Entanglement swapping and Bohmian mechanics

[Demystifier]

Since the recent thread on Bohmian mechanics (BM) is now closed, I open a new thread in which I want to explain something that bothers @DrChinese for a long time. How can BM explain the entanglement swapping? But I want to make this explanation simple and intuitive, rather than technical. I want to explain what, in my opinion, is the main conceptual misunderstanding behind DrChinese's impression that BM can't explain entanglement swapping. For that purpose I will start with something completely fictional, not directly related to actual science, because this fiction, I believe, will help much to convey the basic intuitive idea that I want to convey.

Suppose that I have the paranormal powers of clairvoyance and telekinesis. By clairvoyance, I can see things in my mind without seeing them by my eyes. By telekinesis, I can move things without touching them. Clearly, I am talking about such fictional paranormal powers because they are analogous to nonlocal action at a distance in BM.

Now suppose that there is a card which I don't see by my eyes and can't touch. Nevertheless, I can see it in my mind by clairvoyance and move at will by telekinesis. And suppose that, for some reason, I decide to follow the following rule: It the card is red, move it to the left. If the card is blue, don't do anything.

Now the crucial conceptual question that I want to address is the following: When the card is blue, do I really have paranormal powers at all? Someone looking from the side might think that I don't, because I don't move the card and don't show any sign that I know the color of the card. And yet, from my own point of view, I do have paranormal powers because I do know that the color is blue and it is precisely this knowledge why I don't move the card. From my perspective, the fact that I don't move the card is a demonstration that I do have the power of clairvoyance. I could even move it if I wanted, but I don't do it because I have chosen so. I just follow the rule that I decide to follow by my own. In other words, my paranormal powers do not cease when the card is blue. They in fact never cease, they just don't manifest themselves explicitly under certain conditions so it looks as if they ceased, but in reality they didn't.

Now we can move to physics. BM is very similar to these paranormal powers. According to BM, particles always have the power of clairvoyance. Each particle instantaneously knows the positions of all other particles in the universe. However, it doesn't mean that they always use this power for telekinesis. Instead, the particles follow a rule, and the rule itself changes. The rule is encoded in the pilot wave (the wave function of the universe), and this pilot wave changes in time, according to the Schrodinger equation. One of the rules encoded in the pilot wave says the following: If the wave function is not entangled, then don't apply the telekinesis powers. For instance, if the wave function of two particles A and B, with positions $x_A$ and $x_B$, has the product form $\psi(x_A,x_B)=\psi_A(x_A)\psi_B(x_B)$, then the rule says that velocity of A does not depend on the position of B, and vice versa. In other words, when the particles are not entangled it looks as if all nonlocal powers of BM vanish. But that's an illusion, they don't vanish, they just don't manifest themselves explicitly.

Let us illustrate this by a simple example. Suppose that, at a certain time $t$, $\psi(x_A,x_B)$ has a form
$$\psi(x_A,x_B)=\psi_A(x_A)\psi_B(x_B) \;\;\; {\rm for} \;\;\; x_B>0$$
$$\psi(x_A,x_B) \neq \psi_A(x_A)\psi_B(x_B) \;\;\; {\rm for} \;\;\; x_B\leq 0$$
This should be considered as one wave function, written separately for $x_B>0$ and $x_B\leq 0$. The full wave function, valid for all $x_A,x_B$, is not a product. It is an entangled wave function. Any yet, for $x_B>0$ it looks like a product wave function without entanglement. So if the B particle happens to have the Bohmian position $X_B>0$, then the rule says that the particle A has to move by velocity that does not depend on the position of B. But in order to obey this rule, the particle A has to know that $X_B>0$. So, the motion of A "independently" on B actually depends on B. This demonstrates that motion always depends on positions of all particles, even when this dependence is not manifest.

