A Is delayed choice remote entanglement of photons derived from TDSE?

[DrChinese]

TL;DR Summary

Is theory around Delayed Choice remote polarization entanglement swapping of photons derived from TDSE or TISE?

Is theory around Delayed Choice remote polarization entanglement swapping of photons derived from Time Dependent Schrodinger equation (TDSE) or Time Independent Schrodinger equation (TISE)? I say the answer is no. I collectively group TDSE and TISE under the umbrella SE. And the following experiments are for us to use to discuss regarding the state of the art in entanglement theory/experiment:

A. High-fidelity entanglement swapping with fully independent sources
Rainer Kaltenbaek, Robert Prevedel, Markus Aspelmeyer, Anton Zeilinger (2008)
Abstract: Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fidelity high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication experiments as well as for novel tests on the foundations of quantum physics.

B. Experimental delayed-choice entanglement swapping
Xiao-song Ma, Stefan Zotter, Johannes Kofler, Rupert Ursin, Thomas Jennewein, Časlav Brukner, Anton Zeilinger (2012)
Abstract: Motivated by the question, which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be "produced a posteriori, after the entangled particles have been measured and may no longer exist". In this work we report the first realization of Peres' gedanken experiment. Using four photons, we can actively delay the choice of measurement-implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator-on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one definite of two mutually exclusive quantum states in which either the photons are entangled (quantum correlations) or separable (classical correlations). This can also be viewed as "quantum steering into the past".

C. Bell's Theorem Without Inequalities
Daniel M. Greenberger; Michael A. Horne; Abner Shimony; Anton Zeilinger (1990)
Abstract: It is demonstrated that the premises of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two‐particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin‐correlation and multiparticle interferometry examples are given of suitable three‐ and four‐particle arrangements, both at the gedanken and at the real experiment level.

I am not debating the importance of SE to QM. What I am saying is that modern entanglement theory requires additional theory that cannot be directly traced back to the SE. And I am using what I consider the farthest possible elements of modern entanglement theory to demonstrate how far away the SE is. Those elements being:

i) Application of SE to polarization states of spin 1 photons;
ii) Creation of entangled photons pairs via parametric down conversion;
iii) Entanglement swapping by use of a Bell State Measurement (BSM) apparatus (requiring indistinguishable photon detections);
iv) Polarization entangling photons from independent sources;
v) Polarization entangling photons by a distant BSM operation;
vi) Polarization entangling photons after they cease to exist; and
vii) Creation of GHZ states (a bonus requirement).

Basically, I am disputing there is any direct derivation or connection of any of these well known and well tested phenomena with the SE. And in fact, since most of these were discovered prior to 2000, I would ask for references that precede this date. Here is a chapter from a 2023 book, entirely about the SE, which contains a chapter on the SE for photons:

A Schrödinger Equation for Light (Daniel R.E. Hodgson)

None of the above 7 items are discussed. However, there are numerous references to Maxwell's equations. Further, there are some basic derivations of an SE for the photon in his E25. That might count for i) above.

But I don't think there exists pre-2000 references reasonably connecting the SE to the experimental results of references A, B or C above. I am asking for those. If the authors of my references were able to deduce everything in their papers from the earlier works using the SE, where are those references?

For example: How do you get the 4 two-particle Bell states (with their Entangled polarization correlations) from the SE? That would be a good start. Bell didn't need anything like that in his 1964 paper: "With the example advocated by Bohm and Aharonov [1957], the EPR argument [1935] is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. ... " Presto, here's a Bell state, and no SE required.

---

So what is the point of even asking this question in the first place? It has been argued by @PeterDonis and others in another thread (and we have discussed off and on at various times) that any new interpretation that recreates the basic SE must naturally lead to predictions fully consistent with all existing entanglement experiments - without any need to explain how. That deduction doesn't really follow, because the entire point of a novel interpretation is to ADD "something" to existing canon in the way of explanation. Maybe that novel explanation itself contradicts an experiment! It should be clear that in the year 2000, the SE had long been left behind as a basis for most entanglement research. Things like quantum nonlocality (remote entanglement swapping) and quantum causality (delayed choice) have no practical analog in the various forms of the SE. So I'm not sure how anyone can make the proposed leap that I am criticizing.

So if someone wants to put forth a new interpretation of QM, to add to an already overloaded list, they at least better address my 3 references. Because you cannot dismiss the incredible theoretical advances of the past 30+ years as being an "obvious" derivation of the SE. And in fact, the SE is not mentioned in any of these references. You really wouldn't expect it too, either, as the well-discussed limitations of the SE as it can be applied to the photon does not naturally lead to the usual Bell states and their quantum nonlocality in the first place.

 

[PeterDonis]

Is theory around Delayed Choice remote polarization entanglement swapping of photons derived from Time Dependent Schrodinger equation (TDSE) or Time Independent Schrodinger equation (TISE)?

