observer equivalence and observer democracy that I mentioned several times in other treads. It replaces "constraints" with "evolutionary emergence". This is like other ideas where you equate laws instead by equations of state of underlying details.

/Fredrik

 

[pines-demon]

I see that @DrChinese has convinced us that entanglement swapping as the ultimate criteria to discuss entanglement.

I don't get what this all about, sure if Barandes equivalence holds you can make the same predictions of entanglement swapping using his non-Markovian processes. However verifying Barandes principle of causal locality is pointless (as discussed in the other thread) because is always true for both classical and quantum mechanics. I would prefer if you show what assumption of Bell "local causality" is not followed.

 

[DrChinese]

I see that @DrChinese has convinced us that entanglement swapping as the ultimate criteria to discuss entanglement.

Touche

Actually, I'd be happy if I could at least make folks aware of some experiments that have some bearing on the subject. Some of these papers might not have been familiar to some.

I would prefer if you show what assumption of Bell "local causality" is not followed.

Not saying that all would agree with me on this, but for causality to be followed in the Einsteinian sense: Causes must precede effects. Delayed choice experiments deny this basic principle.

 

[Morbert]

a) How does the word "stochastic" (as used by Barandes or anyone) have any application to this experiment as I have presented it?

The procedure would be to write down the relevant spectrum of magnitudes for the seven subsystems (four particles + Alice, Bob, and Charles), compute the relevant directed conditional probabilities, and show that, according to the principle of causal locality, Charles has no effect on Alice or Bob.

d) And tying back to Morbert's OP and his representation of causal locality: Aren't his last 2 equations simply a restatement of the idea of signal locality? If those equations DIDN'T hold, we could use that to signal... right?

This question is probably easier to think about with the standard EPRB case Barandes explores in section VIII. The more I consider it, the more I think his account does not reduce to a no-signalling theorem. If Bob can nonlocally influence Alice's particle, and Alice performs the same measurement as Bob, then he nonlocally influences Alice even if no signalling is possible. E.g. if the particles were prepared in one of the $\Phi$ Bell states, and Bob registers some outcome, then he has changed the likelihood of Alice recording that outcome from 50% to 100%. That is an effect that would be visible in the directed conditional probabilities of Alice, and hence would violate Barandes's principle of Causal locality.

 

[DrChinese]

The procedure would be to write down the relevant spectrum of magnitudes for the seven subsystems (four particles + Alice, Bob, and Charles), compute the relevant directed conditional probabilities, and show that, according to the principle of causal locality, Charles has no effect on Alice or Bob.

Hmm... that is exactly what I did in my posts above. The f() function considers everything you mention. f(SSM) is 0 when remote Charles inserts the K polarizer (producing no distinguishing information) in the path of photon R, f(BSM) is 1 otherwise (ideal case of course).

The only note here: The f() function includes both Alice's and Bob's results, which remotely change relative to each other based on the free choice of Charles. But you need at least a single bit of classical information from Charles to recognize that.

E.g. if the particles were prepared in one of the Bell states, and Bob registers some outcome, then he has changed the likelihood of Alice recording that outcome from 50% to 100%.

Yes, that happens. Of course, that is only one possible description. Ordering of measurements is irrelevant. The experiment can be performed with Charles' decision before or after measurements of Alice and Bob; and Alice's measurement can be made before or after measurement by Bob.

The only statement I think is fair: the final f() outcome is dependent solely on a decision by Charles to swap (BSM) or not (SSM), regardless of order. So there is no requirement that his decision - which changes the outcome - be executed prior to the other measurements in order to be considered the "cause". Because Charles' decision is the independent variable being observed. This is standard scientific practice.

That is an effect that would be visible in the directed conditional probabilities of Alice, and hence would violate Barandes's principle of Causal locality.

The f() function does not represent a change visible to Alice, Bob, or [Alice+Bob] alone. Otherwise, FTL signaling is possible. No one is claiming that. So by any standard I can see: To the extent that an action by Charles can change the 4-fold outcomes, Barandes' Causal Locality IS violated because the 4-fold outcomes visibly change.

To the extent that his Causal Locality more stringently requires that 2-fold outcomes [Alice+Bob] visibly change for its violation, then it is merely a mimic of a no-signaling assumption. Which isn't much of an assumption, since 100+ years of physics has failed to produce any FTL signaling - despite plenty of attempts.

 

[Sambuco]

Not saying that all would agree with me on this, but for causality to be followed in the Einsteinian sense: Causes must precede effects. Delayed choice experiments deny this basic principle.

This is a perfectly valid interpretation but not the only one (see below).