And now we can finally discuss the entanglement swapping. It involves 4 particles, A, B, C and D. Initially the wave function has the form $\psi_{AB}\psi_{CD}$, so A is entangled with B, and C is entangled with D, but there is no entanglement between A and D. Nevertheless, each particle knows positions of all other particles. In particular, A knows the position of D, and vice versa, but this knowledge does not have a direct manifestation. In other words, the motion of A depends on the position of D, and vice versa, but this dependence is not manifest. The entanglement swapping is a way to make this dependence manifest.

More specifically, one brings the waves of B and C into an interaction, making B entangled with C. The details can be found in the standard literature and they are not important here. The point is that this changes the full wave function of all 4 particles and the result is that A and D become mutually entangled. In other words, now the Bohmian motion of A depends on the position of D, and vice versa. What seems to be confusing to DrChinese is how can suddenly the motion of A may start to depend on the position D, if there was no such dependence from the beginning? How can such a dependence be created without the interaction between A and D? And what exactly creates such a dependence? The answer is that the dependence was there from the start, it was never really created. It is only that certain changes in the system changed the rules of the game (encoded in the change of the pilot wave), so that, at the time when B and C interacted, the dependence of A on D became manifest.

 

[martinbn]

What about the case where the measuremtns on A and D are done, the particles no loger exist and only then B and C are measured? This a point @DrChinese makes often.

 

[Demystifier]

What about the case where the measuremtns on A and D are done, the particles no loger exist and only then B and C are measured? This a point @DrChinese makes often.

If particles no longer exist, then something else absorbed their energy, momentum and quantum information. For example, a photon is absorbed by an electron, so the energy, momentum and quantum information of the photon is now encoded in the electron. Instead of photons A and D, now we have electrons A' and D' which are entangled with other particles in a similar way as photons would be if they haven't been destroyed.

 

[Demystifier]

In the other thread, @DrChinese says: "Show me any Bohmian step by step explanation of the mechanics - in precise time order as required by Bohmian theory. These experiments clearly defy Bohmian cause and effect concepts, which specifically require instantaneous action at a distance in a forward time direction only."

To respond to this, I propose the following. First DrChinese will show step by step explanation in standard QM - in precise time order as required by standard QM (in the laboratory frame of reference). After that, by using his own standards of precise step by step explanation, I will do the analogous analysis in BM. Is it fair enough?

 

[martinbn]

If particles no longer exist, then something else absorbed their energy, momentum and quantum information. For example, a photon is absorbed by an electron, so the energy, momentum and quantum information of the photon is now encoded in the electron. Instead of photons A and D, now we have electrons A' and D' which are entangled with other particles in a similar way as photons would be if they haven't been destroyed.

The point is not just that they are gone, but also the measuremnt on A and D happens before that on B and C. Is it action in the past? Or is it action from A and D on B and C?

 

[Morbert]

The point is not just that they are gone, but also the measuremnt on A and D happens before that on B and C. Is it action in the past? Or is it action from A and D on B and C?

If you are carrying out the textbook standard QM calculation of unitary evolution -> measurement -> collapse (preparation) -> unitary evolution, and if, in the lab reference frame, measurements on A and D happen before measurement on B and C, then the wavefunction collapses upon measurements on A and D, and then at a later time, on B and C. This calculation by itself does not demand one interpretation over another, but it is readily augmented with Bohmian mechanics without any need to invoke retrocausality.

 

[Demystifier]

The point is not just that they are gone, but also the measurement on A and D happens before that on B and C. Is it action in the past? Or is it action from A and D on B and C?

There is no action to the past. Suppose that at time $t_1$ you measure A and D, and later at $t_2>t_1$ put B and C into the interaction. Since you look for correlations, you actually do all this with many copies of the system, so that you can analyse your data statistically. At $t_1$ you store your experimental results on a computer, so that you can perform a statistical analysis whenever you want. If you perform the statistical analysis of the measurement results at $t_1$, you will not see any correlation, showing that there is no entanglement between A and D. If you perform the same analysis later, at time $t_2$, you will confirm that there is no correlation.

