A Consistent Histories and Locality

[PeterDonis]

Different frameworks offer complementary descriptions of the same reality.

That seems to contradict what Griffiths says about the "principle of uniticity" being violated by QM, because "complementary descriptions of the same reality" seems like the principle of uniticity is not violated.

 

[gentzen]

Different frameworks offer complementary descriptions of the same reality.

What do you mean by „descriptions of the same reality“? Those are your words. Some frameworks are unrelated to physical reality. Computations using those frameworks won‘t produce contradictions, but they are useless nevertheless. As Roland Omnes quipped: They belong in the waste-paper basket.

 

[javisot20]

"descriptions of the same reality" = descriptions/correspondences capable of explaining with the same precision the set of experimental data that make up QM

https://en.wikipedia.org/wiki/Penrose_interpretation, this is an example of incorrect interpretation because it does not achieve the objective

 

[Morbert]

What do you mean by „descriptions of the same reality“? Those are your words. Some frameworks are unrelated to physical reality. Computations using those frameworks won‘t produce contradictions, but they are useless nevertheless. As Roland Omnes quipped: They belong in the waste-paper basket.

I mean very plainly that they are descriptions of the same reality. From Griffith's Consistent Quantum Theory textbook

In order to avoid the mistake of supposing that incompatible descriptions are mutually exclusive, it is helpful to think of them as referring to different aspects of a quantum system

From https://arxiv.org/abs/1704.08725

In classical physics it is usually the case that only a single sample space need be considered when discussing a particular physical problem, and so its choice needs no emphasis, and it may not even be mentioned. In quantum physics this is no longer the case: many mistakes and numerous paradoxes, e.g., the Kochen-Specker Paradox (see Sec. V E), are based on not paying sufficient attention to the sample space in circumstances in which several distinct and incompatible sample spaces may seem like reasonable choices. For this reason it is convenient to use a special term, framework, to indicate the sample space or the corresponding event algebra which is under discussion.

Any system, quantum or classical, can be described by many different sample spaces and event algebras. For a classical system, we can identify a maximally refined sample space for which all other sample spaces are coarse grainings. We cannot do this for a quantum system, but the different samples spaces describing a quantum system are still describing that system.

Re/ Omnes: I suspect I know the context of his statement but to be sure, can you give me the source?

 

[gentzen]

I mean very plainly that they are descriptions of the same reality.

Then your statement is simply wrong, and no amount of quotes from Griffiths which don‘t use the word „reality“ can fix this.
Edit: Feel free to defend your statement in your own words as your own reasoning. I am simply opposed to use it to describe Griffiths‘ position.

Re/ Omnes: I suspect I know the context of his statement but to be sure, can you give me the source?

It is from his book „quantum philosophy“, where he addresses the objection that the existence of incompatible frameworks would undermine CH.

 

[Morbert]

Then your statement is simply wrong, and no amount of quotes from Griffiths which don‘t use the word „reality“ can fix this.

Why do you think it is wrong? How, for example, do you interpret the following from Griffiths?

https://arxiv.org/abs/quant-ph/9708028

There are many posable consistent families or frameworks which can be used to describe the same quantum system, and the choice of which of these to employ is a choice made by the physicist based upon pragmatic considerations, namely the type of physical problem he is trying to study or the question he wants to answer.

It is from his book „quantum philosophy“, where he addresses the objection that the existence of incompatible frameworks would undermine CH.

i) Remember that Omnes's position is different from Griffiths. Omnes understands CH as offering "trustworthy" logic for quantum systems. Griffiths more ambitiously presents CH as a realistic interpretation.
ii) His waste-paper basket comment is about frameworks not relevant to what a physicist is specifically interested in. Different frameworks will be useful/useless depending on what the physicist is investigating. [edit to add] There may be some frameworks that are useless for all experiments (e.g. ones with macroscopic quantum superpositions) but they still pertain to the same system.

 

[gentzen]

Why do you think it is wrong? How, for example, do you interpret the following from Griffiths?

The question is how to interpret your words. I have no trouble interpreting Griffiths words in various defensible ways. I don‘t see how to do that with your words, and PeterDonis seems to have a similar problem.

You don’t seem to see the difference between the concrete (physical) reality and an abstract quantum system.

 

[Morbert]

The question is how to interpret your words. I have no trouble interpreting Griffiths words in various defensible ways. I don‘t see how to do that with your words, and PeterDonis seems to have a similar problem.

You don’t seem to see the difference between the concrete (physical) reality and an abstract quantum system.

I'm asking you to point out where my reading of Griffiths is wrong.

 

[gentzen]

I'm asking you to point out where my reading of Griffiths is wrong.

When Griffiths is talking about different aspects of a quantum system, I can interpret quantum system just like in other discussions I had here, for example with vanhees71 when we talked about the polarization of silver atoms leaving an „oven“. Here a silver atom „prepared“ in this way (and especially its polarization) is interpreted as a quantum system.

This sort of interpretation would feel very forced for your words „same reality“.

 

[Morbert]

When Griffiths is talking about different aspects of a quantum system, I can interpret quantum system just like in other discussions I had here, for example with vanhees71 when we talked about the polarization of silver atoms leaving an „oven“. Here a silver atom „prepared“ in this way (and especially its polarization) is interpreted as a quantum system.

This sort of interpretation would feel very forced for your words „same reality“.

Assuming you are referring to the Stern-Gerlach experiment: Griffiths, in the same paper I referenced re/ his ontology

Choosing a description is choosing what to talk about, and what physicists choose to talk about has very little (direct) influence on what actually goes on in the world. Shall we discuss the location of Jupiter’s center of mass, or its rate of rotation? Either is possible, and neither has the slightest influence on the behavior of Jupiter. What about a silver atom approaching a Stern-Gerlach apparatus? Shall we discuss its (approximate) location or the value of Sx or the value of Sz ? Any one of these is possible, and the single framework rule allows location to be combined with Sx, or with Sz . But not with both, since it is impossible to put both Sx and Sz , at least when referring to a single particle at a particular time, in the same framework. In this case, no less than for Jupiter, the physicist’s choice of framework has not the slightest influence on the silver atom

It's clear here that Griffith believes CH can offer a realistic description of the silver atom. It's also clear he believes the multiple frameworks possible when describing the silver atom are different descriptions of the same reality (the silver atom) and not different, mutually exclusive versions of reality.

