# B Entanglement when I "produce" positron-electron pairs one at a time

#### vanhees71

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Yay !

I don't see any serious disharmony with @vanhees71 's position, maybe just an adjustment required.
It only underlines the problem to communicate about QT in a clear way. Again our understanding was undermined by using philosophical gibberish instead of clear physics language. As I more and more find confirmed: Philosophy can do great harm to the natural sciences :-(.

#### vanhees71

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Gold Member
In quantum field theory, it does not have to be the case that there is no causal connection between spacelike separated measurements. All that has to be the case is that the measurements must commute: their results cannot depend on the order in which they are made.

Discussions of the Bell inequalities and EPR experiments that do not recognize this point are leaving out something important, IMO.
Can you elaborate on this? I don't see how your statement is compatible with the very foundations of QFT. Don't we choose the usual local microcausal QFTs (restricting ourselves to the unitary irreducible representations of the proper orthochronous Poincare group with $m^2 \geq 0$) to build QT-models for relativistic particles?

The measurements on several single particles in an entangled multi-particle state at far distances then cannot affect each other in an instantaneous way.

#### stevendaryl

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Science Advisor
Let me try to illustrate my understanding of the issue with entanglement and interference. Consider the following experimental setup:

You produce an electron at point A. From there it can take one of the following paths:
1. Travel from A to B and emit a photon and then travel to C and finally to D, where it is detected.
2. Same as path 1, except that it goes from C to E, where it is detected.
3. Travel from A to G and emit a photon and then travel to F and finally to D.
4. Same as path 3, except after F it travels to E.
Assume that at each decision point, A, C and F, the electron has a 50/50 chance of going in either direction.

Ignoring the photons, then the amplitude for the electron to be detected at D would involve interference between paths ABCD and AGFD. The amplitude for the electron to be detected at E would involve interference between paths ABCE and AGFE.

Let's assume that amplitudes are such that, without the photons, the probability would be 0% chance of arriving at D and 100% chance of arriving at E.

If there is no interference, then there is an equal probability of the electron being detected at D or E. So in the absence of interference, there is a 50/50 chance of the electron being detected at D or E. With interference, there is a 0/100 chance.

Entanglement is involved because whether you see the interference or not depends on what is done with the photon. The photon is entangled with the electron. If you measure the photon in such a way that it is possible to determine whether it came from B or G, then that gives "which path" information, and that will destroy the interference pattern. If instead, you erase the "which path" information (by routing the photon from B or G to the same final destination, where information about where it came from is lost), then you restore the interference.

What I don't understand about this type of experiment is the timing. If whether there is interference or not depends on what happens to the photons, it seems that you could delay measuring the photons until after the electron is detected. But by then, the interference or lack of interference would have already come into play.

#### vanhees71

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Gold Member
In this way you cannot say anything, because you don't know the states of the electron and the photon. You have to clearly define the specific experiment you are doing. Otherwise we cannot analyze it.

#### stevendaryl

Staff Emeritus
Science Advisor
In this way you cannot say anything, because you don't know the states of the electron and the photon. You have to clearly define the specific experiment you are doing. Otherwise we cannot analyze it.
I'm not asking you to analyze it. I'm explaining why entanglement is relevant to whether interference patterns are seen, or not. You can fill in the details yourself, if you care enough.

#### Mentz114

Gold Member
[..]

Entanglement is involved because whether you see the interference or not depends on what is done with the photon. The photon is entangled with the electron. If you measure the photon in such a way that it is possible to determine whether it came from B or G, then that gives "which path" information, and that will destroy the interference pattern. If instead, you erase the "which path" information (by routing the photon from B or G to the same final destination, where information about where it came from is lost), then you restore the interference.

What I don't understand about this type of experiment is the timing. If whether there is interference or not depends on what happens to the photons, it seems that you could delay measuring the photons until after the electron is detected. But by then, the interference or lack of interference would have already come into play.
I think I can see what you're saying but not sure about the conclusion.

Single photon interference is shown by the two-point zero-order correlation of the single-photon state, as observed.
For the two-photon state the correlations are there in higher orders as well. ( see Ballentine page 560, chapter 19).

But entangled photons are in a singlet-state which shows no interference but a huge correlation.

The Hong-Ou-Mandel experiment (I think) predicts the equivalent.

