Cramer's Backward Causality Experiment

[RandallB]

Nothing here that could be used as a non-local communicator.

Check some of the early work by Mandel and his associates at Rochester to understand this more thoroughly.

Of course there is something there to serve as a non-local communicator.
You need to recognize “non-local” as meaning; Not maintaining Locality and/ or Not Realistic.
The unrealistic appearance of Backwards Time Causality would obviously be the non-local communicator.

Most of us think that this nor any other experiment is capable of demonstrating Backwards Time Causality as better than say OQM as a Non-Local solution. The hallmark of a free Science is we get to criticize, but we don’t get to control how Cramer and his supporters spend their experimental resources.

Also, do the many readers of Physics Forums a favor;
If you have a useful resource from Mandel give a detailed reference.

 

[peter0302]

Cramer makes a big mistake when he states that the coincidence circuit only filters a little noise. Actually the coincidence circuit is necessary to see any fringing at all. As with all the previous quantum erasure experiments, the Dopfer experiment is no different. In a quantum erasure experiment there usually is a fringe pattern and an equal antifringe pattern. The coincidence circuit removes the antifringe pattern.

In DCQE yes. In Dopfer, no. That is why Dopfer is so tantalizingly close to what Cramer is trying to do. No one had shown, prior to Dopfer, that you could make a fringe pattern by sending an entangled photon through a double slit (DCQE sends the original photons through double slits and THEN creates the entangled pairs).

But what is even more tantalizing about Dopfer is that as you move the detector away from the focal point slowly, you get something inbetween an interference pattern and a gaussian pattern - at the other detector - showing that the quality of the pattern is directly proportional to the number of photons for which you destroy which-path info. In other words it doesn't necessarily have to be perfect.

In dopfer, there is no doubt that all the coincidence circuitry does is eliminate noise. No doubt. It is a filter that makes sure that we're only looking at photons which we _know_ correspond to ones we've done something to (either destroyed which-path or not destroyed). But if we could ensure that we do the same thing to MOST of the photons -we should not need the counter. But how do we ensure that we get them all without violating the HUP? That's the problem.

 

[RandallB]

then move onto eliminating loopholes as you suggest

In dopfer, there is no doubt that all the coincidence circuitry does is eliminate noise. No doubt.

As I don't believe there are any real Loopholes in EPR testing worth considering I don't recall suggest any need to eliminate them - I consider those efforts just as pointless as Cramer's.

I do not see 'that all the coincidence circuitry does is eliminate noise' at all.
Coincidence tracking is much more significant than that and is subject to noise itself.
The important demonstration in the Dopfer example is showing how a DCQE configuration is affected by the near field walk off issue as that setup is in the very near field.
An issue Cramer is accounting for very carefully in his set up to ensure he is just far enough into the far field to eliminate walk off.

 

[mickeyp]

In Dopfer the double slit is close to the pdc. Furthermore, the pdc has a finite aperature and a thickness -- which is important. The wavefunction at the double slit is phase scrambled. It is equally likely that the wavefront at bolth slits is in-phase or completely out-of-phase. Thus there is no significant fringing behind the double slit.

The coincidence circuit, with the lens at f from the detector, filters out an antifringe, thus the coincidence only records photons with a similar phase condition in front of both slits.

One could also produce fringes after the double slit with a pinhole at the pdc output, or one could move the double slit further away from the pdc. Both of these approaches limits the phase variations in the wavefunction but in neither case would one be capabile of controlling the fringes from the other path.

 

[mickeyp]

The Dopfer / Cramer thing probably is a lost cause.

However, an experiment that met my eye as might show some reverse causality is:

B. Hessmo, P. Usachev, H. Heydari,and G. Bjork, PhysRevLett.92.180401, 7 MAY 2004

If you can get a hold of this please note that the rotation of the birefringent plate changes the photon rate at detectors D1 and D2.

