Effect Preceding Cause: A Quantum Physics Thought Experiment on Usenet

[Robert Noel]

The concept of distinguishability is not only important in this experiment, but in any experiment concerning interference. Niels Bohr thought of the concept of complementarity as being fundamental in quantum mechanics.

Maybe you know the famous delayed choice quanum eraser experiments, in which you can either have which way information or an interference pattern. If you can distinguish photons this means you can track them back to their source in principle, which is the same as having which way information. The Englert-Greenberger duality relation even predicts quantitatively how the amount of distinguishability affects the interference pattern.

Aha! I agree with that totally. But in this experiment we are purposely destroying the interference pattern by bringing about distinguishability (if that's what you mean...that by forcing the photons to take only one path or the other we are bringing about distinguishability...?). But if all the photons that are blocked or diverted near the end of the long path are now distinguishable, then how can the photons at the end of the short path have remained indistinguishable for an additional 40ns until we block/divert the long path (that makes no sense whatsoever to me), that is, how can the interference keep occurring until we block the long-path beam? That, again, would imply faster than light photons (if they can sneak past the point in time when we obstruct or divert the long path in order to interfere with the "part of themselves that took the short path").

So let's take a beam of light, send it through a beam splitter and send both beams through another beamsplitter, which "reunites" them. If you detect a photon in one of the two beams, which come out of the reuniting beam splitter, do you determine in which of the two beams between the first and the second beamsplitter the photon would have been detected?

No, you, of course, could not. But in this case of ideal interference (assuming we can keep the beam perfectly collimated over such a long distance..or use corrective optics to do so), the phase of the beams is such that we have light exiting one port of the recombining beamsplitter only (which we discard and ignore), and no light reaches the detector at the other exit port (due to destructive interference) until the "pattern" is destroyed. We are not trying to determine "which way" while preserving the interference pattern in this case (that's impossible), we are trying to determine "how much time" while destroying the interference pattern...the "which-way" is obvious.

Edit: I am referring to the second image I posted, as the paragraph above wouldn't make much sense while looking at the first image.

 

[Cthugha]

Aha! I agree with that totally. But in this experiment we are purposely destroying the interference pattern by bringing about distinguishability (if that's what you mean...that by forcing the photons to take only one path or the other we are bringing about distinguishability...?).

Yes, exactly. This is one way to destroy indistinguishability.

But if all the photons that are blocked or diverted near the end of the long path are now distinguishable, then how can the photons at the end of the short path have remained indistinguishable for an additional 40ns until we block/divert the long path (that makes no sense whatsoever to me), that is, how can the interference keep occurring until we block the long-path beam? That, again, would imply faster than light photons (if they can sneak past the point in time when we obstruct or divert the long path in order to interfere with the "part of themselves that took the short path").

Ah, now it gets very interesting. Now we have to take the exact kind of light source we use into consideration. The results are different for two kinds of light sources, which one might take into account here.

Let me at first state, that I think the usual explanation of single photon interference by damping the intensity down to one photon per rather long time interval can be extremely misleading for beginners. So let me tell you why by looking at the two kinds of light sources:

a) A photon source, which emits a single photon at a well defined moment.

This kind of photon source would never produce an interference pattern in your kind of setup. If the time delay between both arms is longer than the uncertainty of the moment of emission, there are no indistinguishable paths anymore and therefore there is nothing left to interfere. If you know the moment of emission, the time of detection tells you, which of the two arms the photon took. I will comment on how to create interference with a single photon source at the end of this post.

b)A coherent light source with very low average photon number

Here one has to keep in mind that an average photon number of 1 does not mean, that there really is exactly one photon per interval. Your light source will usually consist of lots of emitters. Each emitter creates an em-field. As an easy model you can imagine, that photons are emitted completely independent of each other. If you now detect a photon, you do not know, whether it was emitted 5 ns before and took the short path or whether it was emitted 50 ns before and took the long path and therefore you see some interference.