You have put this thread in the interpretations subforum, but this question is not really an interpretation question; it's a straightforward mathematical question of what standard QM predicts. What interpretation aspect are you intending to discuss?

 

[PeterDonis]

modern entanglement theory requires additional theory that cannot be directly traced back to the SE.

What additional theory are you talking about? (And again, this does not seem to be an interpretation question. Either standard QM makes correct predictions about these experiments, or it doesn't.)

 

[PeterDonis]

i) Application of SE to polarization states of spin 1 photons;
ii) Creation of entangled photons pairs via parametric down conversion;
iii) Entanglement swapping by use of a Bell State Measurement (BSM) apparatus (requiring indistinguishable photon detections);
iv) Polarization entangling photons from independent sources;
v) Polarization entangling photons by a distant BSM operation;
vi) Polarization entangling photons after they cease to exist; and
vii) Creation of GHZ states (a bonus requirement).

If this is your answer to the question I posed in #3, I don't see that it is a good one.

For purposes of these experiments, the only aspect of photon polarizations that is relevant is that they lie in the same Hilbert space as qubits, i.e., the spin-1/2 Hilbert space. Non-relativistic QM and the SE handles this just fine. All the complexities involved with photon propagation through space are irrelevant, because in these experiments the spatial paths followed by the photons are determined by the experimenters and are not allowed to vary in ways that would involve any of those complexities. And all the complexities involved with photons interacting with matter are also irrelevant, because they are buried in the details of the photon preparation processes and the photon detectors and don't affect the aspects that are significant for things like entanglement swapping. As far as analyzing entanglement swapping goes, you can treat the preparations and the detections as black boxes.

And once you have that as a basis, all of the items you list are accounted for the same way you would account for them if the experiments were done with electrons or neutrons or other massive spin-1/2 particles for which non-relativistic QM and the SE are already known to work. And the results would have all of the same counterintuitive features that make these experiments such a challenge for alternative models, for reasons which I posted in the other thread you reference, and which you agreed with. In other words, the aspects that are actually significant for discussing the counterintuitive aspects are completely "orthogonal", if you will, to the aspects that make photons different from massive spin-1/2 particles. The latter aspects can safely be ignored when analyzing the counterintuitive aspects.

In short, I simply do not see the fact that photons are used in these experiments as a problem for analyzing them using non-relativistic QM and the SE. Sure, if you want to get into the gory details of how to justify using the non-relativistic approximation for photons under these conditions, you're going to have to get into the weeds of QFT--but nobody disputes that that can be done either. The physicists who are actually doing these experiments don't appear to view this as an issue at all. In some papers they explicitly write down non-relativistic photon wave functions. (To be fair, there are also some papers that use a QFT framework and write down occupation numbers of Fock states. But that seems to be more a matter of personal preference than anything else.)

 

[PeterDonis]

if someone wants to put forth a new interpretation of QM

Overriding the SE is not putting forth a new interpretation of QM. It would be a different theory from standard QM. Or at least standard non-relativistic QM.

If what you actually mean is that you think the relativistic aspects that require QFT to capture are significant, that, in itself, would not be a change to standard QM, but I think you need to make an argument for that claim. That doesn't seem to be what you are claiming, though.

 

[PeterDonis]

the well-discussed limitations of the SE as it can be applied to the photon does not naturally lead to the usual Bell states and their quantum nonlocality in the first place.

Do you have a reference for this claim?

 

[DrChinese]

Do you have a reference for this claim?

You do a great job of turning things around! I'm the one asking for references!! No matter how I ask, all I ever see is self-quotes. And by the way, I already provided a reference for what I said, from a recent textbook exclusively on the SE.

A Schrödinger Equation for Light (Daniel R.E. Hodgson)

You have put this thread in the interpretations subforum, but this question is not really an interpretation question; it's a straightforward mathematical question of what standard QM predicts. What interpretation aspect are you intending to discuss?

I'm perfectly fine with it being in the main QM area.

 

[PeterDonis]

I'm perfectly fine with it being in the main QM area.

Ok. I have moved it. Please note that that makes interpretation discussions off topic for this thread: the topic is whether standard non-relativistic QM can be used to derive delayed choice entanglement swapping with photons.

 

[PeterDonis]

I'm the one asking for references!!

You made a specific claim; I'll quote it again:

the well-discussed limitations of the SE as it can be applied to the photon does not naturally lead to the usual Bell states and their quantum nonlocality in the first place.

This amounts to the claim that the answer to the title question of this thread is "no". That's not asking for references for other people's answers to the question. That's giving your answer to the question, for which you need to provide a reference.

 

[DrChinese]

I'll say it again: GHZ was not derived from the SE. Quantum teleportation was not discovered because of the SE. And delayed choice was not discovered because of the SE. None of these have the slightest to do with SE, other than they are all a part of standard garden variety QM, no QFT required.

ANY new interpretation MUST be able to address modern entanglement theory and experiment. There is absolutely nothing controversial about this point. And in fact, all EXISTING interpretations must do the same! This is basic scientific method, and applies in all areas of science.