As with Dopfer, Hessmo et. al. uses coincidence, but in this case the coincidence isn't to remove an antifringe but is to remove background noise and increase the fringe visiblity to exceed the Bell inequality.

 

[RandallB]

In Dopfer the double slit is close to the pdc. Furthermore, the pdc has a finite aperature and a thickness -- which is important.

That is where “walk off” comes from “close” means near field relative to the size and thickness of the down converter.

Also wrt B. Hessmo and if they “might show some reverse causality”:
If as you say they are using coincidence counting or correlations then they Cannot.

 

[mickeyp]

That is where “walk off” comes from “close” means near field relative to the size and thickness of the down converter.

Also wrt B. Hessmo and if they “might show some reverse causality”:
If as you say they are using coincidence counting or correlations then they Cannot.

In Hessmo, the control in one path, after a beamsplitter, changes whether a "hit" on a detector is one photon or two photons. Due to the constant photon rate this is half as many two photon "hits" as one photon "hits". This could be thought of as the "signal" - the rate of photon bunch "hits" where a bunch is either one or two photons.

Since the "hits" from noise is much higher than the controlled one/two photon signal, Hessmo et. al. utilized coincidence to filter the noise -- achieving a near 100% signal.

Unlike Dopfer / Cramer where the antifirnge term is exactly ( and I mean exactly) the negative of the desired fringe term, in Hessmo there is no such exactly equal negative term -- just a "signal" which is covered by a random noise term.

 

[peter0302]

The Dopfer coincidence circuitry does not filter out an antifringe. It is quite clear that when the one detector is placed at the focal point of the Heisenberg lens, the other detector (for the entangled twin), as it scans along the x-axis, shows a visible interference pattern. There is no filtering of an anti-fringe.

This is in stark contrast to DCQE, where there are two interference patterns which must be differentiated from one another or else they show up as gaussian at the signal photon detector. That is *not* the case in Dopfer. There is *one*, perfect interference pattern at the signal photon end - not one half of a fringe/anti-fringe pattern.

The coincidence circuitry is necessary to ensure that the photons we're looking at at the signal end COINCIDE with the ones that were sent to the focal point of the Heisenberg lens. Its function is nothing more than that. *If* all of the idler photons could be sent to the focal point of the Heisenberg lens somehow, there would be no need for coincidence circuitry at all. But, I believe it is impossible to force all the photons to a single point, which is why we filter out only those that happen to reach that point.

 

[mickeyp]

That doesn't make any sense. The experiment should generate a visible interference pattern on a screen just as easily as it can generate one on a CCD - if he's right.

I think you misread the actual Dopfer experiment. At no time was there any measurements without the coincidence circuit involvement. Both detectors were on some sort of movable platform, the detector on the lens leg was kept stationary and then the detector on the double slit side was moved to create the interference pattern in coincidence.

the process is similar in the other direction, that is, the detector in the double slit leg is kept stationary while the detector in the lens leg is moved - again providing some sort of pattern.

Without coincidence the actual photon distribution in front of both detectors is just a fog. It takes the coincidence circuit to bring out any pattern.

 

[peter0302]

I read Dopfer correctly. I never said she didn't use coincidence circuitry. She did. But no one seems to understand _why_ that circuitry is necessary.

Again, it has nothing to do with fringe/anti-fringe patterns. It has to do with finding the idler photons that COINCIDE with the signal photon whose which-path information was destroyed. When we detect signal-photons with ambiguous which-path information, we see interference in the idler-photons directly proportional to our certainty as to the which-path. This is reflected in the fact that as the signal photon detector is moved away from the focal point, we have a slightly better idea of where it came from and so get less and less of an interference pattern.

Bottom line: when we destroy which-path information for the signal photon by detecting it at a point where it is impossible to tell where it came from (the focal point) we see a perfectly symmetric (not fringe/antifringe) pattern from the idler photon. If we could detect EVERY signal photon in this fashion, we'd see a pattern in EVERY idler photon, and hence a visible interference pattern without coincidence counting.