However, now comes the crucial twist. At $t_2$ you can also perform a different statistical analysis of the data collected at $t_1$. Depending on the result of measurement of B and C on each copy, you either through away the data of that copy, or include it in the analysis. Now you don't analyse all the data, but only a subensemble of it. It's called postselection, because you select only a subset of data, depending on the results of other measurements at a later time. If you do that, you can see a correlation between A and D on this postselected subensemble. So the question is, what caused this correlation? Naively, it looks as if the correlation was caused by measurement of B and C, but this measurement happened later, so it looks as an action to the past. But this is wrong. Correlation is not causation. There was no action at a distance between A and D, and there was no action to the past. Instead, the correlation is an artefact of throwing away part of the data collected at $t_1$. At $t_1$ there was no direct correlation between A and D. But there was correlation between A and B, and also between C and D, and later at $t_2$ there was also a correlation between B and C due to interaction, so postselection of the data from $t_1$ depending on the measurement results at $t_2$ created spurious (indirect) correlation in the subensemble of the data collected at $t_1$. Such a correlation does not require action to the past. In particular, BM explains it without action to the past.

 

[PeterDonis]

postselection of the data from $t_1$ depending on the measurement results at $t_2$ created spurious (indirect) correlation in the subensemble of the data collected at $t_1$.

Is the word "spurious" really justified here?

After all, when B and C come together just before $t_2$, B is entangled with the A environment (whatever took over A's entanglement with B by storing the information about A when it was measured and destroyed, per your post #3) and C is entangled with the D environment. Those entanglements affect the motion of B and C when the entanglement swapping operation is done. Or, to put it another way, even though A and D were already measured and destroyed before B and C came together, the measurement results on A and D still affect the motion of B and C, and that affects what happens at the entanglement swap. That being the case, I don't think it's justified to call the resulting correlations between A and D in the subensembles "spurious"; they reflect a genuine physical effect, just as they do in the case where A and D have not yet been measured when the swap takes place. The only difference is that now the A and D parts of the entanglement get taken over by the A environment and the D environment before the swap happens, instead of after.

 

[PeterDonis]

postselection of the data

Note, though, that you have to do postselection of the data from the A and D measurements regardless of whether A and D are measured before or after the entanglement swap operation is done on B and C. That's because the swap does not always result in the same entangled state of A and D; in the general case it has a equal chance to produce any of the four Bell states. In other words, the full ensemble of A and D data will be a mixture of different possible entangled states of A and D, and will show zero correlation between A and D; the only way to see the A and D entanglement after the swap is to post-select based on the swap results, i.e., to post-select the data to pick out the subensembles corresponding to each of the individual Bell states of A and D that the swap can produce.

There are papers in the literature that use the above observation to claim that the apparent entanglement between A and D is always spurious, even in the case where A and D are not measured until after the swap takes place. We have had discussions of this in a number of previous threads on the topic. I personally don't agree with that position: I think the entanglement is not spurious. But my point here is simply that, if you are going to say the A and D entanglement is spurious based on having to post-select the A and D measurement data, that argument applies to any entanglement swap experiment, not just to one in which A and D are measured before the swap.

 

[Demystifier]

@PeterDonis you are right, the word "spurious" was not appropriate.

 

[DrChinese]

...

Now the crucial conceptual question that I want to address is the following: When the card is blue, do I really have paranormal powers at all? Someone looking from the side might think that I don't, because I don't move the card and don't show any sign that I know the color of the card. And yet, from my own point of view, I do have paranormal powers because I do know that the color is blue and it is precisely this knowledge why I don't move the card. From my perspective, the fact that I don't move the card is a demonstration that I do have the power of clairvoyance. I could even move it if I wanted, but I don't do it because I have chosen so. I just follow the rule that I decide to follow by my own. In other words, my paranormal powers do not cease when the card is blue. They in fact never cease, they just don't manifest themselves explicitly under certain conditions so it looks as if they ceased, but in reality they didn't.

