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

[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.

 

[Demystifier]

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.

Everything comes from a few axioms (or rules), the Schrodinger equation being one of them. See e.g. https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

 

[Demystifier]

The same should occur naturally with Interpretations of QM. Many supply specific mechanisms or claims that can now be refuted.

I strongly disagree.

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.

That's not a good example, because the true issue with MWI (as with the standard QM too) is what it means that MWI is "local" or "nonlocal". This is more philosophy than the scientific method in the narrow sense.

 

[Demystifier]

I am denying the important new developments in modern entanglement theory (already listed) were deduced directly with help from the SE. They weren't.

I think we all agree with that. But do you agree with the rest of us that SE was nevertheless used indirectly? And if you agree, why is that important?

 

[mattt]

TL;DR Summary: Is theory around Delayed Choice remote polarization entanglement swapping of photons derived from TDSE or TISE?

That's a strange question, isn't it?

Those experiments are explained by non-relativistic quantum mechanics, the results of those experiments are predicted by non-relativistic quantum mechanics.

The dynamics in non-relativistic quantum mechanics is defined by the Schrodinger equation (plus update of state after measurement).

So, obviously, the answer to your question is: yes.

By the way, there is no "theory" in those experiments different than non-relativistic quantum mechanics and, optionally, quantum field theory.

 

[PeterDonis]

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".

the true issue with MWI (as with the standard QM too) is what it means that MWI is "local" or "nonlocal". This is more philosophy than the scientific method in the narrow sense.

One more time: interpretations are off topic in this thread.

 

[DrChinese]

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

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

C. I think we all agree with that. But do you agree with the rest of us that SE was nevertheless used indirectly? And if you agree, why is that important?

D. Or to put it blatantly, I have no idea what's your point in this whole thread.

A. I listed those in an earlier post. GHZ, Delayed Choice/Remote Entanglement Swapping (references provided in post #1): none of these existed as theoretical ideas until the 1988 to 2000 time period. And numerous others mentioned here as well.

Surely you must believe that as new cosmological experiments provide new data points, and theory must be added to match, that some previous theories/concepts become untenable. What am I saying different here?


B. I don't think Born rule is referenced so much in the latest entanglement theory. But yes, it is relevant even if it is not a "cornerstone". Again, any reference you have that can show otherwise (directly, not indirectly) would be appreciated.

And just to be clear: I have provided a pretty solid list of seminal papers that build us up to today regarding entanglement. EPR, Bohm, Bell, CHSH, Aspect et al being what I call the old line papers. Hong-Ou-Mandel, GHZS, Bennett-Peres-Wooters, multiple Zeilinger-Ma-Pan teams being the more modern. Of course this is not exhaustive. This is NEW theory, NEW experiment. So pre-existing interpretations and explanations MUST adjust. Again, this is basic scientific method.


C. Sure, the SE is down there somewhere. But a new (or pre-existing!) interpretation - one that is fully consistent with the kinds of quantum behavior that the SE models in textbooks - need not be consistent with the works I mention. This is our point of departure in this thread.

The SE equations largely ceased to be a relevant tool - when discussing or developing entanglement theory/experiment - approximately after Bohm's work in the 1950's. I have a 1958 edition of his "Quantum Theory" (1951) that I received as a gift. On page 618 of 628, something akin to a Bell state appears (this is of course pre-Bell). It is in context his famous spin basis version of the EPR paradox (page 611). And yes, the SE is discussed in quite some detail earlier in the book. (So are various methods using the Heisenberg picture, Hamiltonians, Dirac functions, Born approximation, etc. etc.)

So is this early Bell state a result of calculations using the SE? I guess you could say so. But that version of a Bell state doesn't imply everything that came later! In fact, Bohm specifically mentions that the experimental implementation was not currently possible; and it was not clear what the result might be - whether or not the quantum mechanical prediction of perfect EPR type correlations would be validated.

Bell of course doesn't use the SE in his 1964 paper at all. So the Bohm book is the last direct connection (assuming you agree that it is a direct connection) between the SE and a Bell state representation. Nothing of the SE after Bohm was critical to the (heretofore listed) development of entanglement theory. At least nothing in the historical record I am aware of.


D. So the $64,000 question: why this thread?

As I have said: there have been a lot of developments in entanglement theory that must be addressed in ALL interpretations of QM that expect to remain viable. Entanglement theory - a small subset of QM - is the area in which most interpretations begin to struggle. So if a particular interpretation of QM is able to replicate the predictions of QM in many areas - such as the SE, Born rule, or any other subset of the rules of NRQM for that matter - that does NOT automatically imply that they can reproduce ALL the predictions of the current complete Quantum Mechanical canon.

If the bar is set to 1951 (and the book of Bohm, important as it was): well, that was 73 years ago. If we were comparing 1951 cosmology to 2024 cosmology, everyone would laugh. But in this thread, no one seems to see the humor in discussing the SE (1926) as compared to today's QM. Two different animals.

 

[PeterDonis]

Sure, the SE is down there somewhere.

In other words, you already have what you say you have been asking for: a treatment of these experiments using NRQM that relies on the SE. So what are we having this thread for?

But a new (or pre-existing!) interpretation

there have been a lot of developments in entanglement theory that must be addressed in ALL interpretations of QM that expect to remain viable.

This thread is not about intepretations. If you have something you want to discuss about interpretations and what's missing from them, that (a) belongs in the interpretations subforum, and (b) is irrelevant to the question of whether the SE is involved, that question is a simple question about what NRQM, independent of any interpretation, includes.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

After moderator review, the thread will remain closed.