 

[PeterDonis]

I already provided a reference for what I said

As far as I can tell from the abstract, that references says you can treat photons using the Schrodinger Equation.

In any case, the topic of this thread is not the general question of treating photons using the SE. It is treating photons using the SE in one specific case: delayed choice entanglement swapping. As far as I know nobody has claimed that this specific scenario involves any relativistic effects, so the non-relativistic approximation should be fine. Certainly, as I have already posted, it would seem fine if we were doing the experiment with electrons or neutrons or other massive spin-1/2 particles.

So let me ask you another question: suppose someone did a delayed choice entanglement swapping experiment with massive spin-1/2 particles. Would you still be challenging them to provide a derivation of the results using the SE?

 

[DrChinese]

As far as I can tell from the abstract, that references says you can treat photons using the Schrodinger Equation.

In any case, the topic of this thread is not the general question of treating photons using the SE. It is treating photons using the SE in one specific case: delayed choice entanglement swapping. As far as I know nobody has claimed that this specific scenario involves any relativistic effects, so the non-relativistic approximation should be fine. Certainly, as I have already posted, it would seem fine if we were doing the experiment with electrons or neutrons or other massive spin-1/2 particles.

So let me ask you another question: suppose someone did a delayed choice entanglement swapping experiment with massive spin-1/2 particles. Would you still be challenging them to provide a derivation of the results using the SE?

You can perform entanglement swapping with spin 1/2 systems (Hensen et al). But the answer to your question is "no" because you have it backwards. I am not asking anyone to explain well known and accepted theory using the SE. SE has little or nothing to do with delayed choice entanglement swapping. You get this from modern entanglement theory, a la Shimony, Zeilinger, Gisin and a great many others.

If someone says, "I can explain A with the SE, but I assume my explanation also works for B and C", then of course their assumption is immediately suspect. Ask the GHZS authors (citation C above) if they would agree that any explanation using the SE had anything to do with their discovery. They would wonder what you were talking about. Ditto for the discovery of remote entanglement swapping. Ask Wheeler (hypothetical of course) about delayed choice concepts and the SE. Again, he'd wonder what you were talking about.

And for the Nth time: can anybody provide a direct quote that fits my request?

 

[DrChinese]

Ok. I have moved it. Please note that that makes interpretation discussions off topic for this thread: the topic is whether standard non-relativistic QM can be used to derive delayed choice entanglement swapping with photons.

That is not my question at all. Please re-read the title.

The question is whether the SE can be used to derive remote delayed choice entanglement swapping with photons, also GHZ. I am the one saying that standard non-relativistic QM can be used to derive those. SE being a portion of QM, but not normally a relevant tool for modern entanglement experiments.

 

[DrChinese]

As far as I can tell from the abstract, that references says you can treat photons using the Schrodinger Equation.

Not for the experiments I cited it doesn't. And that is precisely my point.

 

[PeterDonis]

SE has little or nothing to do with delayed choice entanglement swapping.

I don't understand this claim. The SE is the dynamical equation for non-relativistic QM. Any QM prediction in the non-relativistic domain has to do with the SE. If you believe the contrary, I would really like to have you explain why, or give me a reference that explains why.

modern entanglement theory

Is there a standard reference for this? Can you give it?

can anybody provide a direct quote that fits my request?

I am unable to even comprehend your position at this point. To me you appear to be saying that entanglement swapping can't be predicted by non-relativistic QM. I know you deny this is the case, but your denial is based on the claim that "modern entanglement theory", even though it is within the non-relativistic domain, doesn't rely on the SE. Which is also a claim I am unable to comprehend. So I can't possibly provide what you are asking for since I don't even understand it.

If you can give me some reference that explains why "modern entanglement theory", even though it is within the non-relativistic domain, somehow does not rely on the SE, that would help.

 

[PeterDonis]

How do you get the 4 two-particle Bell states (with their Entangled polarization correlations) from the SE?

You prepare them in one of those states. The SE is a dynamical equation; it assumes an initial state that you prepare. That doesn't mean you aren't relying on the SE for the dynamics.

If you want to model the preparation process itself, you just take two un-entangled particles and subject them to an appropriate interaction Hamiltonian. Or, to look at it another way, you find a unitary operation that entangles them, and express it as $U = \exp(i H t)$; $H$ is then your interaction Hamiltonian. Similar remarks would apply to operations like the beam splitter that does the entanglement swap. None of that means you aren't relying on the SE; you're just dealing with a situation where the non-trivial unitary operations happen over very short time scales (i.,e., the non-trivial interaction Hamiltonians are only "turned on" for very short times), so the time evolution looks very different from the textbook cases of the SE.

If this is really the crux of the issue here, I think we might be talking past each other. You say you agree that standard non-relativistic QM can account for the results. That's really the main point that matters. Whether or not you like describing standard non-relativistic QM as "relying on the SE" or not is a matter of words, not physics.

