How To Experimentally Confirm the Wigner-Von Neumann Interpretation

[ChadGPT]

TL;DR Summary

I propose a relatively simple way to test whether or not orthogonal polarizers marking which-path information alone destroys the interference pattern or actually measuring the polarization states destroys the interference pattern.

Consider a simple quantum eraser setup using polarizers: An incident beam polarized at 45º is sent towards a double slit. After slit A there is a horizontal polarizer and after slit B there is a vertical polarizer. At the back screen, if we run this experiment, we will see a particle pattern and no interference pattern. However, if we add a 45º diagonal polarizer before the back screen, the interference pattern reappears! As confirmed here: https://sciencedemonstrations.fas.h...-demonstrations/files/single_photon_paper.pdf

The generally accepted interpretation of what is going on is represented by what is stated in that paper, here:

For single photons, the double-slit interference pattern can be made to disappear by using a marker. [...]the marker consists of two, mutually perpendicular, polarizing filters placed in front of the double-slit. Each filter covers only one slit and “marks” the photon passing through that slit with its polarization. A single-slit pattern is all that remains. One does not need to actually measure the photon’s polarization state to determine which path it took to reach the detector. The mere fact that the which-path information is available is enough to destroy the interference pattern. By placing a third polarizer, oriented at 45º with respect to the other two polarizers, before the camera, the double-slit interference pattern is once more restored! All photons emerging from the third polarizer have the same polarization state and thus the which-path information is erased; the third polarizer is the quantum eraser.

This interpretation states that the orthogonal polarizers at the slits determine the which-path information and thus destroy the interference pattern. It is not necessary that we actually measure the polarization states to know which path they went through. Placing the diagonal polarizer before the screen "unmarks" the which-path information, such that it is now impossible to determine which slit the photons came through to get to the back screen, and thus the interference pattern reappears.

One thing this experiment definitively seems to confirm is that wave function collapse* is not a permanent irreversible process, otherwise an interference pattern could not be recovered by the presence of the diagonal polarizer at the back screen.

However, it is not so clear to me that the above interpretation is confirmed by this experiment. The above interpretation suggests that "One does not need to actually measure the photon's polarization state to determine which path it took to reach the detector. The mere fact that the which-path information is available is enough to destroy the interference pattern." Interpretations, such as the Wigner and Von Neumann interpretations, which suggest that it is necessary to actually measure the photon's polarization state to determine which path it took to reach the detector in order to cause collapse, seems to be refuted.

Yet, as it turns out, (in the case with no diagonal polarizer before the screen) even if the orthogonal polarizers marking the which-path information does NOT cause "collapse", we STILL do not see an interference pattern!

Assuming that the orthogonal polarizers do not cause collapse, the total wave function Ψ at the screen is a superposition of the wave functions from both slits. The one from slit A is horizontal polarized ψA∣H⟩ and the one from slit B is vertically polarized ψB∣V⟩ giving us Ψ=ψA∣H⟩+ψB∣V⟩ at the back screen. The interference pattern is given by the intensity distribution, which is the square of the amplitude of the wave function: I=∣Ψ∣²=∣ψA∣H⟩+ψB∣V⟩∣². However, since ∣H⟩ and ∣V⟩ are orthogonal (⟨H∣V⟩=0), the cross terms vanish. Therefore, I=∣ψA∣²+∣ψB∣².

There is no interference pattern even if the orthogonal polarizers do not cause a collapse. Therefore, we still do not know for sure if we need to actually measure the photon's polarization states to determine which path it took to reach the screen in order to cause collapse or not.

One way of solving the question once and for all would be to introduce a BBO crystal before the setup, creating an entangled pair of photons that are H/V polarized. Send an incident beam into a BBO crystal, resulting in an entangled pair consisting of a signal photon heading to the double slit apparatus, and an idler photon heading to an absorber. (the idler's path to the absorber is shorter than the signal's path to the double slit).

Now what we have is, instead of a 45º polarized incident beam being sent to the double slit, a beam of photons which are in a superposition of being both horizontally and vertically polarized being sent to the double slit.

What we should see in this new scenario is that when there is no diagonal polarizer before the screen, there is no interference pattern. But when there is a diagonal polarizer before the screen, we see the interference pattern reappear. This is because the wave function includes the photon as passing through both slits simultaneously, since it is in a superposition of being both horizontally and vertically polarized.

Even if we assume that the orthogonal polarizers do cause collapse, we should still see an interference pattern at the back screen because the diagonal polarizer before the back screen erases the which-path information.

Right?

Now, if this is correct, and we should see the interference pattern with the diagonal polarizer in place just as before, we can now test to see if measuring the photon's polarization state to determine the path it took to the slide actually makes a difference or not, using the entangled idler photon.