The only statement I think is fair: the final f() outcome is dependent solely on a decision by Charles to swap (BSM) or not (SSM), regardless of order. So there is no requirement that his decision - which changes the outcome - be executed prior to the other measurements in order to be considered the "cause". Because Charles' decision is the independent variable being observed.

There's a subtlety here. As we've discussed in other threads, to evaluate the final f() outcomes we need to partition the subsets from all the runs of the experiments. The construction of these subsets depends not only on Charles' decision, but also on the results of the measurement of R and S, which in turn depend on the measurement results obtained by Alice and Bob on particles Q and T. We have no way of experimentally distinguishing whether the results of Q and T cause the measurement outcomes of particles R and S, or whether, on the contrary, the results of R and S cause the outcomes of Q and T. What is experimentally proved is the correlation, but not the causation. As you said, the temporal order plays no role.

Regarding entanglement swapping, what we know for sure is that if we choose to project out the four-particle state (QRST) based on the results obtained by Charles on particles R and S, then particles Q and T are entangled, but this entanglement is only "real" to Charles (or someone who knows his measurement results). From Alice and/or Bob's perspective, particles Q and T were never in an entangled state, so they conclude that the outcomes of measurements of R and S depend on two conditions: (1) Charles' decision to make a swap, and (2) the Q and T measurement outcomes.

Of course, we can deny causation as fundamental and accept correlations in entanglement experiments as a kind of global constraint. In that case, there is no nonlocal causation, not because there is (Bell) locality, but because there is no causation.

Lucas.

 

[Morbert]

@DrChinese It doesn't sound like your f() function is part of Barandes's reformulation. For a generic system undergoing a generic process, you have an initial distribution $p(0)$ and a transition matrix $\Gamma(t)$ that gives us a final distribution $p(t)$. From these, we compute directed conditional probabilities of the form $p((), t | (), 0)$ and identify violations of, or adherence to, Barandes's principle of causal locality (after the appropriate identification of subsystems and marginalizations).

 

[DrChinese]

This is a perfectly valid interpretation but not the only one (see below). ...

As we've discussed in other threads, to evaluate the final f() outcomes we need to partition the subsets from all the runs of the experiments. The construction of these subsets depends not only on Charles' decision, but also on the results of the measurement of R and S, which in turn depend on the measurement results obtained by Alice and Bob on particles Q and T.

In my setup, there are no subsets at all. That's why I specified this particular f() function. All 4-fold events are considered, and placed together so that there is no criticism on this point. This is normal scientific method, and conclusions drawn from this are scientifically valid.

But I agree that the R and S results could be a result of earlier decisions made by Alice and Bob in the scenario you are proposing (see my next comments).

There's a subtlety here. ... We have no way of experimentally distinguishing whether the results of Q and T cause the measurement outcomes of particles R and S, or whether, on the contrary, the results of R and S cause the outcomes of Q and T. What is experimentally proved is the correlation, but not the causation. As you said, the temporal order plays no role.

Yes, this is a fair point. But now we are jumping through some hoops to avoid the most natural conclusion (that being that a free decision of Charles - and nothing else in this setup - can affect the overall f() outcomes of distant systems). I agree with your subtlety that there is no way to distinguish which way the causal order operates.

First, since ordering plays no role in the f() results (as we agree): We are forced to conclude that causal order does change according to when Charles makes his swap/no-swap decision - but that simply doesn't affect the results. Which kinda defeats the purpose of requiring the cause to precede the effect in the first place.

Second: Let's agree that Charles' decision occurs after Alice and Bob make their observations. In this setup, Alice and Bob get perfect (anti-)correlation at all same polarizer angles (their Q and T).

a) You could say there are an infinite (or at least a very large) number of those angles. But there are only 4 Bell states. Hmmm.

b) Note that at the time Alice and Bob measure Q and T, there is no connection whatsoever between the R and S photons - or between any other entangled partners R'/S' or R"/S" etc existing anywhere in the universe. There is no correlation UNLESS there is an opportunity for R and S to physically overlap - which of course happens remotely to the decisions of Alice and Bob: i.e. to measure at the same angles, of course these are chosen in advance and fixed - but the overall systems don't know that.

c) And now you are almost forced to assert that the results of R and S are actually influencing the free decision of Charles to bring R and S together. Which of course occurs BEFORE R and S are brought together.

Which again defeats the purpose of us trying to assign a classical cause/effect relationship to the experiment in the first place.