 

[PeterDonis]

we can identify a maximally refined sample space for which all other sample spaces are coarse grainings.

Yes, that's the "principle of uniticity" that QM violates.

We cannot do this for a quantum system

Yes.

the different samples spaces describing a quantum system are still describing that system.

None of them are describing all of the measurements that can be made on that system. None of them even describe all the measurements that are made on that system, in a case like entanglement swapping. If one of them did, QM would not violate the "principle of uniticity".

 

[Morbert]

None of them are describing all of the measurements that can be made on that system.

Yes.

None of them even describe all the measurements that are made on that system, in a case like entanglement swapping. If one of them did, QM would not violate the "principle of uniticity".

Any sequence of measurements that are actually carried out will be describable by a single framework (albeit not a unique one). This is because the pointer states recording the measurement results will guarantee decoherence.

 

[PeterDonis]

Any sequence of measurements that are actually carried out will be describable by a single framework

That's not what Griffiths appears to be saying. If it were true, the principle of uniticity would not be violated by QM. But Griffiths says it is.

 

[gentzen]

This is because the pointer states recording the measurement results will guarantee decoherence.

Well, for the existing entanglement swapping experiments, each measurement is done on a different pair of photons. You would probably model those measurements by a tensor product, because the different pairs are effectively distinguishable. But for repeated measurements on the same particle(s), your explanation is fine.

That your answer doesn‘t address PeterDonis‘ and my objections is a different topic.

 

[Morbert]

That's not what Griffiths appears to be saying. If it were true, the principle of uniticity would not be violated by QM. But Griffiths says it is.

In case there are crossed wires:

i) No single framework can describe all measurable properties of a quantum system. This is a violation of the principle of unicity.

ii) No lab protocol can measure all measurable properties of a quantum system.

iii) Even though no single framework can describe all measurable properties of a system, any protocol that is actually executed can be described by a single framework.

A simple example:

i) The spin-x and spin-y properties of a particle cannot be described by a single framework.

ii) No lab protocol can measure both the spin-x and spin-y properties of a particle at the same time.

iii) The protocol to measure the spin-x property of a particle can be described by a single framework. The protocol to measure the spin-y property of a particle can be described a single (different) framework.

 

[Morbert]

Well, for the existing entanglement swapping experiments, each measurement is done on a different pair of photons. You would probably model those measurements by a tensor product, because the different pairs are effectively distinguishable. But for repeated measurements on the same particle(s), your explanation is fine.

My explanation is fine for entanglement swapping experiments too. Histories as chains of projectors is readily applicable to entanglement swapping experiments.

That your answer doesn‘t address PeterDonis‘

My answer did.

 

[DrChinese]

1. Yes, and so below I've constructed histories for the actual $\Phi^+, \Phi^-, \mathrm{fail}$ scenarios. Hopefully it will not be too confusing and we can revisit the quantum state of the experiment if need be.

2. I am including degrees of freedom of the labs so that the experiment can be approximated by a pure state and unitary time evolution. This simplification is common but in the end it will only be relevant if you object to my claim that the histories I construct below are in fact decoherent.

The quantum state is not interpreted as real, and instead only yields probabilities for real alternatives. So yes in reality at II the polarization would be known to the experimenter.

3. Let's now construct a set of histories relevant to describing this experiment. For expediency I will only describe histories for which the probability is > 0. We can place the projector $\left[\psi^-_{12}\right]$ at time $I$ as the first element of our histories. To describe the measurement at $II$, we will add a branch just before, giving us$$\left[\psi^-_{12}\right]\odot\begin{cases}\left[h_\omega\right]_1&\odot&\left[1\right]_{A}\\\left[v_\omega\right]_1&\odot&\left[0\right]_{A}&\end{cases}$$Along the upper branch, the measurement result 1 reveals a horizontal polarization (relative to the chosen aspect), along the lower branch, the measurement result 0 reveals a vertical polarization. We will follow the upper branch, with the understanding that the lower branch has a similar structure. The next relevant event is at $III$, the creation of the 34 pair
$$\left[\psi^-_{12}\right]\odot\left[h_\omega\right]_1\odot\left[1\right]_{A}\odot\left[\psi^-\right]_{34}$$Before the BSM at $IV$ we can describe the polarization of photon 4 with the branch$$\left[\psi^-_{12}\right]\odot\left[h_\omega\right]_1\odot\left[1\right]_{A}\odot\left[\psi^-\right]_{34}\odot\begin{cases}
\left[h_\omega\right]_4\\
\left[v_\omega\right]_4
\end{cases}$$Then, at $IV$, we have the BSM. The $v_\omega$ polarization of 4 will be correlated with a failed BSM, so we have a branching of the form
$$\left[\psi^-_{12}\right]\odot\left[h_\omega\right]_1\odot\left[1\right]_{A}\odot\left[\psi^-\right]_{34}\odot\begin{cases}
\left[h_\omega\right]_4&\odot&\begin{cases}\left[
\Phi^+\lor\Phi^-\right]_\mathrm{BSM}\\
\left[\mathrm{fail}\right]_\mathrm{BSM}\end{cases}\\
\left[v_\omega\right]_4&\odot&\left[\mathrm{fail}\right]_\mathrm{BSM}
\end{cases}$$Following the upper branch again and extending it to the measurement of 4, we have a completed history$$\left[\psi^-_{12}\right]\odot\left[h_\omega\right]_1\odot\left[1\right]_{A}\odot
\left[\psi^-\right]_{34}\odot\left[h_\omega\right]_4\odot\left[\Phi^+\lor\Phi^-\right]_\mathrm{BSM}\odot\left[1\right]_B
$$Each of these histories $C$ has the probability of occurring $p(C) = \mathrm{tr}C^\dagger\left[\Psi_0\right] C$ and we can user them to compute the relevant conditional probabilities that correlate a successful BSM with certain correlation between the polarizations of 1 and 4.

4. Unlike a scenario where the BSM instantly influences photon 4, and retroactively influences photon 1 to entangle them, these histories describe a scenario where a successful BSM reveals a correlation between the polarization of 1 and 4.