On the idler's path, we can now remove the absorber and instead place a calcite crystal, which directs the photon into an upper path if it is horizontally polarized and a lower path if it is vertically polarized. On the upper path we place a detector D1 and on the lower path we place another detector D2. If we get a detection at D1 we know that the entangled signal photon was vertically polarized and therefore went through slit B to get to the back screen, and vice versa for D2. (again, the idler path to D1 or D2 is shorter than the signal path to the screen)

Now, what we should see at the back screen is quite shocking: Even though the diagonal polarizer is still in front of the back screen, we no longer see an interference pattern. We cannot see an interference pattern, because we know which path the photon took to reach the back screen, such that it could not have taken both paths and interfered with itself. We thus confirm that it is not the polarizers marking the path that causes the collapse, but is actually measuring the polarizations that causes collapse.

Where did I go wrong?

* I am using the term "collapse" here out of convenience even though I am well aware that "collapse" is now a controversial term and there is much disagreement over it. Let's not argue of this usage. You know what I mean. if there is a better word that is just as easy to use, please let me know.

 

[PeroK]

One thing this experiment definitively seems to confirm is that wave function collapse* is not a permanent irreversible process,

You need to learn some basic QM. QM works by summing complex probability amplitudes. See section 6 of these notes on repeated Stern-Gerlach experiments:

http://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

 

[ChadGPT]

You need to learn some basic QM. QM works by summing complex probability amplitudes. See section 6 of these notes on repeated Stern-Gerlach experiments:

http://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

Thanks, I will read that. Looks like a good resource. But I am aware that the math of QM works by summing complex probability amplitudes. I was merely pointing out, in this side-note not very pertinent to the main issue of the thread, that it would be incorrect for someone to think that the orthogonal polarizers results in a state projection that causes there to be definite individual physical particles going through one or the other slit with a definite polarization. If that were the case the second diagonal polarizer could not recover the interference pattern. If no one thinks that... great! Like I said, it was just a side-note. :)

 

[PeroK]

Your analysis suggests that you are thinking in terms of definite things happening at these intermediate points of the experiment. Instead, the wavefunction evolves. The only real collapse is the final measurement, when the screen records a photon. That is irreversible.

In Cresser's notes, he cuts through the lazy analysis of the SG experiment and presents something much more quantum mechanical. In particular, intermediate SG magnets or polarizers are not measurements. But, they do force the wavefunction to evolve in a specific way.

 

[PeroK]

If you want to really understand QM and not just say what happens, then likewise you have to drop the lazy heuristic of "which-way" information.

I'm sure this was explained in a previous thread.

 

[ChadGPT]

If you want to really understand QM and not just say what happens, then likewise you have to drop the lazy heuristic of "which-way" information.

I'm sure this was explained in a previous thread.

No, no one has ever suggested to me that "which-way" information is a lazy heuristic. I think I just have a different approach than you. Which should be fine. I'm trying to understand things conceptually, rather than just mathematically (they really do offer Conceptual Physics courses on college campuses!) I can certainly appreciate the clarity that the math offers, but I do want to "just say what happens" because I think it is useful to do so, just like gedanken experiments are useful.

On that topic, I think it was you in my previous thread who suggested I just run the math with regard to that question instead of just trying to say what happens. Well I did, here:

Assuming that the orthogonal polarizers do not cause collapse, the total wave function Ψ at the screen is a superposition of the wave functions from both slits. The one from slit A is horizontal polarized ψA∣H⟩ and the one from slit B is vertically polarized ψB∣V⟩ giving us Ψ=ψA∣H⟩+ψB∣V⟩ at the back screen. The interference pattern is given by the intensity distribution, which is the square of the amplitude of the wave function: I=∣Ψ∣²=∣ψA∣H⟩+ψB∣V⟩∣². However, since ∣H⟩ and ∣V⟩ are orthogonal (⟨H∣V⟩=0), the cross terms vanish. Therefore, I=∣ψA∣²+∣ψB∣².

There is no interference pattern even if the orthogonal polarizers do not cause a collapse.

In retrospect, it was a fairly simple answer to that previous question, and not very hard to just say: "There is no interference pattern even if the orthogonal polarizers do not cause collapse and the superposition is maintained throughout." Now I'm on to trying to settle the question that this raises.

 

[PeroK]

No, no one has ever suggested to me that "which-way" information is a lazy heuristic.

I'm suggesting it now.

Look at the wavefunction, superposition and amplitudes if you want to understand what's happening. That's what I suggested in your previous thread

It's like studying biology without looking at the genes. You can have heuristic arguments, but the real understanding is in the genome.

 

[Morbert]

Now, what we should see at the back screen is quite shocking: Even though the diagonal polarizer is still in front of the back screen, we no longer see an interference pattern. We cannot see an interference pattern, because we know which path the photon took to reach the back screen, such that it could not have taken both paths and interfered with itself. We thus confirm that it is not the polarizers marking the path that causes the collapse, but is actually measuring the polarizations that causes collapse.

The the presence or absence of an interference pattern across all experimental runs can be anticipated by understanding the dynamics of the experiment, including any polarizers or BBO crystal, and is not contingent on a particular interpretation. In what way do you think such an experiment challenges the Wigner/von Neumann interpretation?