Regarding entanglement swapping, what we know for sure is that if we choose to project out the four-particle state (QRST) based on the results obtained by Charles on particles R and S, then particles Q and T are entangled, but this entanglement is only "real" to Charles (or someone who knows his measurement results).

The f() function requires all results to be brought together, yes. Again: this is normal scientific method. I don't see how claiming that the results are not "real" or are less "real" because of that is a factor.

If I measure the speed of light from Paris to Versailles*, I must bring together information from both locations to obtain results. How is this different?

Of course, we can deny causation as fundamental and accept correlations in entanglement experiments as a kind of global constraint. In that case, there is no nonlocal causation, not because there is (Bell) locality, but because there is no causation.

Lucas.

You could deny causation as fundamental, or perhaps say that all inputs to the setup jointly operate as causes. In the generalized f() function for all possible setups (not just the specific one I described earlier), there are many variables.


* I visited these beautiful cities a few days ago.

 

[DrChinese]

@DrChinese It doesn't sound like your f() function is part of Barandes's reformulation. For a generic system undergoing a generic process, you have an initial distribution $p(0)$ and a transition matrix $\Gamma(t)$ that gives us a final distribution $p(t)$. From these, we compute directed conditional probabilities...

Not so fast*! I described an experiment. It doesn't matter what Barandes "reformulation" is!!

Unless, of course, you are saying he'd make a different prediction for the outcome probabilities as compared to what I claim (which in turn matches the results of my citations).


* I attribute this to Lee Corso, an American football sportscaster.

 

[Morbert]

Not so fast*! I described an experiment. It doesn't matter what Barandes "reformulation" is!!

Unless, of course, you are saying he'd make a different prediction for the outcome probabilities as compared to what I claim (which in turn matches the results of my citations).


* I attribute this to Lee Corso, an American football sportscaster.

Barandes's reformulation makes all the same predictions as standard QM, hence its status as a reformulation. The question is whether the the resultant microphysics obeys causal locality according to the proposed theory of microphysical causality. In the original post, I said I suspect it does, and I have since worked through the same procedure Barandes applies to the EPRB scenario, and the microphysics of entanglement swapping indeed obeys causal locality. Specifically, I consider the transition $\Gamma(t\leftarrow t')$ from time $t'$ after Alice's and Bob's measurement (but before Charles's measurement) and construct the analogs to equations 70 and 71 here. I have also relabeled the paticles to $P,Q,R,S$ such that Alice performs a measurement on $P$, Bob performs a measurement on $S$, and Charles performs a measurement on $Q,R$. The density matrix is\begin{eqnarray*}
\rho(t) = U(t\leftarrow t')( \rho_{ABPQRS}(t') \otimes\ket{c_0}\bra{c_0}_C) U^\dagger(t\leftarrow t')
\end{eqnarray*}the reduced density matrix for Alice, Bob, and their respective particles P and S is
\begin{eqnarray*}
\rho_{ABPS}(t) &\equiv& \mathrm{tr}_{CQR}\big( \rho(t) \big)\\
&=& \mathrm{tr}_{CQR}\big( U(t\leftarrow t')( \rho_{ABPQRS}(t') \otimes\ket{c_0}\bra{c_0}_C) U^\dagger(t\leftarrow t')\big)\\
&=& \mathrm{tr}_{QR}\big( U_{ABPQRS}(t\leftarrow t')\rho_{ABPQRS}(t') U^\dagger_{ABPQRS}(t\leftarrow t')\big)
\end{eqnarray*}Notice that there is no dependency on $c_0$, Charles's initial state. And so we have the marginalization\begin{flalign*}
&p((a_t, b_t), t | (a_0, b_0, c_0, p_0, q_0, r_0, s_0), 0)&&\\
&= \sum_{c_t, p_t, q_t, r_t, s_t} p((a_t, b_t, c_t, p_t, q_t, r_t, s_t), t | (a_0, b_0, c_0, p_0, q_0, r_0, s_0), 0)&&\\
&= p((a_t, b_t), t | (a_0, b_0, p_0, q_0, r_0, s_0), 0)&&
\end{flalign*}The directed conditional probabilities for Alice and Bob do not depend on Charles, and hence there is no causal influence.

This sketch does not exhaustively cover all entanglement swapping experiments, and some simplifying assumptions have been made (namely the particles are not destroyed after measurement), but a similar exercise can be carried out for any experiment of interest.

This theory of causality can be critiqued, but I think it is clear what it asserts: In the same way Bob has no influence on Alice in the standard EPRB experiment (according to this theory), Charles has no influence on Alice or Bob in entanglement swapping experiments. Before any critique can begin, we should agree on that.