1. The experiment only considers the Φ- cases.

2. We start with just one entangled pair, and you adding the extraneous stuff serves no purpose I can see. So I ask again: After photon 1 is measured, do we know the polarization of photon 2 or not? Because according to the usual local concepts, its polarization on the L/R basis should be known/certain and its polarization on the V/H basis should be completely unknown/uncertain. Well according to CH, is it?

You seem to agree with the L/R portion of my statement. But you model the R/L portion as being a superposition of H and V (your upper/lower paths) in the 3. section. But now you run afoul of the CH concept of frameworks: you have both the L/R and V/H frameworks modeled together. You previously pointed out (as Griffiths does): "The spin-x and spin-y properties of a particle cannot be described by a single framework." And "No lab protocol can measure both the spin-x and spin-y properties of a particle at the same time." And yet, here you are describing both the L/R and H/V properties of a photon at the same time.

I would state that there is no correlation whatsoever between the L/R and H/V and properties of any photon, since they are mutually unbiased. Similarly, I would state that there is no correlation whatsoever between the L/R or H/V properties of a photon in a superposition, with the L/R or H/V properties of a different photon in a superposition - UNLESS these photons are entangled. Coming from different sources, they can't start out that way. How can you object to any element of this paragraph? This is basic.

3. My objections are not addressed, and there are no answers to the points I made in my previous commets/posts. Specifically, once I know the photon 1 is (say) |L>, which tells us the polarization of photon 2 by inference; and then it is measured on the "inconsistent" basis V/H: How does any of this bring about or otherwise lead us to the correlation of photon 4 on yet another "inconsistent" basis L/R (since photon 3 was measured on the V/H basis).

4. There is no correlation whatsoever between the 1 and 4 photons UNLESS a swap occurs. You completely and totally skip over the critical point of this scientific experiment, which is: For the swap to occur, there must be physical overlap at the BSM. That is controllable by the experimenter. According to your logic, that shouldn't matter. The results say that the choice of the experimenter creates a correlation that does not otherwise exist.

---

And as I am fond of adding: The speculative concept of a "hidden" relationship between photons 1 & 4 is completely contrary to the concept of Monogamy of Entanglement. Where is this addressed by CH? Or is MoE wrong? I would point out that MoE theory is newer than CH.

And as I also keep pointing out: The authors of these papers say precisely the opposite of your claim of there being a correlation waiting to be "revealed" (because the relationship is created by the BSM, not revealed):

Kaltenbach et al: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4."

Ma et al: "This [BSM] effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations)."

Megadish et al: "This [experiment] is a manifestation of the non-locality of quantum
mechanics not only in space, but also in time."

 

[Morbert]

1. The experiment only considers the Φ- cases.

2. We start with just one entangled pair, and you adding the extraneous stuff serves no purpose I can see. So I ask again: After photon 1 is measured, do we know the polarization of photon 2 or not? Because according to the usual local concepts, its polarization on the L/R basis should be known/certain and its polarization on the V/H basis should be completely unknown/uncertain. Well according to CH, is it?

You seem to agree with the L/R portion of my statement. But you model the R/L portion as being a superposition of H and V (your upper/lower paths) in the 3. section. But now you run afoul of the CH concept of frameworks: you have both the L/R and V/H frameworks modeled together. You previously pointed out (as Griffiths does): "The spin-x and spin-y properties of a particle cannot be described by a single framework." And "No lab protocol can measure both the spin-x and spin-y properties of a particle at the same time." And yet, here you are describing both the L/R and H/V properties of a photon at the same time.

I would state that there is no correlation whatsoever between the L/R and H/V and properties of any photon, since they are mutually unbiased. Similarly, I would state that there is no correlation whatsoever between the L/R or H/V properties of a photon in a superposition, with the L/R or H/V properties of a different photon in a superposition - UNLESS these photons are entangled. Coming from different sources, they can't start out that way. How can you object to any element of this paragraph? This is basic.

3. My objections are not addressed, and there are no answers to the points I made in my previous commets/posts. Specifically, once I know the photon 1 is (say) |L>, which tells us the polarization of photon 2 by inference; and then it is measured on the "inconsistent" basis V/H: How does any of this bring about or otherwise lead us to the correlation of photon 4 on yet another "inconsistent" basis L/R (since photon 3 was measured on the V/H basis).

4. There is no correlation whatsoever between the 1 and 4 photons UNLESS a swap occurs. You completely and totally skip over the critical point of this scientific experiment, which is: For the swap to occur, there must be physical overlap at the BSM. That is controllable by the experimenter. According to your logic, that shouldn't matter. The results say that the choice of the experimenter creates a correlation that does not otherwise exist.

2. If the result of the linear polarization measurement of photon 1 is H, then this reveals the linear polarization of photon 2 is V, and vice versa, as the 1,2 photons were prepared in the $\psi^-$ state.

An important point about the CH notation: Different branches represent mutually exclusive alternatives, not superpositions. Histories here are represented by chains of projectors. More specifically, the square brackets are time-evolved projectors (e.g. $\left[H\right]$ = $U(t,t')|H\rangle\langle H | U(t',t)$ and $\odot$ is just $\otimes$. Griffiths uses $\odot$ to demarcate projectors at different times. As such, the histories I wrote above only reference the linear polarization of photons 1 and 4, and make no reference to the circular polarization of any photon. If we instead measure the circular polarization of 4, we can build the branching$$\left[\psi^-_{12}\right]\odot\left[h_\omega\right]_1\odot\left[1\right]_{A}\odot\left[\psi^-\right]_{34}\odot\begin{cases}
\left[R\right]_4\\
\left[L\right]_4\end{cases}$$The mutually unbiased nature of these bases means a measurement of the linear polarization of 1 will tell us nothing about the circular polarization of 4, whether or not a BSM is carried out.

3. I'm not sure I understand this. If a BSM is carried out, then photon 2 is not measured in any basis. Instead the 2,3 photons are measured in a Bell basis. If photons 2,3 are measured in some separable state basis like {HH, VV} described by Ma, then the measurement result of 1 reveals nothing about 4.