Now we can move to physics. BM is very similar to these paranormal powers. According to BM, particles always have the power of clairvoyance. Each particle instantaneously knows the positions of all other particles in the universe. However, it doesn't mean that they always use this power for telekinesis. Instead, the particles follow a rule, and the rule itself changes. The rule is encoded in the pilot wave (the wave function of the universe), and this pilot wave changes in time, according to the Schrodinger equation. One of the rules encoded in the pilot wave says the following: If the wave function is not entangled, then don't apply the telekinesis powers. For instance, if the wave function of two particles A and B, with positions $x_A$ and $x_B$, has the product form $\psi(x_A,x_B)=\psi_A(x_A)\psi_B(x_B)$, then the rule says that velocity of A does not depend on the position of B, and vice versa. In other words, when the particles are not entangled it looks as if all nonlocal powers of BM vanish. But that's an illusion, they don't vanish, they just don't manifest themselves explicitly.

Through this point, there is no issue. There are rules associated with theory. Entangled systems follow some different rules. That's fair too.

Further, the Bohmian rules are different for both unentangled systems and entangled systems when compared to orthodox QM. As we already know from Norsen: "...the pilot-wave theory adds something to the state descriptions of ordinary quantum mechanics..."

This is fine too. BM adds to the state descriptions of oQM. BM=oQM+, hopefully this is not controversial. That's from Norsen's first paragraph, and if there is already a conceptual problem, let's call it now.

 

[PeterDonis]

BM adds to the state descriptions of oQM.

Yes: it adds the actual position and velocity of each particle.

But it also changes how the wave function, which is also present in oQM, is interpreted. In oQM, the wave function is either the state of the system (in realist interpretations, which are the ones you seem to prefer) or a description of an abstract ensemble of systems (or, equivalently, a state preparation process that produces such an ensemble, a la Ballentine). But in BM, the wave function is neither of these things. Instead, it's a part of the equation of motion of the particles; the actual state of the system is the particle positions and velocities.

 

[Sambuco]

But my point here is simply that, if you are going to say the A and D entanglement is spurious based on having to post-select the A and D measurement data, that argument applies to any entanglement swap experiment, not just to one in which A and D are measured before the swap.

I think these types of delayed-choice experiments are somewhat "tricky". For example, suppose we have a bunch of electron-positron pairs and we measure the spin of each of them in arbitrary directions. After that, one by one, we make them collide. Some of them will annihilate and give rise to a pair of photons, according to process $e^- + e^+ → \gamma + \gamma$. If, at the end of the experiment, we take only those runs in which two photons were generated (post-selection), it seems to me that we will see that the results of the measurements of the electron and positron spins in these runs violate Bell's inequalities. Can I say that the subset of post-selected electron-positron pairs is entangled? I support some information-based interpretation, such as RQM, so I have no problem saying yes, but I wouldn't be surprised if many say no. I think experiments with delayed-choice entanglement swapping are not so different.

Lucas.

 

[PeterDonis]

If, at the end of the experiment, we take only those runs in which two photons were generated (post-selection), it seems to me that we will see that the results of the measurements of the electron and positron spins in these runs violate Bell's inequalities.

What are you basing this on? Are you assuming that the "bunch of electron-positron pairs" was created by a process that ensures that each pair is entangled? That would seem necessary if you're going to expect Bell inequality violations. But if so, why would you need to post-select? If every pair is entangled, then the entire ensemble of data on the spin measurements would show Bell inequality violations. So I don't understand what role the post-selection is playing here.