 

[gentzen]

How To Experimentally Confirm the Wigner-Von Neumann Interpretation​

[...]

Where did I go wrong?

* I am using the term "collapse" here out of convenience even though I am well aware that "collapse" is now a controversial term and there is much disagreement over it. Let's not argue of this usage. You know what I mean. if there is a better word that is just as easy to use, please let me know.

You did go wrong in your assumption that writing more text would make it easier for us to understand what is bugging you. You went wrong in assuming that there is a Wigner-von Neumann interpretation, you went wrong in assuming "You know what I mean".

You also went wrong in assuming that ChadGPT is just a harmless joke. Your texts read as if you would understand most of the maths, but how can I know that you didn't use the assistance of ChatGPT? (Not sure why PeroK keeps harping that "You need to learn some basic QM".) Also note that PeterDonis especially skeptical of ChatGPT: https://www.physicsforums.com/insights/why-chatgpt-is-not-reliable/

The common language statement that "marking which-path information"... "destroys the interference pattern" is easy to translate into math: $c_l(x)\ket{\psi}\otimes\ket{\phi_h} + c_r(x)\ket{\psi}\otimes\ket{\phi_v}$. If you measure the $\ket{\psi}$ component by a screen while $\ket{\phi_h}$ and $\ket{\phi_v}$ are still orthogonal to each other (such that the marking is reliable), you get the probability distribution $|c_l(x)|^2+|c_r(x)|^2$. If you first filter both $\ket{\phi_h}$ and $\ket{\phi_v}$ to a common state $\ket{\phi_d}$, and then measure the $\ket{\psi}$ component of $c_l(x)\ket{\psi}\otimes\ket{\phi_d} + c_r(x)\ket{\psi}\otimes\ket{\phi_d}$, you get the probability distribution $|c_l(x)+c_r(x)|^2$.

A similar analysis can also be done for the "fringe and anti fringe interference pattern" mentioned in your previous thread. And my impression is that you basically even know how to do those analyses. But there seems to be something bugging you, related to all that talk about "measurement" and "collapse".

 

[PeroK]

(Not sure why PeroK keeps harping that "You need to learn some basic QM".)

I believe the basics are important. They are the foundations on which everything depends. You see a lot of threads where the confusion is a mixture of a fundamental lack of understanding of QM and the specific details of an experiment.
Which I suspect is the case here.

 

[ChadGPT]

The the presence or absence of an interference pattern across all experimental runs can be anticipated by understanding the dynamics of the experiment, including any polarizers or BBO crystal, and is not contingent on a particular interpretation. In what way do you think such an experiment challenges the Wigner/von Neumann interpretation?

The Von Neumann-Wigner Interpretation predicts that orthogonal polarizers will not collapse the wave function since the which-path information is not made available to a conscious observer. Standard Quantum Theory predicts the opposite (it not necessary for any conscious observer to actually be able to measure the polarization states, it is enough that they are determined by the presence of the polarizers). I'm merely pointing out that existing experiments have not yet falsified the Von Neumann-Wigner Hypothesis, as for example the experimental results of the simple quantum eraser linked in the OP are consistent with both Von Neumann-Wigner and Standard Quantum Theory (the results are the same in both cases). I'm then submitting a new experimental setup which would actually falsify it (results would be different in one case versus the other), or possibly verify it, and my question is regarding whether or not you all agree that it would falsify the VNWI, and what you think the results of the experiment would be.

 

[ChadGPT]

You went wrong in assuming that there is a Wigner-von Neumann interpretation

??? : https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_interpretation

You also went wrong in assuming that ChadGPT is just a harmless joke. Your texts read as if you would understand most of the maths, but how can I know that you didn't use the assistance of ChatGPT? (Not sure why PeroK keeps harping that "You need to learn some basic QM".) Also note that PeterDonis especially skeptical of ChatGPT: https://www.physicsforums.com/insights/why-chatgpt-is-not-reliable/

I did use the assistance of ChatGPT. I can't produce the math myself but I can read it and mostly understand it. If the math is correct, I don't see the issue. Math is math. The math you produced below describes what I already know is the case. Whether it's expressed in common language or math doesn't seem relevant to what I'm asking.
https://www.physicsforums.com/insights/why-chatgpt-is-not-reliable/

The common language statement that "marking which-path information"... "destroys the interference pattern" is easy to translate into math: $c_l(x)\ket{\psi}\otimes\ket{\phi_h} + c_r(x)\ket{\psi}\otimes\ket{\phi_v}$. If you measure the $\ket{\psi}$ component by a screen while $\ket{\phi_h}$ and $\ket{\phi_v}$ are still orthogonal to each other (such that the marking is reliable), you get the probability distribution $|c_l(x)|^2+|c_r(x)|^2$. If you first filter both $\ket{\phi_h}$ and $\ket{\phi_v}$ to a common state $\ket{\phi_d}$, and then measure the $\ket{\psi}$ component of $c_l(x)\ket{\psi}\otimes\ket{\phi_d} + c_r(x)\ket{\psi}\otimes\ket{\phi_d}$, you get the probability distribution $|c_l(x)+c_r(x)|^2$.