4. I was following the Megedish convention of a successful BSM or a failed BSM (due to temporal distinguishability). We could just as readily, say, model a BSM or separable state measurement of 2,3 with a quantum random number generator like Ma does.

Ultimately, what CH allows us to say is i) for any given run, a measurement of photon 1 and a successful BSM will reveal the associated property of photon 4. ii) For all runs, there will be a correlation between a successful BSM of 2,3 and Bell-inequality-violating correlations between measurements on 1 and 4.

And as I am fond of adding: The speculative concept of a "hidden" relationship between photons 1 & 4 is completely contrary to the concept of Monogamy of Entanglement. Where is this addressed by CH? Or is MoE wrong? I would point out that MoE theory is newer than CH.

As CH is an interpretation of standard QM (and QFT) without any extension of the theory, it doesn't and can't contradict any feature of the theory. CH is 100% consistent with MoE. [edit] For example, CH never permits us to make a statement like: "Photon 1 is maximally entangled with photon 2, and photon 1 is also maximally entangled with photon 4"

I think the quotes by Ma et al would bring us back into a general discussion of nonlocality. For the time being I'll try to focus on CH as it applies to entanglement swapping experiments or other experiments involving Bell-inequality-violating correlations.

 

[martinbn]

4. There is no correlation whatsoever between the 1 and 4 photons UNLESS a swap occurs. You completely and totally skip over the critical point of this scientific experiment, which is: For the swap to occur, there must be physical overlap at the BSM. That is controllable by the experimenter. According to your logic, that shouldn't matter. The results say that the choice of the experimenter creates a correlation that does not otherwise exist.

I know that this is the point of disagreement and we have discussed it many times. But this, as stated, is not correct.

The pair 1&4 has a density matrix, which does not change no matter what is done or not done on the reset of the system, the pair 2&3. This density matrix gives the probability of the possible outcomes on any possible measurement done on 1&4. Which means that in each series of trials there will be a subset of the full set of results that have outcomes of the corresponding Bell state of 1&4. If Victor has been measuring 2&3 in the Bell state basis the subset will be precisely those trials on which Victor got $|\Phi^-\rangle$ (I might be using the wrong notation) as a result. If Victor has being doing measurements in a different basis or no measurements at all, the full set will not show the same correlations, but there will be a subset with those correlations.

The fact that the probabilities for outcomes of measurements on 1&4 are independent of what is done on 2&3 shows that there is no action at a distance. At least to me this is the only possible conclusion. Clearly many people think otherwise. Why? I still don't know! Of course it is a possibility but I don't see any indication for it from the theory nor the experiments. They only confirm the theory.

 

[Morbert]

CH proponents in general don't like to frame QM as concerning the statistics of ensembles. E.g.

Understanding Quantum Mechanics

Some people believe, on the contrary, that the probabilistic character of quantum physics is best expressed if one considers conceptually infinite ensembles of identical systems, as in statistical mechanics. This approach, however, must be excluded when one intends to include classical physics within the quantum framework. In that case, considering an infinite collection of copies of the solar system would certainly then be odd

Probabilities and Quantum Reality: Are There Correlata?

The theory should describe individual systems — not just ensembles

The theory should describe individual systems because the world contains individual systems. . . and the theory ought to describe the world and its subsystems. . . In a nondeterministic world probability has nothing to do with incomplete knowledge, and ought not to require an ensemble of systems for its interpretation. . . The fact that physics cannot make deterministic predictions about individual systems does not excuse us from pursuing the goal of being able to describe them as they currently are.

On these five desiderata I agree two hundred percent with Mermin. In some cases I may be giving his words a slightly different interpretation from what he intended, but at least in broad outline and probably in most of the details, I could not agree with him more, even though I could not possibly have expressed it with such clarity and enthusiasm.

If statistical statements are insisted on, then we would say a history $C$ represents a subensemble of experimental runs where measurement results asserted by that history occur. The relative frequency of all events asserted by the history occurring is $\mathrm{tr}C^\dagger\rho C$.

Over the full ensemble, i.e. over all histories, there will be no Bell-inequality-violating correlations between 1 and 4 measurement outcomes.

Over all histories where a BSM with possible results $\{\left[\phi^+\right]_{23},\left[\phi^-\right]_{23}, I - \left[\phi^+ \lor \phi^-\right]_{23}\}$ occurs, there will be no Bell-inequality-violating correlations between 1 and 4 measurement outcomes.

Over all histories where a BSM with the result $\left[\phi^-\right]_{23}$ occurs, there will be Bell-inequality-violating correlations between 1 and 4 measurement outcomes

 

[PeterDonis]

the probabilities for outcomes of measurements on 1&4 are independent of what is done on 2&3

One has to be very careful phrasing this. As you state it, it could be true or it could be false, depending on how your ambiguous wording is interpreted.

It is impossible to send signals to observers measuring photons 1 & 4 by choosing whether or not to allow a swap operation to take place on photons 2 & 3 at the BSM. In that sense your statement is true.

However, if you do two experiments, one in which the swap operation is done and one in which it is not, and you hand the two sets of data (the measurement results by run for all four photons) to someone, without telling them which set is the "swap" set and which is the "no swap" set, they can tell which is which by looking at the photon 1 & 4 correlations in each subset picked out by the four possible combinations of photon 2 & 3 results. In the "swap" set, there will photon 1 & 4 correlations in each subset, and those correlations can violate the Bell inequalities, whereas in the "no swap" set there will be no correlations even by subset. In that sense your statement is false.

 

[martinbn]

One has to be very careful phrasing this. As you state it, it could be true or it could be false, depending on how your ambiguous wording is interpreted.

It is impossible to send signals to observers measuring photons 1 & 4 by choosing whether or not to allow a swap operation to take place on photons 2 & 3 at the BSM. In that sense your statement is true.

However, if you do two experiments, one in which the swap operation is done and one in which it is not, and you hand the two sets of data (the measurement results by run for all four photons) to someone, without telling them which set is the "swap" set and which is the "no swap" set, they can tell which is which by looking at the photon 1 & 4 correlations in each subset picked out by the four possible combinations of photon 2 & 3 results. In the "swap" set, there will photon 1 & 4 correlations in each subset, and those correlations can violate the Bell inequalities, whereas in the "no swap" set there will be no correlations even by subset. In that sense your statement is false.

