# Resolution to the Delayed choice quantum eraser?

1. Jun 16, 2009

### Gothican

I've been thinking about this weird experiment for a while and came up with a couple of insights:

* This experiment presents before us the paradox between our concept of time, and the photon's nature of living outside of time. For the photon, the idler and the signal were measured at the same instant. But for us, time passed between the two measurements.

* Furthermore, the idler and the signal are entangled particles which means, that when the idler is measured of erased, then it immediately effects the signal - even though for us it is very far away.

Could these assessments be true?
I'd like to know what you think of them...

2. Jun 17, 2009

### Demystifier

There is nothing mysterious, strange or paradoxical about delayed choice experiments, provided that you adopt any of the well developed interpretations of QM, such as Copenhagen, many world, Bohmian, or such. Delayed choice is confusing only to those who have still not chosen some coherent interpretation existing at the market, but try to think on QM in terms of concepts that represent a meaningless mixture of various mutually incompatible interpretations.

The fact that Wheeler (who first proposed a variant of the delayed choice experiment) was also confused with that only shows that he did not took his own interpretation of QM (many world) really seriously.

Last edited: Jun 17, 2009
3. Jun 17, 2009

### Gothican

I don't think you get it. You can use which ever interpretation that you want, but you still won't be able to explain the time paradox.
Let's say you use the Bohmian interpretation; he says that this is an nonlocal universe and therefore the measurement you made on the idler photon (which catches him at a certain position guided by the wavefunctions) immediately effects the signal one - understandable. But what about the fact that the idler photon was measured after the signal was already recorded?
As far as I know, no quantum interpretation explains this time problem. If one does please enlighten me.

The only explanation that I've heard so far was that the measurement of the idler photon gives us an explanation of the signal's past path. Which was kind of hard for me to accept - I mean, each signal photon when recorded, had to either interfere with itself, or not!

4. Jun 17, 2009

### Cthugha

There is no time paradox at all.

You do not have self interference here. Delayed choice experiments are all about two-photon interference. You will never see any interference without doing coincidence counting. In fact the signal you record is a superposition of two interference patterns, which are exactly shifted out of phase so that the sum of both shows no interference pattern at all. Detecting the idler too and doing coincidence counting now allows you to pick a subset of all detected photons depending on the position of the detector at the idler side. One of these subsets is one of the interference pattern. If you move the detector at the idler side a bit, you will see the other interference pattern in coincidence counting. This is more or less a question of filtering out the right information - and this filtering can be done any time. Therefore there is no time paradox present.

5. Jun 17, 2009

### Coldcall

Wheeler and many-worlds? I dont think so. His student Everett formulated many-worlds but I dont remember ever reading that Wheeler was an advocate.

Wheeler's Participatory Anthropic Principle is quite explicit in that he identified at face value the seemingly observer-centric nature of qm. And he cleverly used that interpretation of qm to explain why the universe appeared so fine tuned for life. Paul Davies recently expressed his preference for Wheeler's theory over many-worlds in his Goldilocks book.

6. Jun 17, 2009

### Gothican

Wow. I finally got it. Thanks Cthugha.

Just could you please explain to me the reason that the D0/D1 coincidence count is exactly mirrored by the D0/D2 coincidence (as seen http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser" [Broken].)

Why would the two detectors result in different patterns?

Thanks again.

Last edited by a moderator: May 4, 2017
7. Jun 17, 2009

### SW VandeCarr

I've always been skeptical of QM interpretations although I know less about the Bohmian model. Both Copenhagen and Many Worlds are frankly metaphysical in that there's no known way to verify or falsify them. Perhaps I'm wrong about this. If so, please enlighten me.

I just posted a question here about the Ensemble model which bypasses the problems with the other interpretations although it may have been falsified in recent experiments using Bose-Einstein condensates.

8. Jun 17, 2009

### Cthugha

Here is a simplified explanation of these different patterns in the DCQE experiment as performed by Kim et al, which I posted earlier somewhere on this forum. It is a bit long, but maybe it helps you understand (and I am too lazy to write a completely new description ;) ).

You can treat this experiment as if every photon here originates from either point A or B (following the pictures in the DCQE paper by Kim). Now the setting is as following:

a) In entangled photon experiments each photon on its own behaves like incoherent light. This means, there is no or at least not much correlation between the phases ($$\phi_1$$ and $$\phi_2$$) of the fields originating from points A and B at the same moment. For the sake of simplicity I will now treat the phase of these fields as completely random and the amplitude as constant and equal.

b) The two-photon state has a well defined phase. This means that the fields of both paths (signal and idler), which originate from the same point (A or B) have a fixed phase relationship. For the sake of simplicity I will now assume, that the initial phase is the same for signal and idler.