A similar analysis can also be done for the "fringe and anti fringe interference pattern" mentioned in your previous thread. And my impression is that you basically even know how to do those analyses. But there seems to be something bugging you, related to all that talk about "measurement" and "collapse".

The thing bugging me is that the Standard Model gives you the math that predicts the right answer, but if you assume the Standard Model is wrong you still get the same answer. There is thus an ambiguity as to what is actually going on. Therefore, I am proposing a way to settle the ambiguity, and I'm just asking you guys to analyze the setup as I've described it, and tell me if you think it would actually settle the issue, and what you predict the results of such an experiment would be.

If all you all are going to do is critique my understanding and gatekeep because I can't do the math on my own then I can look elsewhere for help with my questions.

 

[Morbert]

The Von Neumann-Wigner Interpretation predicts that orthogonal polarizers will not collapse the wave function since the which-path information is not made available to a conscious observer. Standard Quantum Theory predicts the opposite.

Standard quantum theory will correctly predict the pattern produced on the back screen over many experimental runs, no matter the experimental setup, and the language of standard quantum theory can be consistently framed in terms of a conscious/material divide in line with literature by Wigner and von Neumann, as irreversibility is all but guaranteed once the degrees of freedom of the conscious observer are correlated with the experiment.

Your original post is very long so I can't claim to have read it carefully, but I suspect the mistake you're making is conflating i) collapse in the Wigner sense of an observer discarding an Everettian style wavefunction with the observer in a superposition with ii) the presence/absence of an interference pattern on the back screen which can be predicted with the correct dynamics and traces.

 

[ChadGPT]

I suspect the mistake you're making is conflating i) collapse in the Wigner sense of an observer discarding an Everettian style wavefunction with the observer in a superposition with ii) the presence/absence of an interference pattern on the back screen which can be predicted with the correct dynamics and traces.

The Standard Quantum Theory says that it is interaction with the environment that causes collapse, and mere detection alone is enough to collapse the wave function.

However, the Von Neumann-Wigner Interpretation posits that the which-path information must be made available to a conscious observer in order for there to be a collapse. Mere detection alone is not enough.

These are two mutually exclusive views on what defines a "measurement." Both cannot be correct.

In the simple quantum eraser case where the orthogonal polarizers are in place and there is no diagonal polarizer before the screen, the which-path information is detected but not made available to a conscious observer.

Thus we have two different predictions with this setup: Standard Quantum Theory predicts there will be a collapse of the wave function, and Von Neumann-Wigner predicts there will not be a collapse.

This setup therefore seems like a fairly simple way to test which view is correct, as they make completely opposite predictions. The result of this experiment is a particle pattern at the back screen. This would tend to suggest that a collapse of the wave function occurred, just as Standard Quantum Theory predicts.

However, because of the way the orthogonal polarizers alter the wave function, it turns out that even if there is no collapse we still should see a particle pattern. No interference pattern can emerge even if Von Neumann-Wigner is correct and not collapse occurs. Therefore, this experiment does not test which view is correct.

I have therefore introduced a more complex experiment that should answer the question and settle the matter. This is because if the Standard Quantum Theory is correct the result of the experiment will be no interference pattern, and if Von Neumann-Wigner is right there will be an interference pattern, unlike the previously mentioned situation which resulted in an ambiguity.

My question is simply whether the more complex experiment I have presented will actually produce different results depending on which view is correct, or if I am mistaken.

 

[ChadGPT]

Perhaps if I share an image representing the proposed experiment it will help focus my question:

The source sends single photons at a time. The BBO crystal creates an entangled pair of photons where one is polarized either vertical or horizontal, and the other is the opposite. The signal photon travels the blue line towards the double slit which has orthogonal polarizers, and there is a diagonal polarizer before the back screen R3. The idler photon travels the red line and just ends up at an absorber.

QUESTION #1: According to Standard Quantum Theory we should get a particle pattern at R3, right?

QUESTION #2: But according to Von Neumann-Wigner, since no which-path information is ever made available to any conscious observers, we should get an interference pattern at R3. This is because there are no optics issues preventing the interference pattern from showing in the case were there is no collapse, right?

 

[Morbert]

The Standard Quantum Theory says that it is interaction with the environment that causes collapse, and mere detection alone is enough to collapse the wave function.

However, the Von Neumann-Wigner Interpretation posits that the which-path information must be made available to a conscious observer in order for there to be a collapse. Mere detection alone is not enough.

These are two mutually exclusive views on what defines a "measurement." Both cannot be correct.

In the simple quantum eraser case where the orthogonal polarizers are in place and there is no diagonal polarizer before the screen, the which-path information is detected but not made available to a conscious observer.