 

[DrChinese]

Modern entanglement theory: entanglement swapping, GHZ, etc. There are thousands of experiments and theory papers in this general area.

SE: a tool to do a job, like a hammer is a tool. SE is not QM, and vice versa. SE is not a tool generally used in papers on entanglement. Instead, think of that canon as the screwdriver tool. Use the right tool for the right job.

All interpretations of QM must be able to account for entanglement experiments. What's there to contest about that statement. I have called for references from anyone who thinks the hammer can do the job of the screwdriver. If you can show me those, we're good. But I can't provide you proof that the hammer can't do the job of the screwdriver, because the craftsmen all know which tool to pull out already. The SE was first presented in 1926. Pretty obvious that hammer isn't going to do the job forever.

 

[PeterDonis]

All interpretations of QM must be able to account for entanglement experiments.

True, but irrelevant to this thread, since we've moved it out of the interpretations subforum.

 

[PeterDonis]

Modern entanglement theory: entanglement swapping, GHZ, etc. There are thousands of experiments and theory papers in this general area.

Ok, fine, but I don't have time to read thousands of papers. Is there a standard reference that explains what this thing is and how it doesn't rely on the SE?

I can't provide you proof that the hammer can't do the job of the screwdriver

I didn't ask for "proof". I asked for a reference that explains what the heck the screwdriver is in the first place. The only references I've read all talk about the hammer. I haven't seen any reference that talks about the screwdriver that isn't a hammer.

 

[Demystifier]

Entanglement (of photons) is a consequence of superposition principle in the multi-partite Hilbert space. The multi-partite Hilbert space is (a part of) Hilbert space on which the Hamiltonian $H$ of QED acts. The superposition principle is a consequence of the linearity of the Schrodinger equation with the QED Hamiltonian $H$. Hence entanglement can be explained by TDSE. The fact that some aspects are discussed with Maxwell equations rather than with TDSE just means that some aspects are discussed in the Heisenberg picture rather than the Schrodinger one. But the two pictures are equivalent (at least formally, up to Haag-theorem-like subtleties).

 

[DrChinese]

A. You prepare them in one of those states. The SE is a dynamical equation...

B. If this is really the crux of the issue here, I think we might be talking past each other. You say you agree that standard non-relativistic QM can account for the results. That's really the main point that matters. Whether or not you like describing standard non-relativistic QM as "relying on the SE" or not is a matter of words, not physics.

A. Again, you have it backwards. We can read any entanglement swapping paper to see how the experiment is performed. We can also read the theory they rely upon. The SE isn't mentioned. Ever.

B. Of course we are talking past each other, you haven't read the title of the thread or what I have requested. Of course we agree "standard non-relativistic QM can account for the results" and I have said that over and over. The SE, as a tool, is not an important element of modern entanglement theory or experiment. And by modern, I mean the work of the last 30 years or so.

If anyone has a reference that says something to the effect that: application of the SE led to the discovery of entanglement swapping... then please, share that.

You, Peter, claim that it (SE) is a critical element of these developments - the theory around modern entanglement - and I deny it. Having read a thousand papers at least on the subject, I have never seen it mentioned. But who knows, maybe I missed it and you didn't. Certainly by now you know how many references I have on various sides of entanglement. So... instead of asking me to cite more references (which I already had), why don't you back up a single claim you make with a matching reference?

Or perhaps acknowledge that ALL QM interpretations SHOULD be able to account for a relevant set of modern entanglement experiments. That is what I am really saying (since you don't want to discuss particular interpretations in this forum). Certainly the most amazing of those experiments, those worth of a Nobel. If we were discussing modern cosmology, we would expect new theory to account for existing phenomena - including the latest results. Well, that applies here in QM too.

Hey, but if I'm wrong, I'm happy to learn something new. That's what I'm here for.

 

[PeterDonis]

We can read any entanglement swapping paper to see how the experiment is performed.

Sure.

We can also read the theory they rely upon.

Not that I can see. I've read the experimental papers you linked to in the OP. There is no theory in them, if by "theory" we mean actually deriving anything from the general principles of QM. There are just states written down that are pulled out of the air, and it is simply assumed that the experimental operations being performed take this state to that other state.

If we can read the theory they rely upon somewhere else, then please tell me where.

 

[DrChinese]

Entanglement (of photons) is a consequence of superposition principle in the multi-partite Hilbert space. The multi-partite Hilbert space is (a part of) Hilbert space on which the Hamiltonian $H$ of QED acts. The superposition principle is a consequence of the linearity of the Schrodinger equation with the QED Hamiltonian $H$. Hence entanglement can be explained by TISE. The fact that some aspects are discussed with Maxwell equations rather than with TISE just means that some aspects are discussed in the Heisenberg picture rather than the Schrodinger one. But the two pictures are equivalent (at least formally, up to Haag-theorem-like subtleties).