That's what Cramer's TRYING to do. Unfortunately he has not shown us a viable way of doing it.

 

[mickeyp]

If the experimenter reduces the size of the area of radiation of signal and idler photons from the pdc, let's say by use of pinhole(s), then one would see an interference pattern behind the double slit without the use of the coincidence circuit.

However, in this case, and with the Heisenberg detector at 2f, the two detected triangle pattern intensities behind the Heisenberg lens are broadened wherein both are on top of each other, thus the experimenter cannot deduce path.

The pinhole between the pdc and the double slit acts to reduce the uncertainty in the momentum which increased the uncertainty in position. For there to be signaling from the lens leg to the double slit leg the Heisenberg's uncertainty principle must be revoked -- a violation of quantum mechanics.

I read Dopfer correctly. I never said she didn't use coincidence circuitry. She did. But no one seems to understand _why_ that circuitry is necessary.

Again, it has nothing to do with fringe/anti-fringe patterns. It has to do with finding the idler photons that COINCIDE with the signal photon whose which-path information was destroyed. When we detect signal-photons with ambiguous which-path information, we see interference in the idler-photons directly proportional to our certainty as to the which-path. This is reflected in the fact that as the signal photon detector is moved away from the focal point, we have a slightly better idea of where it came from and so get less and less of an interference pattern.

Bottom line: when we destroy which-path information for the signal photon by detecting it at a point where it is impossible to tell where it came from (the focal point) we see a perfectly symmetric (not fringe/antifringe) pattern from the idler photon. If we could detect EVERY signal photon in this fashion, we'd see a pattern in EVERY idler photon, and hence a visible interference pattern without coincidence counting.

That's what Cramer's TRYING to do. Unfortunately he has not shown us a viable way of doing it.

 

[mickeyp]

Being new to this foum I hadn't realized, until now, that I could upload an attachment.

Here is the Hessmo, et. al. experiment that I mentioned earlier.

Although this experiment uses coincidence to extract a high fringe visibility, one can logically say this:

observation 1: With the phase shift at 180 degrees (FIG. 3) there is no coincidence between detectors D1 and D2 (FIG. 2)

observation 2: With the phase shift at 0 degrees there is maximum coincidence between detectors D1 and D2

assumption: The photon rate going to beamsplitter BS is independent of the rotation of the birefringent crystal (FIG. 2)

conclusion 1: No coincidence implies that two (or more) photons are striking D1 or D2 together.

conclusion 2: Maximum coincidence implies “single photons” are striking D1 and D2 at the same time

conclusion 3: with the assumption of a constant photon rate illuminating the beamsplitter BS then there must be ½ as many two photon hits on D1 and D2 as there are single photon hits – a signal controlled by the rotation of the birefringent crystal.

Conclusion 4: the control of the number of hits at detector D1 by the rotation of the birefringent crystal, which is after the beamsplitter in the D2 path, constitutes a non-local communicator.

 

[RandallB]

Being new to this foum I hadn't realized, until now, that I could upload an attachment.

Here is the Hessmo, et. al. experiment that I mentioned earlier.

You can also just provide the appropriate link for us to access whatever is available.

This is still a corralation example, it doesn't address J C's experiment.

 

[peter0302]

If the experimenter reduces the size of the area of radiation of signal and idler photons from the pdc, let's say by use of pinhole(s), then one would see an interference pattern behind the double slit without the use of the coincidence circuit.

However, in this case, and with the Heisenberg detector at 2f, the two detected triangle pattern intensities behind the Heisenberg lens are broadened wherein both are on top of each other, thus the experimenter cannot deduce path.

The pinhole between the pdc and the double slit acts to reduce the uncertainty in the momentum which increased the uncertainty in position. For there to be signaling from the lens leg to the double slit leg the Heisenberg's uncertainty principle must be revoked -- a violation of quantum mechanics.