Thus we have two different predictions with this setup: Standard Quantum Theory predicts there will be a collapse of the wave function, and Von Neumann-Wigner predicts there will not be a collapse.

Standard quantum theory is used to compute the likelihood of outcomes of experimental tests. It does not commit you to a particular understanding of the language of the theory, so long as experiments are modeled appropriately.

In the simple case where the orthogonal polarizers are in place without a diagonal polarizer, quantum theory will predict no interference pattern. This is consistent with von Neumann's and Wigner's accounts of quantum theory. The contradiction you imply is not there.

 

[ChadGPT]

In the simple case where the orthogonal polarizers are in place without a diagonal polarizer, quantum theory will predict no interference pattern. This is consistent with von Neumann's and Wigner's accounts of quantum theory. The contradiction you imply is not there.

In the more complex case which I depicted above, what will Standard Quantum Theory predict? And will its prediction contradict what Von Neumann-Wigner predicts?

 

[PeterDonis]

The Von Neumann-Wigner Interpretation predicts that orthogonal polarizers will not collapse the wave function since the which-path information is not made available to a conscious observer.

Where are you getting your information on the "Von Neumann-Wigner Interpretation"?

Standard Quantum Theory predicts the opposite (it not necessary for any conscious observer to actually be able to measure the polarization states, it is enough that they are determined by the presence of the polarizers).

This is not correct.

A correct statement is that in the double slit experiment, with the orthogonal polarizers present, there will be no interference pattern at the detector, whereas without the polarizers, there will. This both a prediction of "Standard Quantum Theory" (by which I assume you mean the basic math of QM without adopting any particular interpretation) and an experimentally confirmed fact. However, this is true independent of any interpretation, and says nothing about "collapse" at all.

 

[PeterDonis]

I propose a relatively simple way to test whether or not orthogonal polarizers marking which-path information alone destroys the interference pattern or actually measuring the polarization states destroys the interference pattern.

We already know the experimental answer to this question: just the presence of orthogonal polarizers is sufficient to destroy the interference pattern. There is no need to measure the polarization states.

What exactly is an open question here?

 

[PeterDonis]

QUESTION #1: According to Standard Quantum Theory we should get a particle pattern at R3, right?

We do, but not for the reason you think.

First consider the signal arm of your experiment with an ordinary, non-entangled photon as input (i.e., no BBO crystal and no idler photon). Then the diagonal polarizer cancels out the effects of the orthogonal polarizers at the slits, and you get an interference pattern.

However, the fact that in your setup, the photon in the signal arm is entangled with the photon in the idler arm, destroys the interference pattern, regardless of whether there are any polarizers in the double slit setup. If that were not the case, if interference could be produced at all in the signal arm, then it would be possible to set up a scenario to transmit information faster than light, by changing what was done in the idler arm, for example by choosing to measure the idler photon polarization at a different angle, and thereby instantaneously changing whether or not interference was present in the signal arm. This would violate the quantum no signaling theorem. (For a similar scenario, see Exercise 9.6 of Ballentine.)

QUESTION #2: But according to Von Neumann-Wigner, since no which-path information is ever made available to any conscious observers, we should get an interference pattern at R3. This is because there are no optics issues preventing the interference pattern from showing in the case were there is no collapse, right?

Again, where are you getting your information on the "Von Neumann-Wigner" interpretation?

The response I gave above is interpretation independent; it's a prediction of the basic math of QM. So any valid interpretation of QM should agree with it.

 

[DrChinese]

Perhaps if I share an image representing the proposed experiment it will help focus my question:
View attachment 341687
The source sends single photons at a time. The BBO crystal creates an entangled pair of photons where one is polarized either vertical or horizontal, and the other is the opposite. The signal photon travels the blue line towards the double slit which has orthogonal polarizers, and there is a diagonal polarizer before the back screen R3. The idler photon travels the red line and just ends up at an absorber.

It is a quirk of entangled photons that they do NOT produce interference patterns in a setup as you present here. At least not like you imagine. Reference below.

Imagine we have NO polarizers at all in the R3 path. The entangled photons do NOT produce an interference pattern, exactly opposite of your expectation. Since there is no interference in the first place, there is nothing the removed polarizers can do to create it. Now why is that? It turns out that entangled photons lack the coherence necessary to drive the double slit setup in a superposition and produce the usual interference.

You can modify the setup to place a single slit in front of (to the left of) the bottom double slit screen. But if you do, it destroys the entanglement with the photon at the top. Which in turn renders anything you find out from R1/R2 superfluous.

See Experiment and the foundations of quantum physics (1999) by one of the 2022 Nobel winners. See Fig. 2 and related text: "Will we now observe an interference pattern for particle 1 behind its double slit? The answer has again to be negative because by simply placing detectors in the beams b and b' of particle 2 we can determine which path particle 1 took. Formally speaking, the states ... cannot be coherently superposed because they are entangled with the two orthogonal states..."

 

[ChadGPT]

Thank you for your responses @PeterDonis and @DrChinese, I think this conversation is heading in a healthy direction now.