A leads to B, B leads to C, C leads to D... Yes I get all that. You may as well say the addition is responsible for modern entanglement theory. There is always a precursor. In this case: Delayed Choice Entanglement Swapping in 2012, SE from 1926. Maxwell even earlier. Come on.

We aren't supposed to discuss any particular interpretation in this thread (since it was moved at @PeterDonis request). But even Bohmian theory must be able to account for the experiments I reference in the OP, wouldn't you agree? Since all should be held to the same strict scientific standards...

 

[PeterDonis]

it was moved at @PeterDonis request

No, it was moved because of the response you gave in post #7. I did not request that it be moved; I asked you, the OP, what the thread was supposed to be about. If it's supposed to be about a specific interpretation, I'll move it back to the interpretations subforum.

 

[DrChinese]

If we can read the theory they rely upon somewhere else, then please tell me where.

Funny, they provided a full list of references. So maybe start there.

And somehow, one of the authors eekked out a Nobel from that work. So I kinda guess that makes it generally accepted science now. And no one is doubting where they got their theory from, being as the references they provide are all ground-breaking works themselves.

 

[DrChinese]

No, it was moved because of the response you gave in post #7. I did not request that it be moved; I asked you, the OP, what the thread was supposed to be about. If it's supposed to be about a specific interpretation, I'll move it back to the interpretations subforum.

I trust you to know where this best belongs. I placed it in Interpretations because I thought that was perhaps a better audience. However, it is not about any particular interpretation. What I assert applies to all.

 

[PeterDonis]

they provided a full list of references. So maybe start there.

Sigh. If you're going to claim that there is this theoretical area called "modern entanglement theory", that does non-relativistic QM without using the SE, it would seem to me that the least you could do would be to provide some kind of standard reference for this claimed theoretical area instead of just pointing me at a list of, by my count, 55 references, 48 of which (all but the first in the first paper) don't even have titles provided so I can't even do a quick check to see if they're likely to be relevant. All the more so as I can go into QM textbooks published a lot more recently than 1926 and still find entanglement treated in the standard way using the SE.

If you can't point me at some kind of standard reference for this "modern entanglement theory" that doesn't rely on the SE, I'm just going to bow out of this thread.

 

[PeterDonis]

it is not about any particular interpretation. What I assert applies to all.

Then it belongs here.

 

[PeterDonis]

one of the authors eekked out a Nobel from that work. So I kinda guess that makes it generally accepted science now

The fact that delayed choice entanglement swapping is an experimentally demonstrated phenomenon is indeed "generally accepted science".

That, however, does not establish that your claim that there is this thing called "modern entanglement theory" that does non-relativistic QM without using the SE is "generally accepted science".

 

[Demystifier]

We can read any entanglement swapping paper to see how the experiment is performed. We can also read the theory they rely upon. The SE isn't mentioned. Ever.

But SE is implicitly there, it doesn't need to be mentioned explicitly. For instance, whenever a paper refers to measurement, it is understood that the system interacts with the measuring apparatus, due to which the state of the system+apparatus changes. This interaction and change are described by the TDSE, even if this is not mentioned explicitly because it is understood that the reader should already know that.

 

[DrChinese]

A. All the more so as I can go into QM textbooks published a lot more recently than 1926 and still find entanglement treated in the standard way using the SE.

B. If you can't point me at some kind of standard reference for this "modern entanglement theory" that doesn't rely on the SE, I'm just going to bow out of this thread.

A. That's what I've requested: Something between 1926 and 2000 that uses the toolkit of the SE to describe/deduce/derive entanglement swapping, GHZ, and/or delayed choice.

B. I can assure you, the references from my references don't mention the SE. SE as a calculational tool is just a part of non-relativistic QM, so that shouldn't be a surprise. So to point out, per your request for a standard reference: Here is the very first appearance of the GHZ theorem, which contains no references whatsoever to the SE. In fact, it only has 4 references.

Going Beyond Bell's Theorem (the link is a 2007 reprint.)
Daniel M. Greenberger, Michael A. Horne, Anton Zeilinger (1989)

Its references:
1. A. Einstein, B. Podolsky, and N. Rosen, (1935) Phys. Rev., 47, 777.
2. N. Bohr, (1935) Phys. Rev., 48, 696.
3. D. Bohm, (1951) “Quantum Theory”, Prentice-Hall, New York.
4. J.S. Bell, (1965) Physics (N.Y.) 1, 195.

Note that reference 3 is a textbook that does include a discussion of the SE, among numerous other topics in non-relativistic QM. But the only thing taken from that reference is an entangled wave function: ψ = ( |↑↓> − |↓↑> ) / 2. That was about all that existed in entanglement theory in 1951. SE is not a part of this.

I could provide the same for the other seminal theoretical papers on modern entanglement theory, such as: Bell's Theorem (1964), Quantum Teleportation (1993), Bell Tests Enforcing Strict Einsteinian Locality (1998), Peres' Delayed Choice Entanglement Swapping (1999). All of these published prior to 2000, so they have been around over 25 years. This canon should be familiar to anyone who studies entanglement. None have the SE at their core, other than it's all part of standard QM.