My point is that if you give them the two sets of the measurement result only of photons 1&4, then they cannot tell which is which.

 

[PeterDonis]

My point is that if you give them the two sets of the measurement result only of photons 1&4, then they cannot tell which is which.

Yes, but why would you do that? Photons 2 & 3 are part of the total system; photon 2 starts out entangled with photon 1, and photon 3 starts out entangled with photon 4, and those entanglements are stipulated in the preparation of the system. If you leave out those results, you're leaving out relevant information.

It is of course true that a reduced density matrix for a quantum system that traces over other systems with which that system might be entangled, will not show correlations with those other systems. That's a simple mathematical fact that is stated in pretty much every QM textbook. But that doesn't mean those correlations do not exist, or that they are not physically meaningful.

 

[martinbn]

Yes, but why would you do that? Photons 2 & 3 are part of the total system; photon 2 starts out entangled with photon 1, and photon 3 starts out entangled with photon 4, and those entanglements are stipulated in the preparation of the system. If you leave out those results, you're leaving out relevant information.

It is of course true that a reduced density matrix for a quantum system that traces over other systems with which that system might be entangled, will not show correlations with those other systems. That's a simple mathematical fact that is stated in pretty much every QM textbook. But that doesn't mean those correlations do not exist, or that they are not physically meaningful.

But the claim is that measurment on 2&3 affects 1&4. What is the meaning of that if it cannot be observed?

 

[PeterDonis]

the claim is that measurment on 2&3 affects 1&4. What is the meaning of that if it cannot be observed?

It can be observed: when you look at the presence or absence of correlations in the 1&4 subsets corresponding to the four possible combinations of 2&3 results, depending on whether the experimenter made a choice to have a swap take place, you are observing that the experimenter's choice of whether or not to make a swap at 2&3 affects 1&4. In any other branch of science, that would be a commonplace claim: experimenter makes an intervention and the presence vs. the absence of that intervention shows up in a predictable way in the data. Why it somehow becomes problematic when we're talking about QM and entangled systems is not clear to me.

 

[martinbn]

It can be observed: when you look at the presence or absence of correlations in the 1&4 subsets corresponding to the four possible combinations of 2&3 results, depending on whether the experimenter made a choice to have a swap take place, you are observing that the experimenter's choice of whether or not to make a swap at 2&3 affects 1&4. In any other branch of science, that would be a commonplace claim: experimenter makes an intervention and the presence vs. the absence of that intervention shows up in a predictable way in the data. Why it somehow becomes problematic when we're talking about QM and entangled systems is not clear to me.

I don't understand. If you don't make a BMS on 2&3 there is still going to be for subsets of the data for 1&4 with those correlations. We may not be able to tell which trials to look at but they are there. So I still don't understand why in one siruation they were caused by something romote and in the other not? Also in any branch of science if the probabilities of the outcomes do not change base on whether you do something over there or not suggests that the doing or not of something over there is not the cause of the outcoms.

 

[PeterDonis]

If you don't make a BMS on 2&3 there is still going to be for subsets of the data for 1&4 with those correlations.

No, there will not. That's the whole point. If no swap is done on 2&3, then the 1&4 subsets corresponding to each of the four possible combinations of 2&3 results (HH, HV, VH, VV) will not show any correlations, because photons 1&4 are not entangled if no swap is done. But if a swap is done on photons 2&3, then those four subsets of 1&4 results will show correlations, corresponding to the entangled Bell state that is indicated by each of the four 2&3 combinations.

These correlations do not allow signaling, since they are only detectable once the results are all collected and the subsets picked out. But they are a measurable difference between the swap and no swap cases.

 

[martinbn]

No, there will not. That's the whole point. If no swap is done on 2&3, then the 1&4 subsets corresponding to each of the four possible combinations of 2&3 results (HH, HV, VH, VV) will not show any correlations, because photons 1&4 are not entangled if no swap is done. But if a swap is done on photons 2&3, then those four subsets of 1&4 results will show correlations, corresponding to the entangled Bell state that is indicated by each of the four 2&3 combinations.

These correlations do not allow signaling, since they are only detectable once the results are all collected and the subsets picked out. But they are a measurable difference between the swap and no swap cases.

No, i am not saying that the subsets of 1&4 will correspond to the outcomes HH, HV, VH, and VV of the 2&3. I am saying that the data set of the 1&4 can be partitioned into such four subsets.

 

[PeterDonis]

i am not saying that the subsets of 1&4 will correspond to the outcomes HH, HV, VH, and VV of the 2&3.

This makes no sense. Of course you can pick any subsets out of the total 1&4 data set you like, if you don't care what they mean or don't mean. But the subsets that matter, physically, are the ones that correspond to the four possible combinations of 2&3 outcomes--because those are the ones that are predicted by the standard math of QM to show the Bell state correlations if the experimenter chooses to do a swap, but not if the experimenter doesn't. In other words, those are the relevant subsets for testing the theory against experiment.

I am saying that the data set of the 1&4 can be partitioned into such four subsets.

Of course it can. I'm saying the same thing. And I'm also saying that if you partition the 1&4 data that way, then you will see Bell state correlations in each subset if and only if the experimenter chose to do a swap.

If you dispute this, you are disputing both the standard math of QM and the experimental facts.

 

[DrChinese]

So I still don't understand why in one situation they were caused by something remote and in the other not? Also in any branch of science if the probabilities of the outcomes do not change base on whether you do something over there or not suggests that the doing or not of something over there is not the cause of the outcoms.

You have everything backwards. The 4 fold outcomes DO change depending on "whether you do something over there or not"! That's what the point of the experiment is!! To summarize (for the Nth time):

- 4 fold coincidences when experimenter selects SWAP=on (indistinguishable HH or VV for 2&3): Correlation high, as predicted by QM.
- 4 fold coincidences when experimenter selects SWAP=off: (distinguishable HH or VV for 2&3): Correlation negligible, as predicted by QM.