Where are you getting your information on the "Von Neumann-Wigner Interpretation"?

It is just commonly known as the "consciousness causes collapse" interpretation. There are many sources: https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_interpretation

This is not correct.

But then you say this is correct here:

We already know the experimental answer to this question: just the presence of orthogonal polarizers is sufficient to destroy the interference pattern. There is no need to measure the polarization states.

You've just said what I said about Standard Quantum Theory in your own words. Yet for some reason you said my version was not correct.

What exactly is an open question here?

The open question is whether the presence of orthogonal polarizers destroys the interference pattern because 1) their presence reduces the wave function to a single eigenstate resulting in classical-like behavior, or the presence of the orthogonal polarizers destroys the interference pattern 2) merely due to the principles of wave optics despite the wave function remaining in a superposition throughout.

The photon in the signal arm is entangled with the photon in the idler arm, destroys the interference pattern, regardless of whether there are any polarizers in the double slit setup.

Has this been experimentally verified? I thought about that before but I looked at the Zou, Wang, Mandl (ZWM) experiment and concluded that entangled photons emerging from BBO crystals can produce an interference pattern: http://quantmag.ppole.ru/Articles/experiment/Mandel(1991).pdf

I understand the point about the no signaling theorem, and don't want to go off on a tangent there, but seems as though a photon in a superposition of both horizontal and vertical polarizations should produce an interference pattern at R3 no problem. There would need to be some explanation for why the idler photon, despite distinguishing no which-path information after having impacted the absorber, would nevertheless reduce the wave function to a single eigenstate. Is it just to prevent FTLC?

(For a similar scenario, see Exercise 9.6 of Ballentine.)

That page is omitted on the google books version so unfortunately I don't have access to it atm.

Again, where are you getting your information on the "Von Neumann-Wigner" interpretation?

The response I gave above is interpretation independent; it's a prediction of the basic math of QM. So any valid interpretation of QM should agree with it.

Expressed in rough natural language, the basic math of QM includes the wave function reducing to the probability of a single eigenvalue describing a single photon taking a single path and impacting the back screen. The Von Neumann-Wigner interpretation includes the wave function maintaining a superposition of the probability of many eigenvalues taking both paths, albeit with different polarization states for each path, superposing at the back screen. These are two different scenarios, no?

Now why is that? It turns out that entangled photons lack the coherence necessary to drive the double slit setup in a superposition and produce the usual interference.

Interesting. Though the setup described in Figure 3 of your reference (Dopfer, 1998) seems to describe a situation in which interference can be shown. Also in the ZWM experiment linked above it seems that entangled photons emerging from BBO crystals can indeed produce interference patterns. This suggest to me that entangled photons, at least in some scenarios, are coherent enough to drive the double slit setup in a superposition and produce interference. Though, I'll look over these experiments again to see if I'm missing something.

You can modify the setup to place a single slit in front of (to the left of) the bottom double slit screen. But if you do, it destroys the entanglement with the photon at the top. Which in turn renders anything you find out from R1/R2 superfluous.

I don't think I follow. The single slit would create the coherence we're after? Do you mean by adding a second diagonal polarizer before the slit?

See Experiment and the foundations of quantum physics (1999) by one of the 2022 Nobel winners. See Fig. 2 and related text: "Will we now observe an interference pattern for particle 1 behind its double slit? The answer has again to be negative because by simply placing detectors in the beams b and b' of particle 2 we can determine which path particle 1 took. Formally speaking, the states ... cannot be coherently superposed because they are entangled with the two orthogonal states..."

Yes, but place instead an absorber in the beams of b and b' instead, at a distance shorter than the distance a' and a take to the screen. Do we see an interference pattern then?

 

[Morbert]

In the more complex case which I depicted above, what will Standard Quantum Theory predict? And will its prediction contradict what Von Neumann-Wigner predicts?

Standard quantum theory says any coincident signal/idler detection events that resolve which way information will not produce an interference pattern. This is not contradicted by the conscious observer/material divide of Wigner or the observer/system divide of von Neumann.

Yes, but place instead an absorber in the beams of b and b' instead, at a distance shorter than the distance a' and a take to the screen. Do we see an interference pattern then?

No. The only way to recover an interference pattern is to use an eraser instrument (e.g. Heisenberg lens + detector + coincidence register) to select a conditioned subset of all experimental runs. And, as mentioned before, any account of this experiment in line with Wigner or von Neumann will supervene on these facts, not contradict them.

 

[DrChinese]

1. Interesting. Though the setup described in Figure 3 of your reference (Dopfer, 1998) seems to describe a situation in which interference can be shown.

2. Also in the ZWM experiment linked above it seems that entangled photons emerging from BBO crystals can indeed produce interference patterns. This suggest to me that entangled photons, at least in some scenarios, are coherent enough to drive the double slit setup in a superposition and produce interference. Though, I'll look over these experiments again to see if I'm missing something.