Why? In neither case do we ever actually learn which-path info. It just so happens that in one, we see an interference pattern, and in another, we see a single blob. But technically in neither case did we deduce which slit the photon came from.

I have seen complimentarity (I think incorrectly) described as we cannot simultaneously view particle-like and wave-like behavior. In fact, what it means is that we cannot know which-slit a photon came through and still be certain enough as to momentum to generate a coherent interference pattern. But that is not happening here. In the interference case, we don't know which-slit because it was intentionally destroyed. In the blob case, we still don't know which slit because both blobs are superimposed onto one. I don't see how the HUP is violated.

 

[RandallB]

If the experimenter reduces the size of the area of radiation of signal and idler photons from the pdc, let's say by use of pinhole(s), ... .

Mickey your missing the point in Dopher – which has nothing to do with backwards causality.
Contiune the Dopher discussion in:
https://www.physicsforums.com/showthread.php?t=251158"

I’m sure Peter will catch up with you there.
I know your new to the forums so I thought I’d helping out –
There are always tangents in a discussion but it helps to avoid hijacking a thread into a different topic.

Just opening a new thread helps keep each one a little better focused each different subject rather than becoming a string of random topics like you find in a blog.
Plus by including Dopher in the title of the thread makes it easier for others to find the discussion even years from now. Just as you can finds a lot of past info with a title search on “Dopher”

 

[peter0302]

Randall, all due respect, but I think Dopfer's experiment is *directly* relevant to Cramer's experiment. Cramer got hsi entire inspiration from the Dopfer experiment. He believes it proves that his concept will work, so the question of whether/how the coincidence counting could be removed from Dopfer is really the central question to Cramer's concept.

 

[RandallB]

Randall, all due respect, but I think Dopfer's experiment is *directly* relevant to Cramer's experiment. Cramer got hsi entire inspiration from the Dopfer experiment. He believes it proves that his concept will work, so the question of whether/how the coincidence counting could be removed from Dopfer is really the central question to Cramer's concept.

No his real inspiration comes from the peer reviewed and published work of the Shih group. The Dopher notes help illustrate his concern and attention to the near fields vs. far field effects in setting up his modified Shih group experiment to test Backwards Causality.

In any case a detailed discussion of Dopher warrants its own thread IMO.

 

[peter0302]

In any case a detailed discussion of Dopher warrants its own thread IMO.

I do agree with you there. :)

Do you have any arix links to the Shih group papers?

 

[RandallB]

Do you have any arix links to the Shih group papers?

There’s a Phys Rev Lett. Reference on page 2 of the Cramer doc you’re familiar with.
http://faculty.washington.edu/jcramer/Nonlocal_2007.pdf

Trim off the file name on the link and you’re on the Prof’s Home page with more info.
I seem to recall one of his lectures listed there going into a little more detail about the Shih group – but that was when I first read about this;
The original old discussion on Backwards C in ’06 ’07 is at:
https://www.physicsforums.com/showthread.php?t=144298

 

[AndreasP]

Randall, all due respect, but I think Dopfer's experiment is *directly* relevant to Cramer's experiment. Cramer got hsi entire inspiration from the Dopfer experiment. He believes it proves that his concept will work, so the question of whether/how the coincidence counting could be removed from Dopfer is really the central question to Cramer's concept.

Peter,

having read this thread one more time, I think I am totally with you. Dopfer's experiment is in essence what Cramer is trying to do, or at least is very close to it. The conincidence circuit in Dopfer's setup is not used to filter out the antifringe but merely to find out which photons belong together.

Do you conclude therefore that Cramer's experiment will work?

It seems to me that by using a precise enough clock one should in principle be able to match photon pairs without the coincidence ciruit. Alternatively, one may leave enough time between the emission of the individual photons to know for sure which photons belong together. This may seem to "slow down" the tranmission rate, but the main point is here is of course that the two detectors can be very far away from each other.