If you now block the long path (let me use your first example for this) for example at a point, from where photons would still travel 6 ns to the detector, the paths are still indistinguishable for these following 6 ns. A photon, which has been emitted more than 44 ns before the path was blocked, will have already passed the position, where the block is put, and therefore in the following 6 ns you cannot tell, whether a detected photon took the short path and was emitted 5 ns before detection or whether it took the long path and was emitted more than 44 ns before the long path was blocked. There will still be interference for these 6 ns.


To get back to case a), you could make it work by using a randomly emitting single photon source, for example in a procedure similar to spontaneous parametric down conversion. If the moment of emission is completely random, once again you cannot tell, which path it took. Case a) is also the reason, why I think single photon self interference is somewhat misleading. Single photons, which are emitted deterministically at extremely precise defined and well known times and are sent to a double slit would NOT show the usual interference pattern, but just a small line of interference at the middle of the screen, which is not immediately clear to most, who hear about single photon self interference for the first time.

 

[Robert Noel]

Yes, exactly. This is one way to destroy indistinguishability.

Here one has to keep in mind that an average photon number of 1 does not mean, that there really is exactly one photon per interval. Your light source will usually consist of lots of emitters. .

Absolutely, and this is why I considered the exact time of emmision as somewhat irrellevant...in the case of a HeNe laser, a single photon could have been emitted from any atom along the length of its plasma tube, and further, could have bounced back and forth in the cavity dozens or millions of times before leaving the partially reflective exit mirror of the cavity...this is why I keep referring to the photons at the moment of "leaving the laser cavity", and where this timing is concerned, I'm always counting backward from when it was absorbed rather than counting forward from when it was emitted.

If you now block the long path (let me use your first example for this) for example at a point, from where photons would still travel 6 ns to the detector, the paths are still indistinguishable for these following 6 ns. A photon, which has been emitted more than 44 ns before the path was blocked, will have already passed the position, where the block is put, and therefore in the following 6 ns you cannot tell, whether a detected photon took the short path and was emitted 5 ns before detection or whether it took the long path and was emitted more than 44 ns before the long path was blocked. There will still be interference for these 6 ns.

Brilliant! I feel like a complete idiot for not having taken this into account! Now do not consider this to be a counter-argument, as my brain is aching from trying to picture what is going on, and I'm likely going to have to stare at diagrams and think about this for quite some time before I can say "I get it!", but for some reason, I can't help but imagine, again, the interference pattern disappearing before the beam is blocked, as predicted, and then reappearing for those few ns after the beam is blocked...that is, if I stick to my guns and consider photons interfering with themselves and not each other. But as I said, I really have to think about it, and I'm rather exhausted from work at the moment.

I may be trying your patience, and I am more confused now than ever, but I can't remember ever having this much fun just sitting down and thinking, and for that, I thank you!

If I can think of an intelligent counter-argument, I'll post it, and if I suddenly "get it", I'll let you know.

Thanks again Cthugha!

 

[Fredrik]

you cannot tell, whether a detected photon took the short path and was emitted 5 ns before detection or whether it took the long path and was emitted more than 44 ns before the long path was blocked.

The experiment described by the picture in #1 can't distinguish between those paths, but we can modify it by putting a detector in the path of the beam immediately after the laser. This should be a detector that registers when a photon goes through it. Now we can know if the photon was emitted <6 ns before detection or >44 ns before detection. I'm not concerned by practical difficulties, since we're discussing a thought experiment. We can even imagine a light source that emits on average one photon per year if that helps.

I really think that what I said in #27 is the answer. We have to consider the contribution from all paths through space-time, not just through space, and include contributions from superluminal paths.

 

[Cthugha]

The experiment described by the picture in #1 can't distinguish between those paths, but we can modify it by putting a detector in the path of the beam immediately after the laser. This should be a detector that registers when a photon goes through it. Now we can know if the photon was emitted <6 ns before detection or >44 ns before detection. I'm not concerned by practical difficulties, since we're discussing a thought experiment. We can even imagine a light source that emits on average one photon per year if that helps.

Of course you can put in such a detector, but given perfect detection efficiency it would destroy any interference in this experiment as explained before. While it is true that Feynman included superluminal and subluminal paths in his "sum of histories" approach, I do not know of any case in optics, where this approach leads to predictions, which are different from just taking luminal paths into account.