As I mention, these concepts must be satisfactorily explained by any and all interpretations of QM, and just saying "it's equivalent to standard QM" won't suffice. This is new theory and experiment, and raises the bar.

 

[Demystifier]

None have the SE at their core, other than it's all part of standard QM.

SE is so deep in their core that you don't even see it.

 

[DrChinese]

SE is so deep in their core that you don't even see it.

This is circular reasoning. The SE is not being used to develop new theory. The new theory I mention has nothing particular to do with the SE. Why pick the SE to hang your hat on in the first place? What about the Born rule, or any of a dozen other major foundational components of QM? Heisenberg Uncertainty Principle? Is that the cornerstone of modern entanglement theory too?

The obvious objection one might have is: One's preferred interpretation cannot reasonably address these modern developments... and so one must fall back on tired arguments to keep it on the table. Marrying one's interpretation to reasoning from nearly a century ago, without updating for new developments, is a perversion of the scientific method. That was why EPR ultimately failed - it worked until new developments came along that were not envisioned until 30 years later.

 

[PeterDonis]

Here is the very first appearance of the GHZ theorem, which contains no references whatsoever to the SE.

That's because the GHZ theorem, Bell's theorem, etc. have nothing to do with QM. They aren't even about QM. They are about ruling out particular kinds of models that aren't QM. Of course they aren't going to talk about the SE because the alternative models they are ruling out have nothing to do with the SE. That is no argument that QM doesn't use the SE when it deals with entangled wave functions.

 

[DrChinese]

That's because the GHZ theorem, Bell's theorem, etc. have nothing to do with QM. They aren't even about QM. They are about ruling out particular kinds of models that aren't QM. Of course they aren't going to talk about the SE because the alternative models they are ruling out have nothing to do with the SE.

This news would be quite a shock to a lot of scientists, who believe they are at the forefront of Quantum Mechanics research.

Bell: Makes a specific quantum mechanical prediction that was previously unknown.
GHZ: Makes a specific quantum mechanical prediction that was previously unknown.
Entanglement swapping: Makes a specific quantum mechanical prediction that was previously unknown.
Monogamy of Entanglement: Makes a specific quantum mechanical prediction that was previously unknown.
Delayed Choice: Makes a specific quantum mechanical prediction that was previously unknown.

Each of the related papers make specific predictions about QM. Those predictions happen to rule out theories that cannot keep up, true, but they represent giant leaps in our understanding of QM. That is in fact the precise objective of all scientific work, theory and experiment interplaying to advance science. Older interpretations, along with newer ones, need to pass these stringent tests to remain viable. Or be moved to the graveyard that also contains all those ol' Local Realistic interpretations.

 

[PeterDonis]

Bell: Makes a specific quantum mechanical prediction that was previously unknown.

What prediction?

GHZ: Makes a specific quantum mechanical prediction that was previously unknown.

What prediction?

 

[Dale]

Is theory around Delayed Choice remote polarization entanglement swapping of photons derived from Time Dependent Schrodinger equation (TDSE) or Time Independent Schrodinger equation (TISE)? I say the answer is no.

So are you saying that there is another theory that is used instead? Similar to how circuit theory is in some sense a separate theory from Maxwell’s equations. And most circuit work does not use Maxwell’s equations?

since most of these were discovered prior to 2000, I would ask for references that precede this date.

I don’t think that is a reasonable restriction. Links between disparate theories can certainly be found later.

 

[PeterDonis]

Peres' Delayed Choice Entanglement Swapping (1999)

You didn't give a reference here, but I assume you mean this paper:

https://arxiv.org/abs/quant-ph/9904042

I had read it previously, but I've just read it again to make sure I wasn't missing anything. Your statement that there is no explicit mention of the Schrodinger Equation in that paper is of course correct. However, there is also no sign whatever of any kind of "modern entanglement theory" that doesn't use the SE. There is, in fact, no deriving of anything at all, in terms of showing from first principles the things you say you are concerned about: how entangled states are prepared, how the "swapping" operation is performed, and how the particles are detected. All of those things are simply assumed in the paper, with no derivation whatever.

In short, this paper is simply irrelevant to the discussion we are having here, which is about how these results are derived from the general principles of non-relativistic QM and the particular Hamiltonians that are relevant for the specific scenarios being discussed.

You might object that such details are to be found in the references of that paper. Let's see. No reference is given at all for the paper's assumption that pairs of spin-1/2 particles can be prepared in the given entangled states, or that spin measurements can be carried out on spin-1/2 particles. For the Bell state measurement that does the swapping, the reference given is reference [5]. But all that reference does is derive the eigenstates and eigenvalues for the "Bell state operator", i.e., the unitary operator that mathematically models the "swap" operation. In other words, as I have already posted, this is the unitary operator $U = \exp( i H t )$ that is the "time evolution" operator in the SE for the time period during which the swap operation is being done. It is not any kind of "entanglement theory" that somehow bypasses the SE.