Another thing I am wondering:

If Cramer cannot find funding for his experiment, why does he not just ask Dopfer or Zeilinger to allow him to come to Innsbruck and modify Dopfer's original experiment that she performed in 1998 as part of her PhD thesis in Zeilinger's group (assuming the setup is still available)?

That seems like a more pragmatic approach. Why reinvent the wheel? In the process he could update the experiment with the latest available technology which I am fairly sure is available in the Innsbruck/Vienna labs of the group - which are among the most advanced in the world.


Andreas

 

[Dmitry67]

Interesting, what if we do that experiment with 1 'open' leg?

So we observe an interference pattern pointing 2 other rays to cosmos, to the infinity.
If, in 1000000 years these rays hit an alien astronomer looking at us at telescope (so he can determine which path) our interference pattern disappear right now.
If we accidently point it to the black hole, then our pattern is restored :)

I suspect that this won't work for some reason, and Cramers experiment must fail, however, I did not find any explanations WHY it won't work so far.

 

[DrChinese]

Do you conclude therefore that Cramer's experiment will work?

It seems to me that by using a precise enough clock one should in principle be able to match photon pairs without the coincidence ciruit. Alternatively, one may leave enough time between the emission of the individual photons to know for sure which photons belong together. This may seem to "slow down" the tranmission rate, but the main point is here is of said course that the two detectors can be very far away from each other.

Another thing I am wondering:

If Cramer cannot find funding for his experiment, why does he not just ask Dopfer or Zeilinger to allow him to come to Innsbruck and modify Dopfer's original experiment that she performed in 1998 as part of her PhD thesis in Zeilinger's group (assuming the setup is still available)?

Zeilinger said (click to see reference) this will not work and explains why, see Fig. 2 on page 290. Basically, the which-slit information is available in principle - and thus no meaningful interference pattern arises (i.e. so nothing changes at S1 based on what you do at S2. He also indicated that his paper is based on experiments that have been performed, so I guess he thinks there is no need to re-run the experiment. Probably would explain why everyone is not rushing to do it.

BTW, in Cramer's version of the experiment, coincidence counting is not necessary. If it were, then this would not be a non-local quantum communication device.

Dopfer's setup is discussed specifically as well, see Figures 3 and 4 on pages 290 and 291. Now, here is where I think there is something more to consider. In Dopfer's version, there is an interference pattern formed for a subset of the photons at D2. If the person at D1 changes the location of the detector, that interference pattern at D2 disappears. Clearly, to get the subset you must coincidence count. But consider the entire set at D2, including the data points for which there is not a coincidence (i.e. where the which-path could not be erased. Presumably it does not change based on the actions of the person at D1 (otherwise Dopfer would have noticed this and commented). So that means that as the interference pattern disappears, the data points for the remainder of D2 change in just such a way that the total pattern (a single peak/crest/bar) remains essentially static. Now clearly, the number of clicks at D1 changes as D1 is moved to and from the focal point; that will also affect the coincidences (between D1 and D2).

So the subset of D2 in which could not have the which-path info erased - that subset will see a shift in its D2 pattern based on the actions at D1 as well. And yet the total pattern at D2 doesn't change. So more weird stuff to think about!

 

[RandallB]

Peter,
having read this thread one more time, I think I am totally with you. Dopfer's experiment is in essence what Cramer is trying to do, …..

Do you conclude therefore that Cramer's experiment will work?

Andreas
Welcome to PF
Peter will not be replying – when you see a line though a name, as on his, it means for whatever reason they are no longer a member here.

No the Cramer set up is not the same as Dopfer, Cramer requires a Far Field set and Dopfer specifically explained the need for a near field set up in her work (hard to find as here paper in only available in Germen).

And as I’d reported Cramer considers the “Shih group” as the foundation to his plan, but does reference Dopher especially as to the need to use a Far Field rather than a Near Field.

I know this from personal conversations with him.
I did promise to update his progress, but I would not expect a contact from him on lack of progress. It is been almost a year so I’ll see if I can get in touch with him to post a current update.