 

[Sambuco]

@PeterDonis in the closed thread you ask me about a reference for the claim that the quantum potential is not considered fundamental in modern presentations of Bohmian mechanics. I share with you this paper by Dürr-Goldstein-Zanghì. In section 2, they analyze the question we were talking about. I quote:

"Bohmian mechanics should be regarded as a first-order theory, in which it is the velocity, the rate of change of position, that is fundamental in that it is this quantity that is specified by the theory, directly and simply, with the second-order (Newtonian) concepts of acceleration and force, work and energy playing no fundamental role.
From our perspective the artificiality suggested by the quantum potential is the price one pays if one insists on casting a highly nonclassical theory into a classical mold. This is not to say that these second-order concepts play no role in Bohmian mechanics; they are emergent notions, fundamental to the theory to which Bohmian mechanics converges in the “classical limit,” namely, Newtonian mechanics."

Lucas.

 

[Sambuco]

What are you basing this on? Are you assuming that the "bunch of electron-positron pairs" was created by a process that ensures that each pair is entangled? That would seem necessary if you're going to expect Bell inequality violations. But if so, why would you need to post-select? If every pair is entangled, then the entire ensemble of data on the spin measurements would show Bell inequality violations. So I don't understand what role the post-selection is playing here.

What I have done is take a set of electron-positron pairs without any type of initial correlation between the spins. For each pair, the spin of each particle is measured and, after that, they are collided. In some of the pairs, the particles will pass through each other, while in other pairs annihilation processes will occur, in which a certain number of photons will be generated. At the end of the experiment, we take into account only those runs in which exactly two photons have been generated, that is, those that can be represented by the process $e^- + e^+ → \gamma + \gamma$. We know that if we consider the inverse process $\gamma + \gamma → e^- + e^+$, the electron-positron pair will be in a singlet state. Consequently, returning to the original case, if we post-select only those runs in which process $e^- + e^+ → \gamma + \gamma$ occurred, we know that the measurements of electron and positron spins (only in those runs) will show correlations that exactly mimic those arising from a singlet state, i.e. violation of Bell's inequalities.

Lucas.

 

[PeterDonis]

What I have done is take a set of electron-positron pairs without any type of initial correlation between the spins. For each pair, the spin of each particle is measured

So for the entire ensemble, there will be no Bell inequality violations. Ok.

We know that if we consider the inverse process $\gamma + \gamma → e^- + e^+$, the electron-positron pair will be in a singlet state.

If we assume zero orbital angular momentum in the center of mass frame, I think I agree.

However, I don't think that leads to the prediction you're making, because after the electron and positron spins are both measured, they aren't entangled, since you're specifying that nothing else is done to them after the measurement, and if they aren't entangled, they obviously can't be in the singlet state. So I think the correct prediction, if the singlet state is required for annihilation into photons, is that annihilation into photons will be suppressed in your experimental setup.

Or, alternatively, what annihilation events do happen will be for pairs that do not have zero orbital angular momentum in the center of mass frame, so they don't have to be in the singlet state--they can annihilate even though their spins are uncorrelated. Which would again not lead to the prediction you're making.

 

[DrChinese]

In the other thread, @DrChinese says: "Show me any Bohmian step by step explanation of the mechanics - in precise time order as required by Bohmian theory. These experiments clearly defy Bohmian cause and effect concepts, which specifically require instantaneous action at a distance in a forward time direction only."

To respond to this, I propose the following. First DrChinese will show step by step explanation in standard QM - in precise time order as required by standard QM (in the laboratory frame of reference). After that, by using his own standards of precise step by step explanation, I will do the analogous analysis in BM. Is it fair enough?

Fair? Not sure. But I will come as close as I think possible.

Hopefully we agree: BM=oQM+? We're discussing the "+". Stated on a completely different level, but relevant here: Suppose I challenge theory X [oQM] because it doesn't address Y [mechanics of remote action at a distance], but... theory X is otherwise accurate. An analogy might be QM and General Relativity (GR). I can't really object to QM (or BM) because it doesn't purport to explain gravity. The theory doesn't say it does.

oQM does NOT say there is a time order for entanglement swapping mechanics. It (usually silently) implies the diametric opposite, as can be seen by the experiments I cite showing results do not vary when ordering changes. (Let me know if I need to recite.) There is a starting point/context; and an ending point/context; and in relevant terms, the event order in between does not feature any specific drivers of the outcome.