 

[pines-demon]

This theory of causality can be critiqued, but I think it is clear what it asserts: In the same way Bob has no influence on Alice in the standard EPRB experiment (according to this theory), Charles has no influence on Alice or Bob in entanglement swapping experiments. Before any critique can begin, we should agree on that.

Haven't checked the math but everybody agrees already on that in the sense "no signaling". The problem is what kind of "influence" is the measurement of a particle exerting on the other.

 

[Fra]

The problem is what kind of "influence" is the measurement of a particle exerting on the other.

I would say none. None is needed.

/Fredrik

 

[Morbert]

Haven't checked the math but everybody agrees already on that in the sense "no signaling". The problem is what kind of "influence" is the measurement of a particle exerting on the other.

There are two possible responses to this.

i) It's not clear that this reduces to "no signalling". In the standard formulation of QM, and considering an entangled bipartite system, Alice's measurement will not affect the reduced density matrix describing Bob's particle. But under any interpretation where Alice nonlocally influences Bob's particle, Alice nonlocally influences what Bob will record, and hence nonlocally influences Bob. No-signalling does not contradict this.

ii) The directed conditional probabilities can be used to show that, not only do observers not have a causal effect on other spacelike-separated observers, they do not have an effect on spacelike-separated microphysical systems. I.e. Barandes constructs the equation $$p(a_t,t | (q_0, r_0, a_0,b_0), 0) = p(a_t,t | (q_0, r_0, a_0), 0)$$ to show Bob has no influence on Alice. But we could just as readily construct $$p(q_t,t | (q_0, r_0, a_0,b_0), 0) = p(q_t,t | (q_0, r_0, a_0), 0)$$to show Bob has no inflence on Alice's particle.

 

[pines-demon]

ii) The directed conditional probabilities can be used to show that, not only do observers not have a causal effect on other spacelike-separated observers, they do not have an effect on spacelike-separated microphysical systems. I.e. Barandes constructs the equation $$p(a_t,t | (q_0, r_0, a_0,b_0), 0) = p(a_t,t | (q_0, r_0, a_0), 0)$$ to show Bob has no influence on Alice. But we could just as readily construct $$p(q_t,t | (q_0, r_0, a_0,b_0), 0) = p(q_t,t | (q_0, r_0, a_0), 0)$$to show Bob has no inflence on Alice's particle.

How does this translate in the dynamics? What is different before and after the measurement? Isn't the measurement some kind of nonlocal action that modifies the transition matrix all over space?

 

[Fra]

How does this translate in the dynamics? What is different before and after the measurement? Isn't the measurement some kind of nonlocal action that modifies the transition matrix all over space?

The total time dependent transition matrix, is a global "constraint" in Barandes picture. Given this, the rest follows, it implies that the parts have entangled evolutions.

But he does not explain where it comes from beyond the correspondence!

The remaining mystery is how to understand this "constraint" independently. This mystery is the same as in QM. But I think this can be further "interpreted", just like you can "interpret" hilbert spaces.

/Fredrik

 

[pines-demon]

The total time dependent transition matrix, is a global "constraint" in Barandes picture.

If it is global then it is nonlocal (at least in weak sense).

The remaining mystery is how to understand this "constraint" independently.

And that's why I think Barandes idea is nice but does not deflate anything, like with other interpretations he is just using some new "magical" idea (which includes many worlds, conspiracies, pilot waves, retrocausal handshakes and so on).

 

[Morbert]

How does this translate in the dynamics? What is different before and after the measurement? Isn't the measurement some kind of nonlocal action that modifies the transition matrix all over space?

The directed conditional probabilities make up the transition matrix, which plays the role of a dynamical law. Causal relations follow from Bayesian networks of the directed conditional probabilities.

So e.g. in the entanglement swapping experiment, the dynamical law maps the initial distribution to the final distribution, and the directed conditional probabilities determine the causal relations that show Alice Charles and Bob do not causally influence one another.

 

[Morbert]

But he does not explain where it comes from beyond the correspondence!

The directed conditional probability distributions are nomological.

 

[DrChinese]

Barandes's reformulation makes all the same predictions as standard QM... The question is whether the the resultant microphysics obeys causal locality according to the proposed theory of microphysical causality. In the original post, I said I suspect it does...

We all agree that nothing any two of {Alice/Bob/Charles} do that causes a visible change to the one other of {Alice/Bob/Charles} (short of the third receiving information from one of the first two). That is precisely the equivalent statement as saying there is no signaling, no matter how you try to phrase it.

The directed conditional probabilities for Alice and Bob do not depend on Charles, and hence there is no causal influence.