I expect no real progress,
If you go through Peters posts another time I think you can see that he agreed with me that the experiment would never succeed in even the early set up before adding in sufficient time delays to finally address the Causality issue. At the time at least I thought both Peter and I had given enough detail to explain why it could not work even at the level where the sampling intervals were still longer than time separation.
In fact if I remember right Peter doubted the proposal so strongly the he questioned the value of anyone providing the first dime of funding for it.

 

[DrChinese]

No the Cramer set up is not the same as Dopfer, Cramer requires a Far Field set and Dopfer specifically explained the need for a near field set up in her work (hard to find as here paper in only available in Germen).

And as I’d reported Cramer considers the “Shih group” as the foundation to his plan, but does reference Dopher especially as to the need to use a Far Field rather than a Near Field.

I know this from personal conversations with him.

RandallB,

As you mention, Cramer's setup is different from Dopfer's. I noticed that too, and was trying to understand the reasoning there. Cramer has the focal lens before the beamsplitter, that sticks out most to me. Is that what you refer to as the "far field" setup? Can you explain the reasoning for that?

I am guessing that by placing the focal lens there, both photons of *every* entangled pair has its which-path info erased. That way, interference is expected on the "uncorrelated" image at both S1 and S2, and that is why coincidence counting would not be required. Thus is born the idea for the FTL signaling mechanism (although I assume that no one actually expects that to result). Am I close?

So where might this ingenious scheme goes wrong? My guess: the camera at S1 is not actually at the focal point of those photons, and therefore their which-slit info is not truly erased. Ergo there is never an interference pattern at S1 anyway, and consequently nothing done at S2 makes any difference at S1. All you ever see at S1 is the "1" pattern.

 

[RandallB]

RandallB,

As you mention, Cramer's setup is different from Dopfer's. I noticed that too, and was trying to understand the reasoning there. Cramer has the focal lens before the beamsplitter, that sticks out most to me. Is that what you refer to as the "far field" setup? Can you explain the reasoning for that?

I am guessing that by placing the focal lens there, both photons of *every* entangled pair has its which-path info erased. That way, interference is expected on the "uncorrelated" image at both S1 and S2, and that is why coincidence counting would not be required. Thus is born the idea for the FTL signaling mechanism (although I assume that no one actually expects that to result). Am I close?

So where might this ingenious scheme goes wrong? My guess: the camera at S1 is not actually at the focal point of those photons, and therefore their which-slit info is not truly erased. Ergo there is never an interference pattern at S1 anyway, and consequently nothing done at S2 makes any difference at S1. All you ever see at S1 is the "1" pattern.

No - not close
The Lenses in Dopfer are after the Slit locationS (both real and image slits).

Cramer is using a Type II PDC; the only purpose of the lens here is to turn the diverging H & V beams onto the same vector (parallel) so that they can both go through the same beam splitting polarizer before moving on to the double slits (one path to real slits the path other to 'image' slits).

Where does his scheme go wrong,
Just my opinion, (and I have given it to him).
As you know I am convinced that an individual beam from a pair of beams produced by any “entanglement” process when measured in isolation will produce the same results as a “normal” beam of light that is produce to be identical with the exception of not having an “entangled twin” beam to have ever been produced of any type.

Meaning:
A given in classical optics is:
1) A single ‘normal’ beam can never produce a two slit interference pattern when in a near field set up.
2) the same ‘normal’ beam will always produce a two slit interference pattern when in a near field set up.
I am convinced:
any single 'entangled' beam will always produce the same 2 classical results – period.

I know you and I disagree on this point – but unless Cramer can prove me wrong on this point and show that Far field interferance is sometime failed to be seen; there is no reason to moving onto the delayed changes on the idler beam step protion of his testing. I.E. a failure.