---

I can, however, describe the standard events that occur. Here my 1/2/3/4 correspond to your particles A/B/C/D.

a) "Two pairs of entangled photons 1&2 and 3&4 are each produced in the antisymmetric polarization-entangled Bell singlet state such that the total four-photon state has the form |Ψ〉1234 = |Ψ−〉12⨂|Ψ−〉34"

b) Photons 2 and 3 are remotely subjected to a joint Bell-state measurement (beam splitter, PBSs), and they become entangled in one of 4 Bell states.

|Ψ〉1234 = 1/2 (|Ψ+〉14⨂|Ψ+〉23 − |Ψ−〉14⨂|Ψ−〉23 − |Φ+〉14⨂|Φ+〉23 + |Φ−〉14⨂|Φ−〉23)

c) Photons 1 and 4 are remotely subjected to independent polarization measurements.

d) Results are sorted into Bell state bins, 2 of which can be distinguished, demonstrating successful entanglement swap.

Now, we already know that experiments in the order "abcd" yield indistinguishable results from order "acbd". Essentially: bc=cb and the ordering commutes. So we deduce that Bohmiam mechanics must follow rules yielding the same results. I assume you will proceed to demonstrate such. I would hate to see you waste time on that at this point.

---

Ultimately, however, my questions derive from the "acbd" ordering, which is the Delayed Choice version.

Ma et al: "Peres’ idea of “delayed-choice for entanglement swapping... implies that whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured."

There are specific reasons that leads me to these questions that cannot be readily demonstrated on the "acbd" version. So there is really no way for you to "prove" the Bohmian ordering is irrelevant (i.e. bc=cb) without addressing those reasons of mine first. I will be glad to elucidate (ha, never before thought I would use "elucidate" in a sentence - hope I spelled it correctly).

-DrC

 

[DrChinese]

There is no action to the past.

That hypothesis is a feature of BM, and is certainly not a requirement of oQM (which is silent on this point, although most physicists agree with your statement).

I assume you are aware of the Two State Vector Formalism (TSVF). This theory/interpretation (however you choose to classify) features time symmetry and the future is an explicit component of the dynamics. It drops BM's nonlocality and is classed as purely local*. Interestingly (1995): "Both Bohm’s theory and the two-state vector formalism yield the same predictions for the results of experiments as the standard quantum theory." Aharonov and Vaidman discussed this with Bohm.

*On a Time Symmetric Formulation of Quantum Mechanics: "A consequence of the suggested formalism and measurement theory, is that the problem of non-locality and Lorentz non-covariance, of the usual prescription with a `reduction', may be eliminated."

 

[DrChinese]

There are papers in the literature that use the above observation to claim that the apparent entanglement between A and D is always spurious, even in the case where A and D are not measured until after the swap takes place. We have had discussions of this in a number of previous threads on the topic. I personally don't agree with that position: I think the entanglement is not spurious. But my point here is simply that, if you are going to say the A and D entanglement is spurious based on having to post-select the A and D measurement data, that argument applies to any entanglement swap experiment, not just to one in which A and D are measured before the swap.

Completely agree!

Experiments based on post-selection of criteria established in advance are well-established scientifically, and in fact are the cornerstone of almost all medical research*. Further (and as a separate point): It should be obvious that all studies of nonlocality require data from remote locations to be brought together using signals propagating that are not FTL. I am unaware of any serious challenge to the large body of work on entanglement swapping by Zeilinger (and many others) because there is post-selection and/or remote sub-light speed collation of data.