We are simply saying that there is a published experiment by a top team, and we are asking for a description of how an QM interpretation can explain THAT experiment without recourse to nonlocality. Because to the naked eye, the results appear* to clearly demonstrate non-signaling nonlocality.

---

What you are saying is that the 2 fold correlated outcomes don't appear to change because we don't know which bin to place the "subsets" in. So what? That's a different experiment and has nothing to do with entanglement swapping. You can test that with any two sources and get the same results. Imagine you are testing the Earth's gravitational acceleration, 32 ft/sec^2. You let an apple fall 16 feet, but you don't record or report the elapsed time duration. That is essentially what you are describing, half an experiment.


*Of course there are Interpretations that are explicitly nonlocal. Other Interpretations may have features that can explain the apparent nonlocality in some manner that retains locality. Those are the explanations I am requesting.

 

[Morbert]

This makes no sense. Of course you can pick any subsets out of the total 1&4 data set you like, if you don't care what they mean or don't mean. But the subsets that matter, physically, are the ones that correspond to the four possible combinations of 2&3 outcomes--because those are the ones that are predicted by the standard math of QM to show the Bell state correlations if the experimenter chooses to do a swap, but not if the experimenter doesn't. In other words, those are the relevant subsets for testing the theory against experiment.


Of course it can. I'm saying the same thing. And I'm also saying that if you partition the 1&4 data that way, then you will see Bell state correlations in each subset if and only if the experimenter chose to do a swap.

If you dispute this, you are disputing both the standard math of QM and the experimental facts.

The standard math of QM says that Bell-inequality-violating correlations between the appropriate measurements on 1 and 4 will themselves be correlated with outcomes of a BSM on 2 and 3. This is all the math of QM commits us to. It does not commit us to nonlocal influence unless we insist on a hidden variable theory that reproduces these correlations QM predicts.

 

[DrChinese]

The standard math of QM says that Bell-inequality-violating correlations between 1 and 4 will themselves be correlated with outcomes of a BSM on 2 and 3. This is all the math of QM commits us to. It does not commit us to nonlocal influence unless we insist on a hidden variable theory that reproduces these correlations QM predicts.

That is most certainly not true. Any of the following are consistent with Bell:

a) Denial of locality via nonlocal hidden variables interpretations. (Bohmian, etc.)
b) Denial of hidden variables via various "local" interpretations (MWI, Time symmetric, etc.)
c) Denial of both local and realism/hidden variables. (I would personally place standard QM in this bucket.)

We should probably be discussing type c) in order to be consistent with all of the experiments I am aware of. The Heisenberg Uncertainty Principle - and experiments supporting it - strongly imply there is no realism or hidden variables. Swapping experiments strongly imply Einsteinian locality and causality fails.

 

[PeterDonis]

The standard math of QM says that Bell-inequality-violating correlations between the appropriate measurements on 1 and 4 will themselves be correlated with outcomes of a BSM on 2 and 3. This is all the math of QM commits us to. It does not commit us to nonlocal influence

The words "nonlocal influence" do not appear anywhere in my post. I am simply trying to make sure we are all clear about what the standard math of QM and the experimental facts say, because the posts by @martinbn appear to me to indicate that that is not clear to everyone in this thread.

 

[martinbn]

This makes no sense. Of course you can pick any subsets out of the total 1&4 data set you like, if you don't care what they mean or don't mean. But the subsets that matter, physically, are the ones that correspond to the four possible combinations of 2&3 outcomes--because those are the ones that are predicted by the standard math of QM to show the Bell state correlations if the experimenter chooses to do a swap, but not if the experimenter doesn't. In other words, those are the relevant subsets for testing the theory against experiment.


Of course it can. I'm saying the same thing. And I'm also saying that if you partition the 1&4 data that way, then you will see Bell state correlations in each subset if and only if the experimenter chose to do a swap.

If you dispute this, you are disputing both the standard math of QM and the experimental facts.

I don't dispute any of this. May be I don't express myself well. What confuses me is that it seems that we say exactly the same thing except that you and @DrChinese add at the end "Therefore this proves that the measurements on 2&3 affect the outcomes for 1&4". I just don't see it.

 

[martinbn]

The words "nonlocal influence" do not appear anywhere in my post. I am simply trying to make sure we are all clear about what the standard math of QM and the experimental facts say, because the posts by @martinbn appear to me to indicate that that is not clear to everyone in this thread.

I am not questioning QM nor the experimental facts (which confirm QM, so in a theoretical discussion they are not really needed). I am questioning the conclusions @DrChinese makes from these experiments. He does use the words "nonlocal influence". And I was responding to his post that I quoted.

 

[PeterDonis]

What confuses me is that it seems that we say exactly the same thing except that you and @DrChinese add at the end "Therefore this proves that the measurements on 2&3 affect the outcomes for 1&4". I just don't see it.

"Affect" is a very general term. The experimenter's choice of whether or not to do a swap at 2&3 affects whether or not Bell state correlations appear in the measurements on 1&4. That's the experimental fact. What's wrong with using the word "affect" here?

He does use the words "nonlocal influence".

"Nonlocal influence" is a much more specific term than "affect". "Nonlocal influence" is a matter of interpretation; some QM interpretations claim it, some don't. But "affect", as above, is just the experimental fact; whether or not a swap is done at 2&3 makes a difference in whether or not Bell state correlations show up in the measurements on 1&4. If you agree with that last sentence, then I have no issue.

 

[DrChinese]

I am not questioning QM nor the experimental facts (which confirm QM, so in a theoretical discussion they are not really needed). I am questioning the conclusions @DrChinese makes from these experiments. He does use the words "nonlocal influence".

PetersDonis uses “affect” (as a verb). I use the term "nonlocal influence"; the authors of the paper(s) use the terms "quantum steering into the past" and "manifestation of the non-locality of quantum mechanics". These all describe what it looks like to the naked eye, considering that the experimenter can directly (causally?) influence the nature of the correlations observed - regardless of separation in space or time.

But these incredible experiments leave open some paths for interpretation, which is why we discuss this in the Interpretations subforum. My questions are simple: Does anyone know of an interpretations claiming locality that can explain these experiments? If so, I'd like to see the claim explained for the extent experiments. These experiments are roundly ignored by virtually all writers supporting local interpretations (MWI, QBism, Relational, etc.) - other than to merely claim that their (Bell defying) logic applies. These experiments don't need Bell. They are basically extensions of EPR's "elements of reality" updated for modern understanding.