I could be misinterpreting what I'm reading, though.

#### stevendaryl

Staff Emeritus
Science Advisor
I'm not asking you to analyze it. I'm explaining why entanglement is relevant to whether interference patterns are seen, or not. You can fill in the details yourself, if you care enough.
Abstractly, we can describe the situation this way:

We have an initial state $|A, -\rangle$. We have intermediate states $|C, B\rangle$ and $|F,G\rangle$. We have final states $|D,B\rangle$, $|D,G\rangle$, $|E,B\rangle$ and $|E,G\rangle$. The first component of the composite state is the state of the electron, and the second is the state of the photon (the $-$ in the initial state is because there is no photon in that state).

The interaction is such that:

$|A\rangle \rightarrow \lambda_{DB} |D,B\rangle + \lambda_{DG} |D,G\rangle + \lambda_{EB} |E,B\rangle + \lambda_{EG} |E,G\rangle$

where the various $\lambda$s are determined by the details of the experiment.

If states $G$ and $B$ of the photon are macroscopically distinguishable, then there will be probabilities:
1. $|\lambda_{DB}|^2$ is the probability that the electron will be detected at $D$ and the photon will be measured to have come from $B$
2. $|\lambda_{DG}|^2$ is the probability that the electron will be detected at $D$ and the photon will be measured to have come from $G$
3. $|\lambda_{EB}|^2$ is the probability that the electron will be detected at $E$ and the photon will be measured to have come from $B$
4. $|\lambda_{EG}|^2$ is the probability that the electron will be detected at $E$ and the photon will be measured to have come from $G$
The probability of detecting the photon at $D$ is given by: $P_D = |\lambda_{DB}|^2 + |\lambda_{DG}|^2$. The probability of detecting the photon at $E$ is given by: $P_E = |\lambda_{EB}|^2 + |\lambda_{EG}|^2$. The fact that you square and then sum shows that there is no interference.

On the other hand, let's suppose that you erase the information about where the photon came from. The way you can do that is by having some final state $Z$ for the photon which is reachable from both $B$ and $G$. Letting $\lambda_{BZ}$ be the amplitude for the photon to make a transition from state $B$ to state $Z$ and letting $\lambda_{GZ}$ be the amplitude for the photon to make a transition from state $G$ to state $Z$, then the amplitude for the composite system to end up in state $|D,Z\rangle$ is:

$\lambda_{DG}\lambda_{GZ} + \lambda_{DB} \lambda{BZ}$

and the amplitude for the composite system to end up in state $|E,Z\rangle$ is similarly

$\lambda_{EG}\lambda_{GZ} + \lambda_{EB} \lambda{BZ}$

So in this alternative experiment, where the information about where the photon came from is erased, the probability of detecting the electron at $D$ is:

$P_D = |\lambda_{DG}\lambda_{GZ} + \lambda_{DB} \lambda{BZ}|^2$

and the probability of detecting the electron at $E$ is:

$P_E = |\lambda_{EG}\lambda_{GZ} + \lambda_{EB} \lambda{BZ}|^2$

In this experiment, where the electron state is not entangled with the final photon state, there is interference.

#### stevendaryl

Staff Emeritus
Science Advisor
I think I can see what you're saying but not sure about the conclusion.

Single photon interference is shown by the two-point zero-order correlation of the single-photon state, as observed.
For the two-photon state the correlations are there in higher orders as well. ( see Ballentine page 560, chapter 19).

But entangled photons are in a singlet-state which shows no interference but a huge correlation.

The Hong-Ou-Mandel experiment (I think) predicts the equivalent.

I could be misinterpreting what I'm reading, though.
In the experiment I'm talking about, it's not a two-photon entangled state. The state of the photon is entangled with the state of the electron.

#### Mentz114

Gold Member
In the experiment I'm talking about, it's not a two-photon entangled state. The state of the photon is entangled with the state of the electron.
I've just seen your follow-up post.

#### vanhees71

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I'm not asking you to analyze it. I'm explaining why entanglement is relevant to whether interference patterns are seen, or not. You can fill in the details yourself, if you care enough.
You cannot discuss this without defining which experiment is done. Are you talking about the experiment by Dopfer, Zeilinger, et al? Then it's all quite easy to describe by QED, and it's well understood under which setup and for which partial ensembles you see an interference pattern in the single-photon observations or not. To say in the very general "entanglement is relevant to whether interference patterns are seen or not" is an empty phrase.