I emphasize that I am not in any way discounting the huge contribution to our understanding of QM that these experiments provide. They deserve all of the praise they get. They just don't, as far as I can see, give any reason to think that the SE is not involved in the theoretical derivation of predictions in non-relativistic QM.

 

[PeterDonis]

Similar to how circuit theory is in some sense a separate theory from Maxwell’s equations. And most circuit work does not use Maxwell’s equations?

Even if this is the intended analogy, the theory would still ultimately depend on the SE, just as circuit theory ultimately depends on Maxwell's equations. Sure, when you use circuit theory, you aren't using Maxwell's equations directly; but if someone asks you to explain why you think circuit theory is correct, your explanation is going to end up relying on Maxwell's equations.

 

[DrChinese]

A. So are you saying that there is another theory that is used instead? Similar to how circuit theory is in some sense a separate theory from Maxwell’s equations. And most circuit work does not use Maxwell’s equations?


B. I don’t think that is a reasonable restriction. Links between disparate theories can certainly be found later.

A. Normal NRQM is not one single element, such as the SE. There are many such elements that make up QM. Picking SE and saying "that's where everything comes from" is not accurate. I am not denying the importance of anything, nor am I saying it's a completely separate theory. Of course everything builds on everything else.

I am denying the important new developments in modern entanglement theory (already listed) were deduced directly with help from the SE. They weren't. The SE is from 1926, and nearly 100 years later we have entanglement theory/experiment that could have never been dreamed of when EPR wrote their seminar paper in 1935.

B. The new stuff did not come from advances in applications of the SE to entanglement problems, and if it were, you (or someone) could show me where that occurred between (say) 1952 and the year 2002. Because most of the new amazing theory on entanglement occurred prior to about 2002. Sure, you might find links after the fact, but obviously SE has not been used for problem solving in entanglement theory or experiment during that 50 year period. For things other than Entanglement, sure, but that's what I am talking about.

And the significance is: quantum theory has been extended to new areas, but interpretations of QM have not kept up. Even new ones drop the ball, which is what started the discussion in the first place.

I'll repeat what I said earlier: If I'm wrong, I'm happy to learn something new. That's what I'm here for. But for the life of me I cannot understand why there are no direct quotes/references that contradict what I am saying about the SE over a 50 year period if everyone else is so sure they are correct. I can't find anything to support that viewpoint, and I've looked deep. By default, what am I to conclude if I can't find it, and there is nothing being offered for me to see where I might be wrong?

 

[DrChinese]

As an example/analogy: Circa 1964, Penzias and Wilson discovered the CMBR. I would hope that would be more or less the death knell for Steady State theories of the universe. But today we have literally hundreds of experiments that detail so much more, and most of those (excluding the WMAP) have nothing in particular to do with the CMBR. With each new experiment, some theories (hypotheses) gain support and others lose support. That's the scientific method.

The same should occur naturally with Interpretations of QM. Many supply specific mechanisms or claims that can now be refuted. For example, some believe that MWI cannot be local, even though it is usually labeled "local". But it would still be a good interpretation even if it were labeled "nonlocal". That would mean it evolved to match the experimentally demonstrated and generally accepted existence of quantum nonlocality. (I am not arguing for or against a particular interpretation). This paper is an example of nonlocal MWI, modified to be in concert with the GHZ experiment (which demonstrates quantum nonlocality). That's the scientific method at work as well.

But just like the example of the CMBR: the theories that were put forth in 1964 cannot be considered on a par with those of today. We've learned too much since! Ditto with what we have learned in all of QM since 1926!

 

[PeterDonis]

Normal NRQM is not one single element, such as the SE.

This is true. But it's also true that in order to make predictions from normal NRQM, you have to use the SE. You also have to use the other elements. But the other elements are not substitutes for the SE. They work along with it. You can't leave any of them out, including the SE.

I am denying the important new developments in modern entanglement theory (already listed) were deduced directly with help from the SE.

That's because they assumed all of the stuff that was already derived--from "normal NRQM", which, as above, requires you to use the SE--along with the other elements it contains. They didn't bother deriving the fact that you can prepare two spin-1/2 particles in the singlet state, or that spin measurements on such particles will be correlated, or that the particles can be propagated from the source to their respective detectors with their spin states remaining the same--because everybody already knew that stuff was true and why belabor the obvious? But if you actually do want to derive all that stuff, guess what? You'll be using "normal NRQM", which, once more, requires you to use the SE--along with the other elements it contains.

the significance is: quantum theory has been extended to new areas, but interpretations of QM have not kept up.