Of course the joint probabilities for {Alice+Bob} depend on Charles. When there is a swap, their (anti-)correlation is 1; otherwise it is 0. This is the fundamental lesson of entanglement swapping experiments.

This theory of causality can be critiqued, but I think it is clear what it asserts: In the same way Bob has no influence on Alice in the standard EPRB experiment (according to this theory), Charles has no influence on Alice or Bob in entanglement swapping experiments. Before any critique can begin, we should agree on that.

No can do. If Charles executes a swap, Alice and Bob are entangled. Otherwise, they aren't. How can you even think otherwise?

Further: In my setup (posts #2 & 3), the free choice by Charles to swap (or not) means that there are visible changes in the Alice/Bob pairwise outcomes. Of course, Charles must send a bit of information to Alice and Bob (perhaps Alice and Bob are together in the same place) to see that.

 

[PeterDonis]

Before any critique can begin, we should agree on that.

We can't, because the definition of "no influence" that is being used here is not one that all interpretations agree on. Basically you're making an implicit claim that Barandes's interpretation is "right" and everyone must agree to it. That's not going to happen. And it's against the rules of this subforum, which state that claims that a particular interpretation is right are out of bounds. We can discuss what various interpretations state, but eventually we're going to run up against unresolvable disagreements because a particular interpretation wants to define terms a certain way that other interpretations simply won't accept. It looks like we're at that point now.

 

[DrChinese]

Returning to my setup per posts #2 & 3:

Suppose a fourth actor - Donna - is the one who chooses whether to execute a swap (BSM) or not (SSM) - by inserting the K polarizer inline at a suitable spot as previously explained). Donna does not communicate her decision to anyone. Is it possible for Bob to deduce Donna's decision from information obtained from Alice and Charles? Keep in mind that Charles does not know at this point what Donna did, as the setup I specified makes the BSM/SSM (swap/no-swap) signature indistinguishable to Charles. Alice has no clue either (just a click indicating 0>). As a reminder, Bob's detectors are set for clicks on either 0> or 1> basis. Alice and Charles only send Bob a timestamp so Bob knows the Alice/Charles detectors clicked. That meant Alice got a click indicating 0>. Charles gets paired clicks of H> and V>. That same signature happens regardless of whether there was a swap or not (since only Donna knows what she did, and she's not telling). The timestamps are used to communicate to Bob that there was 4-fold coincidence, but those contain no information whatsoever about Donna's decision.

The answer is YES, although Bob's answer will not be 100% accurate. When there is a swap (BSM), only Bob's 1> detector will fire - that's because there is anticorrelation with Alice's 0> result. Bob's 1> detector will also fire half the time when there is no swap (SSM). The other half of the SSM times, Bob's 0> detector will fire instead. Given Donna varies her choices with some degree of randomness, Bob will guess right as to Donna's decision 75% of the time - which could be made higher. (And again, there is no FTL signaling as the timestamp information from Alice and Charles must be sent to Bob classically.) On average, Bob's 1> detector fires substantially more often than the 0> will.

So my point is: Yes, Bob sees a visible change when there is a swap. Only his 1> detector will click when there is a swap, and a click on his 0> definitely indicates no swap. And that sounds like Donna's decision can be detected by Bob without any information about Donna's decision being received from Alice or Charles (who don't know individually or jointly about Donna's decision).

That is precisely the opposite of what Barandes' claims (according to @Morbert ). The conditional outcomes for Bob alone do change in my example.

 

[Morbert]

We can't, because the definition of "no influence" that is being used here is not one that all interpretations agree on. Basically you're making an implicit claim that Barandes's interpretation is "right" and everyone must agree to it. That's not going to happen. And it's against the rules of this subforum, which state that claims that a particular interpretation is right are out of bounds. We can discuss what various interpretations state, but eventually we're going to run up against unresolvable disagreements because a particular interpretation wants to define terms a certain way that other interpretations simply won't accept. It looks like we're at that point now.

I said we need to agree on what the interpretation asserts. I.e. Agree on what it is the interpretation claims.

 

[Morbert]

We all agree that nothing any two of {Alice/Bob/Charles} do that causes a visible change to the one other of {Alice/Bob/Charles} (short of the third receiving information from one of the first two). That is precisely the equivalent statement as saying there is no signaling, no matter how you try to phrase it.

Of course the joint probabilities for {Alice+Bob} depend on Charles. When there is a swap, their (anti-)correlation is 1; otherwise it is 0. This is the fundamental lesson of entanglement swapping experiments.