 

[martinbn]

"Affect" is a very general term. The experimenter's choice of whether or not to do a swap at 2&3 affects whether or not Bell state correlations appear in the measurements on 1&4. That's the experimental fact. What's wrong with using the word "affect" here?

"Nonlocal influence" is a much more specific term than "affect". "Nonlocal influence" is a matter of interpretation; some QM interpretations claim it, some don't. But "affect", as above, is just the experimental fact; whether or not a swap is done at 2&3 makes a difference in whether or not Bell state correlations show up in the measurements on 1&4. If you agree with that last sentence, then I have no issue.

Fine, I am ok with the terms. But I don't understand the reasoning behind the experimental fact. So let me ask you this. Everyone agrees that the full set of measurements on 1&4 show no special correlations. And that there is a subset of 25% of them show correlations that violate Bell's inequality no matter what is done on the rest of the system. If you perform the experiment and do a BMS on 2&3 in 25% of the cases the result will be a projection to the phi minus state, and this subset of trials will match the subset of Bell inequality violating results of 1&4. So far I understand. But then the conclusion that if you don't do the BMS on 2&3 will change the outcome at 1&4 is unclear to me. Since we haven't done the BMS how do we know which subset of result at 1&4 to look at? If I understand you correctly you say that we measure the 2&3 in a different basis and look at the partition for the full set into the four subsets according to the four possible outcomes. But why? We cannot say that one of them would have been the subset with the phy minus state had we done the BMS on 2&3.

 

[martinbn]

PetersDonis uses “affect” (as a verb). I use the term "nonlocal influence"; the authors of the paper(s) use the terms "quantum steering into the past" and "manifestation of the non-locality of quantum mechanics". These all describe what it looks like to the naked eye, considering that the experimenter can directly (causally?) influence the nature of the correlations observed - regardless of separation in space or time.

I am not so hung up on the terminology. It just that the "directly (causally) influence" is not obvious to me. Not to mention that as you state it it implies influence in the past.

But these incredible experiments leave open some paths for interpretation, which is why we discuss this in the Interpretations subforum. My questions are simple: Does anyone know of an interpretations claiming locality that can explain these experiments? If so, I'd like to see the claim explained for the extent experiments. These experiments are roundly ignored by virtually all writers supporting local interpretations (MWI, QBism, Relational, etc.) - other than to merely claim that their (Bell defying) logic applies. These experiments don't need Bell. They are basically extensions of EPR's "elements of reality" updated for modern understanding.

I don't think that any interpretation claims that it is local in the sense of Bell inequality violations. The violations are a mathematical consequence of the theory, so no interpretation can avoid it. I think that all the claim is that they are local in the sense of lac of influence at a distance.

 

[Morbert]

PetersDonis uses “affect” (as a verb). I use the term "nonlocal influence"; the authors of the paper(s) use the terms "quantum steering into the past" and "manifestation of the non-locality of quantum mechanics". These all describe what it looks like to the naked eye, considering that the experimenter can directly (causally?) influence the nature of the correlations observed - regardless of separation in space or time.

The authors of the paper show that, given some sample of measurements on 1 and 4 over multiple runs, an experimenter can use a BSM to sort the sample into subsamples that exhibit Bell-inequality-violating correlations. This is different from showing that data in the sample is altered (immediately, retroactively or otherwise) by the BSM.

But these incredible experiments leave open some paths for interpretation, which is why we discuss this in the Interpretations subforum. My questions are simple: Does anyone know of an interpretations claiming locality that can explain these experiments? If so, I'd like to see the claim explained for the extent experiments. These experiments are roundly ignored by virtually all writers supporting local interpretations (MWI, QBism, Relational, etc.) - other than to merely claim that their (Bell defying) logic applies. These experiments don't need Bell. They are basically extensions of EPR's "elements of reality" updated for modern understanding.

Then entanglement swapping experiments are a red herring as your objections to these interpretations persist even in simpler experiments.

E.g. An experimenter can use CH to model an entanglement swapping experiment run with a set of possible histories and a probability space, and they can infer statements about photon 4 from measurements on photon 1 and photons 2,3 without nonlocal causal influence. Your objections to this approach (e.g. around the violation of the principle of unicity and the non-uniqueness of maximally fine-grained probability spaces) would be present even if we were considering a standard EPRB experiment.

Putting it another way: Entanglement swapping experiments show the establishment of entanglement between distant photons that do not have the same source, or never even coexisted. But none of these local interpretations rely on same-source particles to explain entanglement. They rely on a rejection of realism or on non-unicity or on spacetime state realism or on superdeterminism etc.

 

[PeterDonis]

I don't understand the reasoning behind the experimental fact

The experimental fact is what I described in post #71.

Everyone agrees that the full set of measurements on 1&4 show no special correlations.

Meaning, if you take the entire data set, not splitting it up into subsets based on the 2&3 results. Yes.

And that there is a subset of 25% of them show correlations that violate Bell's inequality no matter what is done on the rest of the system.

NO. Go read my post #71 again, carefully.

 

[PeterDonis]

the conclusion that if you don't do the BMS on 2&3 will change the outcome at 1&4 is unclear to me.

"Don't do the BMS" means "don't allow the swap to take place at the BMS". But photons 2&3 go through the BMS and get measured afterwards in all the runs, not just the ones where a swap takes place.

 

[PeterDonis]

Since we haven't done the BMS how do we know which subset of result at 1&4 to look at?

You pick out the four subsets corresponding to the four possible combinations of photon 2&3 measurement results: HH, HV, VH, VV. Those measurement results are there on every run, whether a swap takes place or not.

 

[Morbert]

You pick out the four subsets corresponding to the four possible combinations of photon 2&3 measurement results: HH, HV, VH, VV. Those measurement results are there on every run, whether a swap takes place or not.