3. I don't think I follow. The single slit would create the coherence we're after? Do you mean by adding a second diagonal polarizer before the slit?

1. The Dopfer setup requires coincidence counting from the 2 sides. There is no visible interference on the lower side alone.

2. Yes, it's true: entangled photons can interfere with each other. Your reference is good, and you can see that also in experiments such as Attosecond-Resolution Hong-Ou-Mandel Interferometry where Fig. 1 shows the pair overlapping in the HOM BS. But... they still don't produce interference patterns individually while still entangled.

3. The standard double slit setup has the single slit before the double slit, per below. The usual explanation is to insure the light is coherent.

 

[PeterDonis]

It is just commonly known as the "consciousness causes collapse" interpretation.

Ok. But then any claim that this interpretation makes different experimental predictions from "Standard Quantum Theory" cannot be right, because the only thing that makes "consciousness causes collapse" viable at all is that it does not make any different experimental predictions--it just puts "collapse" at the furthest possible point, so to speak, in the Von Neumann chain. So your claims that this interpretation does make different experimental predictions (for example that it allows interference under conditions where "Standard Quantum Theory" does not) cannot be right--or else you are using some other interpretation.

 

[PeterDonis]

You've just said what I said about Standard Quantum Theory in your own words.

No, I didn't. You were comparing "Standard Quantum Theory" to "consciousness causes collapse" in terms of what they say causes collapse. But "Standard Quantum Theory" does not say anything at all about "what causes collapse". "Collapse" in "Standard Quantum Theory" is not an actual thing that happens. It's just a mathematical update to our model when we know the result of the measurement.

 

[PeterDonis]

the basic math of QM includes the wave function reducing to the probability of a single eigenvalue describing a single photon taking a single path and impacting the back screen. The Von Neumann-Wigner interpretation includes the wave function maintaining a superposition of the probability of many eigenvalues taking both paths, albeit with different polarization states for each path, superposing at the back screen.

No. The math is the same for any intepretation of QM. If the math is different, you don't have an interpretation of QM: you have a different theory. "Consciousness causes collapse", at least as it appears in the literature I am familiar with, is not a different theory; it's just an interpretation of QM and uses the same math.

 

[ChadGPT]

Thank you everyone for your replies, this is clearing up a lot for me now. Please leave the thread open for a little while longer as I digest these answers and see if I have any more questions.

 

[gentzen]

Thank you for your responses @PeterDonis and @DrChinese, I think this conversation is heading in a healthy direction now.

Glad to hear. Given that you feel less of "If all you all are going to do is critique my understanding and gatekeep" now, let me provide my answer to your reply. It is not intended to "critique your understanding", it is just my personal opinion.

??? : https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_interpretation

Yes, wikipedia created that name. But wikipedia is not a primary source, and doesn't want to be a sort of secondary literature either. There is no evidence that the name Von Neumann-Wigner interpretation was used by anyone before it accidentally got created by wikipedia itself:

I now checked all references (and external links) from the wikipedia article (except the few behind pay walls), and none of them used that unjustified name. The closest was a single use of von Neumann-Wigner quantum theory and multiple uses of von Neumann quantum theory in the article of H. Stapp from 2001

The name von Neumann interpretation was apparently created on 10 January 2010 on wikipedia by the mistake of a single contributor which didn't write anything else on wikipedia. The name Wigner was added on 21 February 2010 in an apparent attempt to fix the previous mistake. Hence this interpretation doesn't deserve the honour of the names of von Neumann and Wigner, one reason being that this honour wasn't even granted intentionally.

It seems that the only one who has seriously argued in favor of "consciousness causes collapse" is Henry Stapp. Wigner did seriously argue for a role of consciousness, but on more subtle general grounds. More widespread is the claim that "This interpretation was hinted at by Von Neumann [Neu55, §VI.1] and later advocated in [LB39, §11], [Wig67]. It was at one time known as the standard interpretation." ([Neu55] -> John von Neumann 1932, [LB39] -> Fritz London and Edmond Bauer 1939, [Wig67] -> Eugene Wigner 1967), apparently even independent of Henry Stapp: (Schreiber, Zvi (1995-01-16). "The Nine Lives of Schroedinger's Cat". arXiv:quant-ph/9501014. Chapter III.3).

My own conclusion from reading the referenced parts (except Wigner) is that they indeed describe the standard interpretation, but that it is a misunderstanding that this would be related to "consciousness causes collapse". To me, making that connection feels feels like arguing over the "Halt" instruction of a Turing machine, its amazing special powers, its absence in real world computers, and the role of consciousness to provide a substitute for it. (Roger Penrose's misuse of Gödel's incompeteness theorem feels like a real world instance of that discussion to me.) What I mean by this is that von Neumann as well as Fritz London and Edmond Bauer explained the analogue of the role of the "Halt" instruction in a Turing machine, and that it is important despite the fact that it won't exist in that literal form in any actual computer.