*See the Cochrane standards on protocol selection, for example.

 

[PeterDonis]

Suppose I challenge theory

Please be aware that according to the rules of this subforum, claims that a particular interpretation of QM is wrong (or right, for that matter) are off limits. That would include claims that a particular interpretation cannot account for a particular experimental result.

Discussion of how a particular interpretation accounts for a particular result are fine. But your use of the word "challenge" could be interpreted as going beyond that into the kind of territory that is off limits per the above (and in the previous thread that is now closed you made that kind of off limits claim explicitly). Please be advised.

 

[PeterDonis]

whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured."

Note that this claim is interpretation dependent: it presupposes an interpretation where the wave function is the state of the system. BM is not such an interpretation. So you should not expect BM's account of what is going on to be describable this way.

BM is not the only interpretation that is not such an interpretation, BTW. An ensemble interpretation a la Ballentine also is not. Such an interpretation would say that the description in the quote above makes no sense, since the term "entangled" does not apply to pairs of photons in an individual run of the experiment (since the wave function in general does not, and "entangled" is a property of the wave function).

 

[DrChinese]

Please be aware that according to the rules of this subforum, claims that a particular interpretation of QM is wrong (or right, for that matter) are off limits. That would include claims that a particular interpretation cannot account for a particular experimental result.

Discussion of how a particular interpretation accounts for a particular result are fine. But your use of the word "challenge" could be interpreted as going beyond that into the kind of territory that is off limits per the above (and in the previous thread that is now closed you made that kind of off limits claim explicitly). Please be advised.

The sentence you are referring to was not an attempt to challenge anything. But I will of course consider myself so advised.

 

[DrChinese]

Note that this claim is interpretation dependent...

What you are commenting on was not a fully accurate quote. The full quote I provided:

Ma et al: "Peres’ idea of “delayed-choice for entanglement swapping... implies that whether their two photons are entangled (showing quantum correlations) or separable (showing classical correlations) can be defined after they have been measured."

This statement, quoted verbatim by top scientists and not myself, is not interpretation dependent. (And the experimental implementation fully supports it.) It's an implication. Can it be explained in other ways by some interpretations? Sure, but that doesn't change the obvious implication. And that implication should certainly be grounds for discussion in this subforum. It is, after all, merely the opinion of some of the best experimentalists in this arena. That might be considered by many to be an excellent starting point for discussion.

 

[PeterDonis]

The sentence you are referring to was not an attempt to challenge anything.

Since it explicitly used the word "challenge", you should not be surprised that readers interpret it that way.

 

[PeterDonis]

What you are commenting on was not a fully accurate quote.

Adding more doesn't change what I said. See below.

This statement, quoted verbatim by top scientists and not myself, is not interpretation dependent.

Yes, it is. The phrase "whether their two photons are entangled" only makes sense for an interpretation where "entanglement", which is a property of the wave function, can be meaningfully applied to "two photons". I already gave an explicit example, with a reference to a textbook, of an interpretation for which that is not the case.

If the "top scientists" did not state that explicitly in what you are referencing, that doesn't mean it's wrong. It should be obvious as a matter of simple logic.

It's an implication. Can it be explained in other ways by some interpretations? Sure, but that doesn't change the obvious implication.

You can't have it both ways. The implication is interpretation dependent; you admit that since you say it can be explained in other ways by other interpretations.

It is, after all, merely the opinion of some of the best experimentalists in this arena.

Experiments can't distinguish between different interpretations, so I don't see why this argument from authority, even if it were not unacceptable simply because it's an argument from authority, would carry any weight when we're talking about what is interpretation dependent and what isn't.

Finally, this is the interpretations subforum, so I don't see why you're so vehemently opposed to simply admitting (as you already have, see above) that your statement is interpretation dependent. To be clear, making interpretation dependent statements in this subforum is not a problem. It's to be expected.