 

[Fredrik]

I must have missed that explanation. I haven't read every post, since most of the discussion seemed to be about things beside the main point. Do you mind explaining it again, or showing me where it was explained? It seems impossible to me that such a detector can destroy the interference. (Did you understand that I meant that it should be put in the path before the first place where the beam splits up?)

A single-photon experiment with one of the paths through space blocked some of the time seems to be the perfect example of a situation such that all paths must be included in the path integral.

 

[Cthugha]

I must have missed that explanation. I haven't read every post, since most of the discussion seemed to be about things beside the main point. Do you mind explaining it again, or showing me where it was explained? It seems impossible to me that such a detector can destroy the interference. (Did you understand that I meant that it should be put in the path before the first place where the beam splits up?)

Yes, I understood, that you intend to put it before the first beam splitter. Nevertheless such a detector would give us two informations: position of the photon and photon number at a certain moment. As you know the position of the photon at a certain moment, the final detectors will measure the photon either at a time corresponding to the long path or at a time corresponding to the short path, so you know, which path the photon traveled and therefore the interference vanishes.

From a different point of view, you can also imagine the system as being in some coherent state at the beginning. The first measurement corresponds to a position measurement and therefore puts the photon into a position eigenstate (strictly speaking, there are no generally accepted position eigenstates for photons, but this stems from the fact, that one cannot measure photon positions without destroying the photon due to their masslessness, so your ideal detector would be able to put them in a position eigenstate). So now the nice properties of the coherent state are lost, especially the long coherence time goes away and tends towards 0. As now the time delay is longer than the coherence time, you will not be able to find any interference.

 

[Robert Noel]

Ok, I've been thinking about it and I've drawn a different conclusion: I realize that I've been ignoring all the photons taking the long path (of their 2-path journey) before before we divert it...that they still do interfere even after the "subject photons" (the ones we force to take only one path or the other) taking the short path have reached the end of the short path...BUT, looking at the second illustation in post #41, if those photons taking the long path (of their 2-path journey), the ones that left the laser cavity before the subject photons, are still interfering, then are they not still avoiding the first detector by exiting the other port of the recombining beamsplitter? Does this really change the experiment if the subject photons taking the short path are being split 50/50 at the recombining beamsplitter while the older photons taking the long-path (of their 2-path journey) are still at 100/0 at the same time? Because now it sounds like photons would be interfering with other photons and not themselves if this isn't so.

 

[Fredrik]

The first measurement corresponds to a position measurement and therefore puts the photon into a position eigenstate

I don't think this is a problem for the path integral description. I'd say it's the exact opposite of a problem! It is what the path integral requires. What the path integral formulation of quantum mechanics tells us is that given an emission event, we can calculate the probability of detection at another event. We're not supposed to start with a superposition of emission events. We're just given one event. In this case, the emission event that we are supposed to plug into the path integral calculation is the event where the photon is detected at this additional detector.

However, if this position measurement destroys the interference in the state vector formulation of QM, it must do it in the path integral formulation too. While trying to use the path integral method to either prove or disprove that there will be interference I have realized that there are a few things about this method that I still don't understand. I'm going to have to think about this some more.

 

[Robert Noel]

Also, in the case of the first image I posted, where it looks as though an interference pattern is formed after both exit ports of the recombining beamsplitters (I really wish I hadn't posted that image, but rather, only the second image in post #41), when we block the long-path beam, I'm now picturing the interference pattern being diminished before we block the beam rather than completely erased, until 5ns after we block the path, and then it is completely erased. After all, only the subject photons would stop interfering, while the photons taking the long path (of their 2-path journey) before we block the long path would keep interfering. That is, we make the short path "subject" photons distinguishable at the detector while the older photons taking the long path (or their 2-path journey) still interfere because they are still indistinguishable...?

As you said: "The Englert-Greenberger duality relation even predicts quantitatively how the amount of distinguishability affects the interference pattern."


No matter which image I look at (though I much prefer the second image), I still see effect preceding cause, unless photons are interfering with other photons and not themselves, which counters everything I've read in books on the subject...sigh!