No can do. If Charles executes a swap, Alice and Bob are entangled. Otherwise, they aren't. How can you even think otherwise?

Further: In my setup (posts #2 & 3), the free choice by Charles to swap (or not) means that there are visible changes in the Alice/Bob pairwise outcomes. Of course, Charles must send a bit of information to Alice and Bob (perhaps Alice and Bob are together in the same place) to see that.

You're still straying from Barandes's interpretation and simply restating your own.

Do you or do you not agree that according to Barandes's account of microphysical causality and his reformulation, that Entanglement swapping does not entail nonlocal influences. I am not asking you whether or not you think Barandes is right. I am asking you whether or not you agree with my telling.

If you don't then I would ask you show, using Barandes's reformulation, that his account of microphysical causality would cast entanglement swapping as nonlocal.

 

[DrChinese]

I said we need to agree on what the interpretation asserts. I.e. Agree on what it is the interpretation claims.

You said: "I think it is clear what it asserts: In the same way Bob has no influence on Alice in the standard EPRB experiment (according to this theory), Charles has no influence on Alice or Bob in entanglement swapping experiments."

OK, maybe that is what it claims. But that is directly contradicted by experiment, see my citations. Correlation upon swap, no correlation with no swap. Kinda hard to argue any point when you skip over experimental fact.

 

[Morbert]

OK, maybe that is what it claims. But that is directly contradicted by experiment, see my citations. Correlation upon swap, no correlation with no swap. Kinda hard to argue any point when you skip over experimental fact.

The reformulation agrees with all experimental results. You might have reasons to prefer your own interpretation, but failure to agree with experiments is not a valid reason. All established interpretations agree with experiment.

 

[DrChinese]

You're still straying from Barandes's interpretation and simply restating your own.

Do you or do you not agree that according to Barandes's account of microphysical causality and his reformulation, that Entanglement swapping does not entail nonlocal influences. I am not asking you whether or not you think Barandes is right. I am asking you whether or not you agree with my telling.

If you don't then I would ask you show, using Barandes's reformulation, that his account of microphysical causality would cast entanglement swapping as nonlocal.

I am not pushing an interpretation. I am comparing Barandes' interpretation to accepted experimental fact as presented by Nobel level teams. With his assertion that "entanglement swapping does not entail nonlocal influences", there is direct and immediate disagreement.

The usual standard for Interpretations is that they do not conflict with generally accepted experiments, nor do they make predictions that conflict with QM theory. This does both.

 

[Morbert]

I am not pushing an interpretation. I am comparing Barandes' interpretation to accepted experimental fact as presented by Nobel level teams. With his assertion that "entanglement swapping does not entail nonlocal influences", there is direct and immediate disagreement.

The usual standard for Interpretations is that they do not conflict with generally accepted experiments, nor do they make predictions that conflict with QM theory. This does both.

To avoid retreading the recently closed thread on entanglement swapping, I'm not going to pursue this more generic line of debate. I'll only restate my position, which is that all established interpretations agree with experiment.

I'd be happy to discuss the particulars of the reformulation [edit] as they apply to entanglement swapping [/edit] , which was my motivation for starting this thread.

 

[DrChinese]

The reformulation agrees with all experimental results. You might have reasons to prefer your own interpretation, but failure to agree with experiments is not a valid reason. All interpretations agree with experiment.

I am not asserting an Interpretation. I am pointing out - as I have done in post after post above: The Barandes interpretation makes a specific prediction that is contradicted by experiment. Remote decisions can be detected by Bob without communicating that information from other channels. See #24, where there is an absolute change in what Bob sees. This is experimental fact, and you have yet to dispute this.

You said that per Barandes: "The causal relations that show Alice Charles and Bob do not causally influence one another." So either Barandes does not agree with the predictions of QM, or what he presents is not a proper representation of his Interpretation.

---

And you might want to re-read what you say above. "Failure to agree with experiments is NOT a valid reason" to prefer an interpretation, true enough. But it is instead a good reason to drop that preference. And the statement that "All interpretations agree with experiment" is blatantly wrong. Bell's Theorem would have no significance if that were true. We now know that Local Realistic interpretations are not viable, because they make predictions at odds with experiment. It is generally accepted here that Bell tests (and many other experiments) are by definition* demonstrations of quantum nonlocality.


*By the definition we follow in this subforum, at least.

 

[DrChinese]

I'd be happy to discuss the particulars of the reformulation [edit] as they apply to entanglement swapping [/edit] , which was my motivation for starting this thread.

Well, I used your example; but I don't think you like where it led.