Let's first consider, what happens at the detector D0, which scans the x axis. Just like in an usual double slit experiment you will not detect any photons, if there is destructive interference and will detect a large number of photons, if there is constructive interference. Each point P on the x axis, which the detector scans, corresponds to a certain path difference between the paths from A to P and B to P, which can be expressed in terms of an additional phase difference $$\Delta \phi$$. So you will have constructive interference at a point if $$\Delta \phi +(\phi_2 -\phi_1) = 2 \pi$$. As $$\Delta \phi$$ is a constant for each point this means that a detection at a certain point P means, that the phase difference between fields at point A and B had a fixed value $$\phi_2 -\phi_1$$ at a certain time short before. So in fact, scanning the x-axis means scanning the phase difference of the fields. As the fields change completely random and independent of each other, each phase difference will be realized and there will be no interference pattern at D0 alone.

Now let's have a look at the other side. There are two detectors, which both fields can reach and two detectors, which can only be reached by one field. Let me explain D1 first. I will assume that the distances from A and B to each of the detectors are equal. Before the field originating from A reaches the detector, it crosses 2 beam splitters (no reflection) and a mirror. This influences the phase of the field. Assuming that the beam splitters are 50-50 each transmission changes the phase by $$\frac{\pi}{2}$$ and each reflection changes the phase by $$\pi$$. So summarizing the phase of the field originating from A will be $$\phi_1$$+$$\pi$$(reflection at the mirror) + 2*$$\frac{\pi}{2}$$ (transmission at the beamsplitters. The field reaching D1 from point B is reflected twice and transmitted once, so the phase will be $$\phi_2$$ + 2*$$\pi$$+$$\frac{\pi}{2}$$, so the phase difference at the detector will be $$\Delta \phi=\phi_2+2*\pi+\frac{\pi}{2}-(\phi_1+\pi+2*\frac{\pi}{2})=\phi_2-\phi_1+\frac{\pi}{2}$$. Of course a detection implies again, that there is no destructive interference and most detections will occur, if $$\phi_2-\phi_1+\frac{\pi}{2}=2 \pi$$ (or a multiple).

Now let's check the other detector. Here the field originating from A is reflected twice and transmitted once and the field originating from B is transmitted twice and reflected once, which leads to a phase relationship of $$\Delta \phi = \phi_2 + \pi + 2* \frac{\pi}{2}-(\phi_1+ \frac{\pi}{2}+2*\pi)=\phi_2-\phi_1-\frac{\pi}{2}$$. So the $$\Delta \phi$$ at the two detectors are exactly $$\pi$$ out of phase. This means that constructive interference on one detector at some certain phase difference automatically implies destructive interference at the other. So each detector selects a set of phase differences. Let me once again stress that the phases are completely random, so there will be no interference on these detectors either. The detectors D3 and D4 are simpler. As there is only one field present, there will be no interference and the phase does not matter. The detections will be independent of $$\phi_1$$ and $$\phi_2$$.

Now we're almost done. Now we have to consider the two-photon state, where the relative phases are not random anymore. As I stated before, a certain spot on the x-axis of D0 corresponds to a certain phase difference $$\phi_2 - \phi_1$$. This very same phase difference will also correspond to a certain amount of constructive (or destructive) interference on D1 and consequently also (due to the different geometries concerning transmission and reflection mentioned above) to an equivalent amount of destructive (or constructive) interference on D2. So you will see this interference pattern in the coincidence counts of D0/D1 and D0/D2 due to the fixed phase difference of the two photon state. Now it is also clear, why there is no interference pattern if you have which-way information. If you have which-way information, there is just one field present, which has a random phase. There is no interference pattern present, which corresponds to the phase difference, which is present at D0 and therefore no interference pattern can show up in the coincidence counts.

I hope this simplified scheme shows, why the choice between the interference pattern and the which-way information can be done after the signal photon has already been detected, why it does not depend on whether we have a look at the data or not and that there are no problems with causality.

9. Jun 17, 2009

### mn4j

See this article for a local deterministic explanation of the delayed choice experiment.

Computer simulation of Wheeler's delayed-choice experiment with photons
S. Zhao, S. Yuan, H. De Raedt and K. Michielsen 2008 EPL 82 40004
http://msc.phys.rug.nl/pdf/DelayedChoice-epl2.pdf [Broken]

Last edited by a moderator: May 4, 2017
10. Jun 18, 2009

### DrChinese

WARNING: This reference is not generally accepted science. De Raedt et al are part of a local realist group which is mostly ignored by mainstream scientists in the field. To the extent this group is not ignored, it has been critiqued. I do not recommend this. (Computer simulations are not theories or explanations anyway.)

Last edited by a moderator: May 4, 2017
11. Jun 18, 2009

### Demystifier

You are wrong. It is true that Everett was first who proposed a variant of this interpretation, but he called it relative-state interpretation. Soon after the Everett work Wheeler has also written a paper where he further developed these ideas. It was Wheeler who called it many-world interpretation. The references are
H. Everett, Rev. Mod. Phys. 29 (1957) 454
J. A. Wheeler, Rev. Mod. Phys. 29 (1957) 463
so you can check it by yourself.