The thing bugging me is that the Standard Model gives you the math that predicts the right answer, but if you assume the Standard Model is wrong you still get the same answer. There is thus an ambiguity as to what is actually going on. Therefore, I am proposing a way to settle the ambiguity, and I'm just asking you guys to analyze the setup as I've described it, and tell me if you think it would actually settle the issue, and what you predict the results of such an experiment would be.

If there is an issue at all (concerning the standard interpretation or "consciousness causes collapse", or a general "role of consciousness"), then it will be more subtle to settle, compared to merely performing an experiment within reach of current technology.

 

[ChadGPT]

Standard quantum theory says any coincident signal/idler detection events that resolve which way information will not produce an interference pattern. This is not contradicted by the conscious observer/material divide of Wigner or the observer/system divide of von Neumann.

There does seem to be a contradiction though. Consider a double slit experiment with detectors at each slit but which have no memory of their own, and relay the w-w information to a recording device that stores the information in a readable way to a conscious observer. Now run the experiment with the detectors on and the recorders off. Standard Quantum Theory says that the detection events resolve the which way information, and regardless of whether or not it is made available to any conscious observers there will be no interference pattern. The information exists *in principle* in the universe, and that is enough. Yet Von Nuemann-Wigner says that if the recorders are not recording the w-w information, such that it will be impossible for any conscious observer to read it, then we should see an interference pattern despite the fact that the detectors have resolved the which way information. There is a definite contradiction.

No. The only way to recover an interference pattern is to use an eraser instrument (e.g. Heisenberg lens + detector + coincidence register) to select a conditioned subset of all experimental runs. And, as mentioned before, any account of this experiment in line with Wigner or von Neumann will supervene on these facts, not contradict them.

So it seems that Standard Quantum Theory is saying that if w-w information is available *in principle* anywhere in the universe, at the time of measurement, then there will be no interference pattern. And one way to recover the interference pattern after detection is to use an eraser instrument, which fundamentally removes the w-w information from the universe *in principle*. Is that right?

Von -Nuemann Wigner seems to suggest that it is not necessary to erase the w-w from the universe entirely, but merely making it unavailable to be read by a conscious observer would be enough.

 

[ChadGPT]

Ok. But then any claim that this interpretation makes different experimental predictions from "Standard Quantum Theory" cannot be right, because the only thing that makes "consciousness causes collapse" viable at all is that it does not make any different experimental predictions--it just puts "collapse" at the furthest possible point, so to speak, in the Von Neumann chain. So your claims that this interpretation does make different experimental predictions (for example that it allows interference under conditions where "Standard Quantum Theory" does not) cannot be right--or else you are using some other interpretation.

Consider a double slit experiment with detectors at each slit but which have no memory of their own, and which each relay the w-w information to a recording device that stores the information in a readable way to a conscious observer. Now run the experiment with the detectors on and the recorders off. Standard Quantum Theory says that the detection events resolve the which way information, and regardless of whether or not it is made available to any conscious observers there will be no interference pattern. The information exists *in principle* in the universe, and that is enough. Yet Von Nuemann-Wigner says that if the recorders are not recording the w-w information, such that it will be impossible for any conscious observer to ever read it, then we should see an interference pattern despite the fact that the detectors have resolved the which way information. Turn the recorders on and the interference pattern disappears. There is a definite contradiction, and different experimental predictions.

No. The math is the same for any intepretation of QM. If the math is different, you don't have an interpretation of QM: you have a different theory. "Consciousness causes collapse", at least as it appears in the literature I am familiar with, is not a different theory; it's just an interpretation of QM and uses the same math.

If I am right and it indeed makes different experimental predictions, then it would require different math I would think.

 

[ChadGPT]

Thanks fellas, I have two more questions and then I think I'm tapped out:

1) Why isn't an absorber considered an eraser? Is it theoretically possible to recover which-path information from an absorber in some way that is not possible using a diagonal polarizer as an eraser? For instance, the position that the photon hits the absorber might theoretically reveal the path it took to get there. But then again, the position the photon hit the diagonal polarizer, (the atoms that make it up) might also reveal which path information *in principle* or even the air molecules it interfered with on the way might reveal w-w information...

2) What is the accepted explanation for why coincidence counters reveal that the photons distributed themselves in a fringe interference pattern when correlated to one path and an anti-fringe when correlated to the other? Is there some non-miraculous explanation for this?

 

[PeroK]

Is there some non-miraculous explanation for this?

This is the question that prehistorical people asked about thunderstorms, the sun and moon, crops, birth and life. Because they lacked the scientific knowldege to explain them otherwise. In the modern world, QM may appear miraculous to those who are reluctant to study it, but who merely wonder at experimental results.

 

[ChadGPT]

This is the question that prehistorical people asked about thunderstorms, the sun and moon, crops, birth and life. Because they lacked the scientific knowldege to explain them otherwise. In the modern world, QM may appear miraculous to those who are reluctant to study it, but who merely wonder at experimental results.

Hyperbole.

 

[PeroK]

Hyperbole.

More parabolic than hyperbolic, I would have said.