I have said everything I can say on the thread subject, so I will bow out to make sure others can weigh in.

 

[PeterDonis]

I said we need to agree on what the interpretation asserts.

We agree that the interpretation defines "no influence" in a certain way.

That agreement is worth very little, however, since we do not agree on whether adopting that definition of "no influence" is reasonable.

You appear to be trying to get agreement on the latter, not the former. That's not going to happen.

 

[Morbert]

I am not asserting an Interpretation. I am pointing out - as I have done in post after post above: The Barandes interpretation makes a specific prediction that is contradicted by experiment. Remote decisions can be detected by Bob without communicating that information from other channels. See #24, where there is an absolute change in what Bob sees. This is experimental fact, and you have yet to dispute this.

There is an exact correspondence between Barandes's reformulation and quantum theory. Like all established interpretations, it agrees with experiment: It agrees with all correlations in the data produced by Alice Bob and Charles.

 

[PeterDonis]

Remote decisions can be detected by Bob without communicating that information from other channels.

You said Bob needs timestamp information from others to make this detection. That's information from other channels.

Taking your statement in the above quote literally would appear to violate the no signaling theorem. But I don't think you meant it quite that literally.

 

[Fra]

The directed conditional probability distributions are nomological.

Yes, could sop there and we can simply pushed the question into the corner, why these nomological distributions?

If we stop there, did that make anyone any wiser? Ok we got rid of the hilbert stuff, but instead got a mysterious nomological total transition matrix for the whole system that is just there for no particular reason? I think there must be a bigger ambition that simply a reformulation.

What defines the particular form of such constraint for a particular physical system? If this question is not easier to handle in this picture than in he hilbert picture, what have we gained?

My personal opinon is that it IS easier and more intutive.. But this still seems beyond the scope of the correspondence per see, so we can distinguish between the correspondence itself, what it means and the opinions on what god it might do.

/Fredrik

 

[Morbert]

We agree that the interpretation defines "no influence" in a certain way.

That agreement is worth very little, however, since we do not agree on whether adopting that definition of "no influence" is reasonable.

You appear to be trying to get agreement on the latter, not the former. That's not going to happen.

No, I'm looking for agreement that, under reformulation of quantum theory and the account of microphysical causation presented by Barandes, entanglement swapping experiments obey his principle of causal locality. DrChinese believes Barandes's interpretation makes predictions that contradict experiment, which means he does not actually understand Barandes's reformulation. So before any discussion can be had about reasonableness, it must be understood what the reformulation actually entails.

 

[DrChinese]

You said Bob needs timestamp information from others to make this detection. That's information from other channels.

Taking your statement in the above quote literally would appear to violate the no signaling theorem. But I don't think you meant it quite that literally.

The timestamp information itself is only used to indicate a 4-fold event. It does not contain any information about whether a swap occurred or not.

Agreed that there is no FTL signaling, as the timestamp info must be transmitted at light speed via classical channel.

It’s still interesting, because all of the transmitted information can be rolled into a single bit to be sent. The observer transmitting it has no way to know whether a swap even occurred. Just that a qualifying 4-fold event occurred for Bob to analyze.

Of course, suitable BSM/SSM events occur randomly and on the order of a few per second in today’s world. It’s something akin to teleporting an unknown quantum state, except that it has a deterministic character. Since it allows for “decoding” of a remote decision.

 

[martinbn]

It’s something akin to teleporting an unknown quantum state, except that it has a deterministic character. Since it allows for “decoding” of a remote decision.

Swapping is teleportation. Teleportation of a mixed state.

 

[PeterDonis]

I'm looking for agreement that, under reformulation of quantum theory and the account of microphysical causation presented by Barandes, entanglement swapping experiments obey his principle of causal locality.

Isn't this true by definition? I mean "his principle of causal locality" is defined so that entanglement swapping experiments meet it. What's the point of belaboring this?

DrChinese believes Barandes's interpretation makes predictions that contradict experiment

Which is a different question from the one implicit in what I quoted from you at the start of this post. The relevant question here is whether Barandes's interpretation does in fact make all of the same predictions as standard QM. That has nothing whatever to do with whether Barandes's interpretation meets Barandes's own definition of "causal locality" (even leaving aside the fact that, as noted above, belaboring the latter point is pointless).

 

[PeterDonis]

Just that a qualifying 4-fold event occurred for Bob to analyze.

But to confirm that a swap occurred, Bob has to know Alice's measurement result as well as his own. That requires transmitting information from other channels.

 

[Morbert]

Isn't this true by definition? I mean "his principle of causal locality" is defined so that entanglement swapping experiments meet it. What's the point of belaboring this?