He will only be able to prove what I’ve already discussed with you about the experimental results you found elsewhere. (we just disagree on how to read those results).
Unfortunately, when Cramer’s testing confirms my position on this, it will result in his approach FAILING and no report will be produced. And that means no formal report or formal confirmation of my positon.

I.E If I'm wrong it will be reported - If I'm right it will not!
A bit of a catch 22 for me.

 

[AndreasP]

Zeilinger said (click to see reference) this will not work and explains why, see Fig. 2 on page 290. Basically, the which-slit information is available in principle - and thus no meaningful interference pattern arises (i.e. so nothing changes at S1 based on what you do at S2. He also indicated that his paper is based on experiments that have been performed, so I guess he thinks there is no need to re-run the experiment. Probably would explain why everyone is not rushing to do it.

Thanks for pointing to this reference. My comments are included below.

Comment 1 (Dopfer's experiment):

In Fig 2. on the top of page 290 of Zeilinger's 1999 article that you reference above, it is definitely true that there cannot be an interference pattern because which-slit information is still available, by virtue of particle b/b' in the same figure.

However, Cramer's setup (see Comment 2 below) looks closer to Fig. 3 on the bottom of page 290, which is Dopfer's experiment.

In Dopfer's setup, the question of whether there is an interference pattern of photon 2 behind the double slit or not, depends on where the Heisenberg detector is placed to register photon 1. There are two cases (quoting from Zeilinger's article):

Case A: The Heisenberg detector is placed in the focal plane of the lens, i.e. at distance f from the Heisenberg lens. In that case registration of photon 1 (in the Heisenberg detector) projects the state of photon 2 (in the double slit) into a momentum eigenstate which cannot reveal any position information about slit passage. In other words, which-slit information is not available. Therefore, in coincidence with a registration of photon 1 in the focal plane, photon 2 exhibits an interference pattern.

Case B: The Heisenberg detector is placed in the imaging plane of the lens, i.e. at distance 2f from the Heisenberg lens. In that case registration of photon 1 (in the Heisenberg detector) projects the state of photon 2 (in the double slit) into a position eigenstate which can reveal position information about the path photon 2 takes through the slit assembly. In other words, which-slit information is available. Therefore, in coincidence with a registration of photon 1 in the focal plane, photon 2 cannot exhibit an interference pattern.

So, which-slit information does not have to be available, at least not in Dopfer's experiment, as described in Fig. 3 on page 290 of Zeilinger's article. It is of course present in Fig. 2 on the same page. But that is not Cramer's experiment.

Comment 2 (Cramer's experiment):

It seems to me that what Cramer is trying to do is to essentially take Dopfer's experiment and (a) increase the distance between the crystal and the double slit, in order to assure that photon 2 behind the double slit is always detected after photon 1, and (b) eliminate the coincidence logic. So it would still very much look like Fig. 3 on the bottom of page 290 in Zeilinger's article, just with a longer distance between the crystal and the double slit, and without the coincidence logic.

The main difference to the situation in Fig. 2 on page 290 in Zeilinger's article is of course that in Fig. 2 one of the entangled photons first goes through the double slit before something else happens to the twin photon, whereas in Cramer's experiment it is the opposite. There, one of the photons is detected in a Heisenberg detector first, then the other one goes through a double slit, possibly at a much later time.

Cramer's question now seems to be this: Would one still see an interference pattern in case A, and no interference pattern in case B?

For example, let's say we are in case A, i.e. the Heisenberg detector is placed in the focal plane of the lens. For simplicity, let's assume that photon 1 is registered in the Heisenberg detector at T1=1s and photon 2 in detector D2 behind the double slit at time T2=2s. Let's also assume that the experimenter always leaves the Heisenberg detector in the focal plane of the lens, i.e. he makes the same type of measurement for all photons that are sent through the apparatus.

Then the registration of photon 1 in the Heisenberg detector (located in the focal plane of the lens) at time T1=1s projects the state of photon 2 (which is still underway to the distant double slit) into a momentum eigenstate. From that moment on photon 2 cannot reveal any position information about slit passage anymore because the which-slit information was erased at that very moment T1=1s, once and forever.