#### vanhees71

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In the experiment I'm talking about, it's not a two-photon entangled state. The state of the photon is entangled with the state of the electron.
Why then don't you give the details of this experiment or a link to a paper describing it? A quite recent "Schrödinger cat experiment" with atoms and photons can be found here:

https://arxiv.org/abs/1812.09604

#### stevendaryl

Staff Emeritus
Science Advisor
Why then don't you give the details of this experiment or a link to a paper describing it? A quite recent "Schrödinger cat experiment" with atoms and photons can be found here:

https://arxiv.org/abs/1812.09604
I did describe it.

#### stevendaryl

Staff Emeritus
Science Advisor
You cannot discuss this without defining which experiment is done. Are you talking about the experiment by Dopfer, Zeilinger, et al? Then it's all quite easy to describe by QED, and it's well understood under which setup and for which partial ensembles you see an interference pattern in the single-photon observations or not. To say in the very general "entanglement is relevant to whether interference patterns are seen or not" is an empty phrase.
Here's a description of the sort of thing I'm talking about.

#### stevendaryl

Staff Emeritus
Science Advisor
I am more and more having complaints about the unfriendly tone of Physics Forums discussions. I think I should probably take a long break.

#### Mentz114

Gold Member
Abstractly, we can describe the situation this way:

We have an initial state $|A, -\rangle$. We have intermediate states $|C, B\rangle$ and $|F,G\rangle$. We have final states $|D,B\rangle$, $|D,G\rangle$, $|E,B\rangle$ and $|E,G\rangle$. The first component of the composite state is the state of the electron, and the second is the state of the photon (the $-$ in the initial state is because there is no photon in that state).

[..]

On the other hand, let's suppose that you erase the information about where the photon came from. The way you can do that is by having some final state $Z$ for the photon which is reachable from both $B$ and $G$. Letting $\lambda_{BZ}$ be the amplitude for the photon to make a transition from state $B$ to state $Z$ and letting $\lambda_{GZ}$ be the amplitude for the photon to make a transition from state $G$ to state $Z$, then the amplitude for the composite system to end up in state $|D,Z\rangle$ is:

In this experiment, where the electron state is not entangled with the final photon state, there is interference.
I've looking at this and at first I thought it was another way to codify 'which path information' and show how it can be controlled. But there is something about it I cannot fathom when I try to envision it.

In the first experiment there are two independently produced (incoherent) photons which one would not expect to interfere.

The second experiment somehow makes then coherent. I'm struggling with that.

Of course, I may be misunderstanding what you're describing ...

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#### DrChinese

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I always fall in this trap :-(. I always fail to translate the word "realism" from my standard every-day meaning, to describe what's real in the sense of the natural sciences, i.e., what's objectively observed in nature, while you used it in the philosophical sense, where it means "classical deterministic worldview", i.e., the contrary to what's really realistic.
Realism a la EPR (what I referred to) is not the philosophical one you mention. It is the one in which all particle properties are well-defined independent of the act of observation. Post-Bell, such realism is highly suspect, as thousands* of varied attempts to locate or deduce such values have failed.

When it comes to entanglement, what is "objectively observed" (the statistical predictions) is dependent on a future context which INCLUDES the nature of the observation. Thus your usage of the word "objectively" is completely counter to meaning of the result being observer independent a la EPR. What can be "objectively observed" is a correlation which is ONLY related to the observers' later choice of measurement basis, and therefore cannot be preexisting in time. That statement is correct even for the Bohmian program, which likewise posits the observer participates to affect the correlations.

*By my best estimate.

#### DrChinese

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I am more and more having complaints about the unfriendly tone of Physics Forums discussions. I think I should probably take a long break.
I hope you don't find a break necessary, but if you do, I hope it is a short one.

To cheer you up: Physicist walks into a bar...

#### vanhees71

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I am more and more having complaints about the unfriendly tone of Physics Forums discussions. I think I should probably take a long break.
I hope you don't refer to me. It's not meant unfriendly. I just ask for a concrete experiment since I don't think that one can discuss these issues clearly without a concrete experiment.