@DrChinese Do you agree that entanglement swapping experiments, when analyzed with Barandes's reformulation, satisfies Barandes's principle of causal locality, whether or not you agree with his microphysical theory of causation?

Which is a different question from the one implicit in what I quoted from you at the start of this post. The relevant question here is whether Barandes's interpretation does in fact make all of the same predictions as standard QM. That has nothing whatever to do with whether Barandes's interpretation meets Barandes's own definition of "causal locality" (even leaving aside the fact that, as noted above, belaboring the latter point is pointless).

Both questions are absolutely relevant.

 

[DrChinese]

But to confirm that a swap occurred, Bob has to know Alice's measurement result as well as his own. That requires transmitting information from other channels.

In my particular example (post #2), Alice always has a |0> result. But yes, more generally that would be true as you say. One way or another, Bob must find out Alice's result.

Alternatively, Alice could simply be co-located with Bob without a loss of functionality. Then he would know her result.

 

[DrChinese]

@DrChinese Do you agree that entanglement swapping experiments, when analyzed with Barandes's reformulation, satisfies Barandes's principle of causal locality, whether or not you agree with his microphysical theory of causation?

I agree with @PeterDonis, Barandes' causal locality definition not surprisingly fits with his interpretation. Who would expect otherwise?

I also say it is nothing more than a restatement of an assumption of signal locality. We already knew that nothing Alice does results in any visible changes at Bob's end. If it did, you could perform FTL signaling. That is essentially the same thing as Barandes' causal locality.

 

[Morbert]

I agree with @PeterDonis, Barandes' causal locality definition not surprisingly fits with his interpretation. Who would expect otherwise?

Great! Previously you have presented entanglement swapping as a foil for some interpretations that otherwise readily handle conventional scenarios where two particles are entangled via a past local interaction. I'm glad you agree that, on its own terms, this interpretation frames entanglement swapping as a causally local process, even if you take general issue with this interpretation.

I also say it is nothing more than a restatement of an assumption of signal locality. We already knew that nothing Alice does results in any visible changes at Bob's end. If it did, you could perform FTL signaling. That is essentially the same thing as Barandes' causal locality.

Barandes remarks that the relevant calculations he performs to resolve causality questions are closely related to no-communication theorem. But I will answer this charge in the other thread as it is a more general charge not related to entanglement swapping.

 

[javisot]

There is an exact correspondence between Barandes's reformulation and quantum theory. Like all established interpretations, it agrees with experiment: It agrees with all correlations in the data produced by Alice Bob and Charles.

So, QM(Barandes)=GR?

Or, by definition, is it just as irreconcilable as nonlocal QM like Copenhagen?

QM(Copenhagen)=QM(Barandes)≠GR?

 

[javisot]

I'm glad you agree that, on its own terms, this interpretation frames entanglement swapping as a causally local process, even if you take general issue with this interpretation.

That the swap of (2&3) are considered strictly local processes does not restrict the existence of non-local consequences, (1&4).

 

[PeterDonis]

@DrChinese Do you agree that entanglement swapping experiments, when analyzed with Barandes's reformulation, satisfies Barandes's principle of causal locality, whether or not you agree with his microphysical theory of causation?Both questions are absolutely relevant.

I cannot understand why, because I cannot understand why it's even a question. You're basically asking whether Barandes agrees with himself. Um, what?

 

[PeterDonis]

In my particular example (post #2), Alice always has a |0> result.

Which means that, while Bob technically doesn't require any information from Alice in this special case, it's only because there is no information from Alice to be had anyway. But that's not the kind of case that creates interpretation problems, precisely because Alice's result is fixed. It's the cases where Alice's result is not fixed, any more than Bob's, that raise interpretation challenges.

 

[Fra]

If it is global then it is nonlocal (at least in weak sense).

Yes, in the obvious sense, ANY global constraint, gets is "nonlocal" in the sense that it is common to all spacetime.

Similarly ANY objective constraint is like an objective beable in the sense that it represents observer/context equivalence.

This is exactly the "generic problem" with the nature of law, nature of spacetime and nature of observer equivalence. When thinking about "causation" it seems equally valid to say that initial conditions "cause" the future, as it is to say that the dynamical law, "cause" the future. The distinction between initial conditions and laws from perspective of causation seem ambigous.

And it is why I think trying to reduce "dynamical" into caually local stochastic is progress, but Barandes only takes a small step and we still need to "interpret" the new constraint of time dependent transition matrix; it is beyond the correspondence.

/Fredrik