Later, photon 2 is registered in detector D2 behind the double slit at time T2=2s.

According to Cramer, there should be an interference pattern on detector D2 if a large number of photons is sent through the apparatus, (presumably) because the state of photon 2 at time T2=2s is still in the momentum eigenstate that it was projected into back at time T1=1s (PS: I wonder whether this statement is actually true. Could photon 2 actually change its state between T=1s and T=2s and become more dispersed again? In any case, I think it will never be able to "re-acquire" the which-slit information that it lost at T1=1s. How would it?)

Finally, Cramer seems to believe that he doesn't need the coincidence logic, if one just uses a sufficiently large number of photons. However, in practice only a small fraction of all pairs emitted by the source is actually registered, as detectors just are not perfect. This is the detection loophole. So how can Cramer filter out the pairs that actually belong together? Perhaps he thinks this is just a practical issue. Of course, if both the source and the detectors were of very high quality (meaning that a large fraction of all pairs emitted by the source is actually registered) I can see why he thinks he doesn't need the coincidence logic. What for? There is no fringe/antifringe pair to be filtered through.

What is going on here?

Perhaps the following can shed some more light into this debate. Cramer's transmission protocal in essence seems to be this: For each bit of information to be transmitted:

(a) The sender (the one in possesson of the crystal and Heisenberg detector D1) decides what he wants to send. He does so by selecting the location of the Heisenberg detector, either in the focal plane or the imaging plane of the lens (representing "0" or "1" by convention).

(b) The sender then sends a large number of entangled photon pairs, say N=1000, through his side of the apparatus. For each photon pair emitted, "his" twin will immediately be detected by the Heisenberg detector, while the other one is still underway.

(c) The receiver (the one in possession of the double slit and detector D2) checks whether or not an interference pattern emerges at detector D2.

I think one key issue here simply is that the photon twin traveling to the receiver still needs a finite amount of time to reach the received, even though the registration of photon 1 at the sender's side instantaneoulsy projects the state of photon 2 into a momentum or position eigenstate.

Where is the catch?

Comment 3 (comment independent of Comment 2):

Another point on Dopfer's experiment I have always wondered about after heaving read her thesis:

In both cases of comment 1 (case A or case B), the distance between the Heisenberg lens and the double slit (i.e. the distance from the Heisenberg lens back to the crystal plus the distance from the crystal to the double slit) seems to be the same -- namely 2f (I am not sure whether I read Fig. 3 correctly, but that is what it looks like in the picture anyway).

In any case, it seems to me that in order for the Dopfer experiment to work, photon 1 must be registered (in the Heisenberg detector D1) before or at least at the same time as photon 2 (in detector D2 behind the double slit).

Otherwise, one would in essence be in the situation of Fig. 2 on the top of page 290 in Zeilinger's article: photon 2 first goes through the double slit, while photon 1 is still underway. In other words, at the time when photon 2 is detected one does not know yet what type of measurement of photon 1 (still underway to the Heisenberg detector) will be made in the future. This scenario therefore represent a kind of delayed choice situation (registration of photon 1 is delayed). In this case I agree with your oroginal comment that one would of course never see an interference pattern on detector D2.

One can only try to filter out the fringe/antifringe pair ex-post, but that would of course require the conincidence circuit (otherwise one could not find out which photons 2 belong to which photons 1).

One curious question here is: What if all photons 1 are detected with the Heisenberg detector in the focal plane of the lens (so always in case A, meaning no which-slit information is available). So there really isn't a pair of fringe/antifringe patterns, but just a single fringe pattern.

On the one hand one clearly cannot see an interference while photon 1 is still underway, so no interference pattern on detector D2. But on the other hand there cannot be an antifringe pattern because all photons 1 are measured with the Heisemberg detector in the focal plane of the lens.

Where is the catch? (it can't be just the detection loophole of course).