#### vanhees71

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Gold Member
Realism a la EPR (what I referred to) is not the philosophical one you mention. It is the one in which all particle properties are well-defined independent of the act of observation. Post-Bell, such realism is highly suspect, as thousands* of varied attempts to locate or deduce such values have failed.

When it comes to entanglement, what is "objectively observed" (the statistical predictions) is dependent on a future context which INCLUDES the nature of the observation. Thus your usage of the word "objectively" is completely counter to meaning of the result being observer independent a la EPR. What can be "objectively observed" is a correlation which is ONLY related to the observers' later choice of measurement basis, and therefore cannot be preexisting in time. That statement is correct even for the Bohmian program, which likewise posits the observer participates to affect the correlations.

*By my best estimate.
The entire EPR paper is flawed. Even Einstein himself didn't like it for being too vague. He lamented that his argument is "buried in erudition" (or something like this).

Indeed that't the great achievement of Bell's studies: You can invent a class of models he calls "local realistic", which I'd call "local deterministic" to avoid the burnt word "realistic", that are in contradiction with QT and thus you can decide by experiments whether EPR's "realism" describes nature better or QT. Since the decision is a zillion to 0 for QT, I don't take EPR's "realism" as a "realistic description" but as the contrary. What's really realistic, i.e., in accord with all experience (among it some of the most accurate experiments ever) is QT not "EPR realism".

The observations on states involving entanglement are completely observer independent. It's only dependent on what's measured, i.e., it's dependent on with which "stuff" the observed object interacts in the process of state preparation and observation. Nothing is changed to the object by choosing which partial ensemble you like to observe. In principle you can decide for any choice long after the entire setup is gone, as long as you have an accurate record about all experimental data. In the Kim erasure experiment it's just the choice of the one or the other partial ensemble of measurement records that "decides" whether you see interference effects or not. That shows that this dependence of the outcome on the choice is an objective property of the system due by the entangled state it was prepared in.

#### vanhees71

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Gold Member
Here's a description of the sort of thing I'm talking about.

That's a great paper (it appeared in APJ, i.e., a respected physics-didactics journal). I've nothing to add to their analysis. It's precisely what I always say: See particularly Eqs. (9a+b). There they explicitly write that the measurement is local, i.e., the projection operator describing the filtering is only acting on the measured part of the entangled system in accordance with locality of the interaction between measurement device and this measured part.

Also here, in principle you can choose to erase the which-way information in the erasure setup after everything is saved in a measurement protocol: The total ensemble doesn't show the interference effect, while choosing the subensemble where $\mathcal{E}$ registered the photon or the complementary one where the photon did not get registered, the interference effect is seen for each of these two subensembles.

Nowhere is an instantaneous collapse at a distance and also no retrocausality or subjectivity by the delayed choice. The particular setup with the source, all the beam splitters and detectors, objectively determines the (probabilistic!) outcome of the measurements. Also note with this setup you can make only the specific kind of delayed choice, i.e., "erasing or not erasing" the which-way information. Any other possibility of thinkable delayed choices needs a corresponding change of the experimental setup.

Indeed, what's objective according to QT depends on the specific experimental setup, and this is in contrast to the "deterministic view" of (E)PR, which makes this view "unrealistic" rather than being "realistic" as claimed by (E)PR.

#### DrChinese

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The entire EPR paper is flawed...
It is a great paper that concludes with the same position you espouse: that the observer reveals a pre-existing local property. Of course, Bell showed us that is not a viable position.

Discussing this is the stuff for a different thread, so with this I will bow out.

#### vanhees71

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Gold Member
I don't espouse anything of the EPR paper. To the contrary I say that QT is correct and the EPR prejudice of predetermined values is flawed. The EPR paper is only hyped, because Einstein is a co-author, and ironically it doesn't even make Einstein's quibbles with QT clear (according to Einstein himself).

I follow the minimal interpretation, i.e., the measurement (not the observer who is not necessarily directly interacting with anything measured, he's only reading off a measurement protocol and chooses different sub-ensembles in the here discussed example) leads with the probabilities given by the QT formalism to the outcomes for the values of the measured observable, and nothing else. There's nothing hidden or anything. If, according to the state preparation, the observable as an indetermined value, then this observable is indetermined, and that's not because of lack of knowledge of the observer but that's inherent in nature, and it's described by the state (i.e., a statistical operator) the system is prepared in.

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