I think I see the point of disagreement: We have four subsets HH, HV, VH, VV when no swap occurs. We have four subsets HH', HV', VH', VV' when a swap occurs (or at least HH' and VV'). I don't think it's the case that HH = HH' and VV = VV'

From Ma:

The Bell-state measurement (BSM) corresponds to turning on the switchable quarter-wave plates. In this case, the phase of the interferometer is π/2 and the interferometer acts as a 50/50 beam splitter. Therefore, the two photons interfere and are projected onto a Bell state by polarization-resolving single-photon detections.

The operation "quarter wave plates off and then polarization measurement" will select a different four subsets from "quarter wave plates on and then polarization measurement"

As this is converging with the other thread I might give my responses there

 

[PeterDonis]

I don't think it's the case that HH = HH' and VV = VV'

I have not claimed that it is. Nor has @DrChinese. Nothing in what either of us has said requires this. You are attacking a straw man.

Again, if you know of an interpretation of QM where the claim you are stating here is relevant, what is it, and what reference do you have to support it?

 

[Morbert]

I have not claimed that it is. Nor has @DrChinese. Nothing in what either of us has said requires this. You are attacking a straw man.

Again, if you know of an interpretation of QM where the claim you are stating here is relevant, what is it, and what reference do you have to support it?

Right now, I am making an interpretation-free statement about the experiment described in the Ma paper

These two measurements [BSM and SSM] are mutually exclusive (complementary in the Bohrian sense) in the same way as measuring particle or wave properties in an interference experiment.

If the subsets identified by the BSM are different from the subsets identified by the SSM (which everyone agrees) then we cannot conclude the BSM has a nonlocal influence without some further interpretational commitment.

@DrChinese disagrees, and believes we are compelled by standard QM to conclude nonlocal influence.

 

[PeterDonis]

If the subsets identified by the BSM are different from the subsets identified by the SSM (which everyone agrees)

Of course they are, since the two subsets represent different sets of actual, physical runs of the experiment. It makes no sense to even ask whether they are "the same".

then we cannot conclude the BSM has a nonlocal influence without some further interpretational commitment.

Obviously you need some "interpretational commitment" since the basic math of QM, without any interpretation, makes no claim whatever about "nonlocal influence".

@DrChinese disagrees, and believes we are compelled by standard QM to conclude nonlocal influence.

@DrChinese is saying that on his preferred interpretation, there is "nonlocal influence"--because his preferred interpretation is basically a "nonlocal realist" interpretation, where each individual run is described by a quantum state, and the final state of the 4-photon system is different for runs where a swap occurs vs. runs where no swap occurs, and since that state involves spatially separated entangled subsystems, it is inherently nonlocal, and so is any change that is made to it by any operation done during the experiment.

There is at least one interpretation where no such claim can be made, namely, a statistical interpretation such as the one used by Ballentine, in which the quantum state never describes individual runs, it only describes ensembles. Such an interpretation makes no claim about "nonlocal influence" because it makes no claim at all about what is happening in individual runs. It only makes claims about statistics.

I am still not clear about exactly what the Consistent Histories interpretation claims--whether it makes claims about what is happening in each individual run or not, and if it does, whether its claims involve any kind of "nonlocal influence".

 

[gentzen]

I am still not clear about exactly what the Consistent Histories interpretation claims--whether it makes claims about what is happening in each individual run or not, and if it does, whether its claims involve any kind of "nonlocal influence".

I guess you can try to go beyond a minimal statistical interpretation with the CH formalism. Hartle and Gell-Mann wanted this, and did try.
Griffiths mentioned (I guess in his SEP article) that some people extended the frameworks such that later projectors and decompositions are allowed to depend on results of earlier „measurements“. I never found the time to study those.

However, Griffiths himself never tries such complicated stuff in his book or in his papers which I have read. There is also a positive side to this, namely that I always found his stuff easy to read (and understand/make sense of), which is not always true for Hartle and Gell-Mann.

Our discussions here reveal another way in which one could try to go beyond a minimal statistical interpretation, which „might“ only be slightly more complicated than the basic CH formalism: „halt“ at an intermediate point (in „logical time“ in the experiment) while some future measurement settings are still open, and hence only give a „partial“ framework that can still be extended to model the measurement settings which „will“ actually be chosen in „the future“. In entanglement swapping experiments, this could be after the swap, but before the measurements verifying the entanglement, for example.

 

[Morbert]

I guess you can try to go beyond a minimal statistical interpretation with the CH formalism. Hartle and Gell-Mann wanted this, and did try.

CH is not a statistical interpretation. It lets the physicist make claims about individual runs. This not just the opinion of Hartle and Gell-Mann. This is explicitly stated by Griffiths and Omnes. See my post #70 in this thread.

I am still not clear about exactly what the Consistent Histories interpretation claims--whether it makes claims about what is happening in each individual run or not, and if it does, whether its claims involve any kind of "nonlocal influence".

CH is firstly a formalism for computing probabilities without recourse to measurement as a fundamental concept, or to an external classical environment separated by a Heisenberg cut. The traditional procedure of unitary evolution + state reduction is replaced by sets of histories and their probabilities. It follows closely from Feynmann's sum-over-histories formalism.

Whether these histories describe actually existing properties of microscopic systems, or whether they are just tools for reliably reasoning about experiments is where CH proponents diverge. Hartle, Gell-Mann, and Griffiths interpret histories as the former.

 

[gentzen]

I guess you can try to go beyond a minimal statistical interpretation with the CH formalism. Hartle and Gell-Mann wanted this, and did try.

CH is not a statistical interpretation. It lets the physicist make claims about individual runs. This not just the opinion of Hartle and Gell-Mann. This is explicitly stated by Griffiths and Omnes. See my post #70 in this thread.

If you claim to be able to go beyond a minimal statistical interpretation, then you should better be able to model situations that no minimal statistical interpretation can interpret.

In that case, considering an infinite collection of copies of the solar system would certainly then be odd

This is an argument against an ensemble interpretation of probability, but not necessarily an argument against a statistical interpretation of QM.

If I have to wait for the end of time before my formalism can give me probabilities for the different possible histories of the universe, then it is a hard call to claim that those probabilities would apply to a single system.

However, since you misinterpreted the "... wanted this, and did try" from my post which you quoted as "just the opinion of ...", I don't really expect that you tried to understand the parts of my post which you didn't quote.