Intepretations are off topic for this thread. If you want to talk about interpretations, I'll move this thread back to the interpretations subforum and just delete pretty much everything that's already been posted. Nobody in this discussion is claiming that QM interpretations all are equally good or all give equally satisfactory accounts of the experiments you are talking about. In this discussion we are talking about your claim that there is a body of theory, independent of any particular interpretation, called "modern entanglement theory" which somehow does NRQM without relying on the SE (and of course on all the other elements that NRQM contains).

 

[Dale]

I can't find anything to support your viewpoint

I don’t have a viewpoint here. I am just trying to understand the debate.

Normal NRQM is not one single element, such as the SE. There are many such elements that make up QM. Picking SE and saying "that's where everything comes from" is not accurate.

OK, so I guess what you are saying is something like Newtonian mechanics is more than Newton’s laws. It includes Newton’s laws but also some force laws like the gravitational law and Hooke’s law. Is that closer to what you are discussing?

If I understand what you are saying, entanglement cannot be derived from SE just like Newton’s law of gravitation cannot be derived from his laws of motion. So in principle a new interpretation of Newtonian mechanics could be compatible with Newton’s laws of motion but not his law of gravitation.

 

[DrChinese]

A. You didn't give a reference here, but I assume you mean this paper:

https://arxiv.org/abs/quant-ph/9904042

B. You might object that such details are to be found in the references of that paper. Let's see. No reference is given at all for the paper's assumption that pairs of spin-1/2 particles can be prepared in the given entangled states...

C. They just don't, as far as I can see, give any reason to think that the SE is not involved in the theoretical derivation of predictions in non-relativistic QM.

A. Yes! (And a mere 25 years old.)

B. Peres included 15 references that cover just such points. For what you mentioned, see reference [8] from 1969, the seminal work on the CHSH inequality using exactly that setup (pairs of spin 1/2 particles). They then reference EPR, Bohm and Bell and their earlier basic theory directly.

But again, no SE anywhere.

C. I have never said otherwise. But SE is not used in predictions for entangled systems. Plenty of other uses, just not that.

---

The bar has been raised quite high in modern times. For those that are unaware of these incredible advances, there is much to learn. And... learning is good.

 

[PeterDonis]

SE is not used in predictions for entangled systems

Because, as I've said repeatedly now, the aspects that are predicted by the SE (along with other elements of "normal NRQM") are simply assumed as true--and for good reason, because they are true and there's no need to belabor their derivation when it's already well established.

You have said nothing to address this point.

 

[PeterDonis]

the seminal work on the CHSH inequality using exactly that setup (pairs of spin 1/2 particles).

It uses that setup. It does not derive that setup from anything more fundamental. It just assumes that such states can be prepared.

 

[Fra]

Is theory around Delayed Choice remote polarization entanglement swapping of photons derived from Time Dependent Schrodinger equation (TDSE) or Time Independent Schrodinger equation (TISE)? I say the answer is no. I collectively group TDSE and TISE under the umbrella SE.

Is your point that analysing entanglement experiments are not done via an initial value problem, with a single preparation and a single hamiltonian evolution via a litteral single schrödinger equation, but with multiple parallell experiments that are related?

/Fredrik

 

[Demystifier]

The SE is not being used to develop new theory. The new theory I mention has nothing particular to do with the SE.

What new theory? Perhaps my reading was superficial, but I haven't noticed that you proposed (or cited a paper about) a new theory.

Why pick the SE to hang your hat on in the first place? What about the Born rule, or any of a dozen other major foundational components of QM? Heisenberg Uncertainty Principle? Is that the cornerstone of modern entanglement theory too?

Yes, Born rule is also a cornerstone of entanglement theory. (HUP maybe not so much, because it's derived from more fundamental principles.)

 

[Demystifier]

The obvious objection one might have is: One's preferred interpretation cannot reasonably address these modern developments...

I don't think it's obvious to anybody but you. Or to put it blatantly, I have no idea what's your point in this whole thread.

 

[Demystifier]

This news would be quite a shock to a lot of scientists, who believe they are at the forefront of Quantum Mechanics research.

Bell: Makes a specific quantum mechanical prediction that was previously unknown.
GHZ: Makes a specific quantum mechanical prediction that was previously unknown.
Entanglement swapping: Makes a specific quantum mechanical prediction that was previously unknown.
Monogamy of Entanglement: Makes a specific quantum mechanical prediction that was previously unknown.
Delayed Choice: Makes a specific quantum mechanical prediction that was previously unknown.

Each of the related papers make specific predictions about QM. Those predictions happen to rule out theories that cannot keep up, true, but they represent giant leaps in our understanding of QM. That is in fact the precise objective of all scientific work, theory and experiment interplaying to advance science. Older interpretations, along with newer ones, need to pass these stringent tests to remain viable. Or be moved to the graveyard that also contains all those ol' Local Realistic interpretations.

Perhaps you have a wrong perception how interpretations of QM are constructed. They are not constructed such that they explain particular QM predictions such as those above. They are constructed such that they explain all predictions at once, because they are constructed so that they explain the general axioms of QM, from which each of the predictions above can be derived.