 

[DrChinese]

Since it explicitly used the word "challenge", you should not be surprised that readers interpret it that way.

Seriously, "challenge" is now a trigger word? What I said:

"Suppose I challenge theory X [oQM] because it doesn't address Y [mechanics of remote action at a distance], but... theory X is otherwise accurate. An analogy might be QM and General Relativity (GR). I can't really object to QM (or BM) because it doesn't purport to explain gravity. The theory doesn't say it does."

I have started a new thread with a different question on the Bohmian perspective. I ask for helpful comments on that.

-DrC

 

[PeterDonis]

I have started a new thread with a different question on the Bohmian perspective. I ask for helpful comments on that.

For reference for other readers, the new thread by @DrChinese is here:

Graduate Thread 'Polarization Entanglement, following Bohmian ideas and/or orthodox QM'

Sunday, 9:39 PM

This question follows recent several threads on Bohmian approach to entanglement concepts, and referencing Norsen also.

We have our usual polarization entangled (|HH>+|VV> photon pair A and B going to Alice and Bob. We measure A and it emerges from the V> port of a Polarizing Beam Splitter. (Let's ignore consideration of anything that might be hypothetically emerging from the H> port in some interpretations.) We know with certainty that the B photon, were it to be measured on the H/V basis, would be seen to be V> also.

How would the Bohmian (or anyone really) describe the...

• DrChinese
• Replies: 13
• Forum: Quantum Interpretations and Foundations

I will refrain from making any posts at all in that thread.

 

[Demystifier]

I think now the real issue is this. If the interaction between B and C happens after the measurement of A and D, are A and D entangled or not at the time of their measurement? The answer is the following. Entanglement is a property of the wave function (not of the Bohmian particles), so to answer the question one needs to say what is the wave function (or more precisely, density matrix, to include also mixed states of subsystems). But the wave function is not unique, there are different ways to associate a wave function with a given system.

In standard QM you can use either a collapsed or non-collapsed wave function, depending on your information. But how do you acquire information? One way is to perform a measurement, but that's not the only way. Another way is to imagine that a measurement will be performed in the future, and to imagine that the measurement outcome will be such and such, and from the corresponding collapsed (projected) function in the future compute the corresponding collapsed wave function in the past. That collapse is induced by imagined information in the future, which is a kind of information too. To compute it, you don't need to actually perform a measurement in the future, it's all just a theoretical analysis allowing you to associate a projected wave function.

In Bohmian mechanics we have some additional ways to associate a wave function with the same system, through the conditional and the effective wave function, depending on the information about Bohmian particle positions (which are hidden variables that can't be measured, so information is again a kind of imagined information).

The moral is, the particles A and D can be considered both entangled and non-entangled, depending on which information we use. And this information itself can be either a factual information based on actual measurements, or imagined information based on certain theoretical assumptions.

A funny thing about QM is that all those imagined theoretical assumptions eventually lead to the same measurable predictions, so we cannot decide by measurements whether those assumptions are true or not. This independence on assumptions can be traced back to linearity of QM. If QM was nonlinear, all these assumptions would lead to different predictions and we could decide which interpretation of QM is right by measurements.

 

[DrChinese]

I think now the real issue is this. If the interaction between B and C happens after the measurement of A and D, are A and D entangled or not at the time of their measurement? ...

Agree with most of the rest you said. Here's an interesting twist (maybe lol). A scientist presumably has the free will to execute the swap. Of course, you might say that is predetermined and that is OK if that's the answer.

Assume there is a swap. In oQM, I would say you must wait until the entire context is known. Even then, you couldn't exactly say that A & D were entangled before the B/C swap. But you sorta could. But of course in BM, the issue is:

i) Whether the future swap - which the universe knows is going to occur? - causes the perfect A/D correlation, thereby creating the illusion of action to the past; or
ii) The outcome of the perfect A/D correlation causes the swap to succeed.

I don't know. Any thoughts?