12. Jun 18, 2009

### Demystifier

I think it is you who don't get it. In the Bohmian interpretation, the wave ALLWAYS goes through both slits, and the particle ALLWAYS goes through one slit only. An experiment made after these travels through the slits does not influence the past. So the Bohmian interpretation does solve the time problem. The Copenhagen and many-world interpretations also do so, but in a different way. In the Copenhagen interpretation the unmeasured past does not even exist, so it cannot be changed. In the many-world interpretation the wave goes through both slits, but after that the wave splits into two "worlds" so that a particular observer observes only one of them.

13. Jun 18, 2009

### Demystifier

Well, you must accept SOME interpretation, because otherwise the quantum theory is useless. Even the "shut-up-and-calculate" interpretation is an interpretation, and certainly a very useful one. Even with this interpretation there is no problem with delayed choice experiments, provided that you stick to this interpretation persistently.

But if you have some your own interpretation that boroughs elements from many different "official" interpretations, you must be very careful because it is very likely that such a mixture is not consistent and that delayed choice will look paradoxical. If you want to be consistent, it is much safer to choose one particular "official" interpretation that you like and to stick to it very strictly and persistently.

Last edited: Jun 18, 2009
14. Jun 18, 2009

### Gothican

Wow Cthugha, You really managed to clarify this for me. Thanks for the great post.

Oh, and just to be sure - each time a idler photon goes through one of those mirrors and gets 'phased out', it immediately changes the signal's phase too (in the same order). Right?

Greetings from Israel.

15. Jun 19, 2009

### Demystifier

Since now you understand what is really going on in the experiment, perhaps you might like this metaphoric explanation as well:
https://www.physicsforums.com/blog.php?b=7 [Broken]

Last edited by a moderator: May 4, 2017
16. Jun 28, 2009

### Gothican

But if we wanted to, we could just add a mirror in front of one of them, so that one of their phases would bump back $$\pi$$. Then the phase of both of the detectors would match - & we would be able to define whether a signal interfered with itself or not, before we would measure the idler!

17. Jun 28, 2009

### Cthugha

No, that would not help. Putting a mirror somewhere will always alter two of the probability amplitudes so that the final situation is the same. If you put the mirror directly in front of a detector, this is trivial. You just have a phase shift of pi for both fields so that he phase difference between them remains the same. If you put a mirror directly in front of BS A or B, you will alter the phase difference at both detectors by pi, which in turn will finally also lead to the same total difference of phase differences.

18. Jun 28, 2009

### Gothican

Ahhhhh, right.
Once again, Thanks a lot.

19. Aug 8, 2010

### charlylebeaugosse

Demystifier, you are right and I LOVE your precision in quoting that is so much absent in present physics (other disciplines would have collapsed with the level of rigor in quoting and citing that one sees in the physics literature since the sixties or a bit before). BUT, isn't it worthwhile and perhaps NECESSARY to try to have an interpretation that would let one expect to go beyond the Copenhagen Interpretation -or CopInt- (and would meanwhile replace the most dogmatic aspects of the Copenhagen quasi religion -even if it is the best complete system so far -I personally prefer the CopInt to Consistent Quantum Theory=CQT )? A theory that would (for instance) use yet unknown coordinates-assuming coordinates are used, as expected by Schrodinger and Einstein, but not naive and worthless as the HV of de Broglie, Bohm, Bell and others. I barely see where this theory would lie between actual Nature laws, QM and the macroscopic physics used to give meaning to QM according to Copenhagen, so do not ask me any detail.
For sure the past is not changed after elapsed in the CopInt, and precisely for the reason that you give, yet the past is defined after elapsed in the CopInt and that is not very nice. I believe that taking non-realism more seriously lets one avoid all the problems of Copenhagen, still respecting what is most respectable in he CopInt. I'll elaborate elsewhere but let me point out that Wheeler's discussion does not take into account that once one gets into the Interference Zone (or IZ, the overlap of the volumes reaches by the rays on both paths, (notice then that MZI's are not good machines for Wheeler's experiment without a slight modification that creates an IZ, but Wheeler missed that point)), the question of where a particle comes from does not make sense any more (I assume here that Welcher Weg (WW) is unknown for all photons or else). IZ is a macroscopically defined object whose structure can be computed in simple cases or observed rather simply using separate observations. Once one understand that WW Determination (WWD an objective state of affairs) is impossible as soon as IZ is reached, it becomes obvious why Afshar's experiment does not allow WWD, and even less WW Knowledge (or WWK, a weaker, subjective status). Back to Wheeler, in all cases, if the observation is made in IZ or beyond IZ, the quantum went both ways. One can now make the observation just before the IZ, but then it is easy to see that the delay is meaningless (except if you believe that small green men transport the info faster than light to the beam splitting apparatus).
So the ONLY real problem remains the one pointed out by Feynman, i.e., the interference.
This is another story that I will not undertake here (but I'd love to discuss that somewhere soon enough).

Last edited: Aug 8, 2010
20. Aug 22, 2010

### hankaaron

You must remember that from the photons point of view (both the signal and idler photons), time does not exists and distances shrink to zero at the speed of light. So as far as the photons are concerned, each arrives at their respective detector simultaneously.