 

[Cthugha]

I don't think this is a problem for the path integral description. I'd say it's the exact opposite of a problem!

Oh, I never intended to say, that it is a problem for the path integral formalism. Putting such a detector in just makes the whole experiment uninteresting by destroying any interference pattern. Path integrals are fine as a model although they are nasty and unpractical when it actually comes to calculate stuff.

Also, in the case of the first image I posted, where it looks as though an interference pattern is formed after both exit ports of the recombining beamsplitters (I really wish I hadn't posted that image, but rather, only the second image in post #41), when we block the long-path beam, I'm now picturing the interference pattern being diminished before we block the beam rather than completely erased, until 5ns after we block the path, and then it is completely erased. After all, only the subject photons would stop interfering, while the photons taking the long path (of their 2-path journey) before we block the long path would keep interfering. That is, we make the short path "subject" photons distinguishable at the detector while the older photons taking the long path (or their 2-path journey) still interfere because they are still indistinguishable...?

No matter which image I look at (though I much prefer the second image), I still see effect preceding cause, unless photons are interfering with other photons and not themselves, which counters everything I've read in books on the subject...sigh!

Ok, letme at first comment on the first image.
Where exactly do you think, that different photons interfere? You can't really say, that photons taking one path keep interfering, while those taking the other path don't. The key to interference is, that you can't distinguish photons taking the short path from photons taking the long path. So in fact the photon taking the long path and the photon taking the short path are the same single photon, which produces the interference pattern. Although this seems counterintuitive, one must keep in mind, that we have a coherent state. The key property of a coherent state is, that the uncertainty of the moment, when one certain photon is emitted is roughly the order of the coherence time. So it is this one single photon, which interferes with itself. It takes the long path and is emitted early or it takes the short path and is emitted later. As long as those paths (or better realizations or histories) are indistinguishable, there will be interference. Just to stress it, you do not need one older photon traveling the long path and one newer photon traveling the short path, but just one photon, which could have taken both paths and could have been emitted at both times with equal probability.

The second image does not change anything in principle.

 

[Robert Noel]

Where exactly do you think, that different photons interfere? You can't really say, that photons taking one path keep interfering, while those taking the other path don't.

I'm not saying that at all. I'm saying that the older photons taking both paths interfere while the newer ones forced to take one path don't.

The key property of a coherent state is, that the uncertainty of the moment, when one certain photon is emitted is roughly the order of the coherence time. So it is this one single photon, which interferes with itself. It takes the long path and is emitted early or it takes the short path and is emitted later. As long as those paths (or better realizations or histories) are indistinguishable, there will be interference. Just to stress it, you do not need one older photon traveling the long path and one newer photon traveling the short path, but just one photon, which could have taken both paths and could have been emitted at both times with equal probability.

This is the part I just cannot get my mind to accept. Each atom emits its own photon, wether only one atom is doing it or billions. This idea that one photon could have come from two atoms, or that an atom could have emitted a single photon at two different times just doesn't sound realistic. I can accept that a photon can "take both paths" (given my strange relativity-inspired view on how a photon might "percieve" its knowable universe), but the idea that we can consider a single photon as having come from two sources, or a single source at two different times, just doesn't fly with me. That said, you do have me thinking...is it any stranger that a photon can be emitted at two different times than that it can be absorbed at two different times? Hmmm...food for thought...I think you've finally convinced me that there's something seriously wrong with how I think...again, thanks!

Edit: I think the main reason for my flawed thinking is in reading about how "an electron drops from a higher orbit to a lower orbit and emits a photon in the process", which suggests a single determined cause (and effect)...obviously it must not be that simple.

 

[Cthugha]

I'm not saying that at all. I'm saying that the older photons taking both paths interfere while the newer ones forced to take one path don't.

Ah, ok. I misunderstood. Sorry.

Edit: I think the main reason for my flawed thinking is in reading about how "an electron drops from a higher orbit to a lower orbit and emits a photon in the process", which suggests a single determined cause (and effect)...obviously it must not be that simple.

Yes, exactly. One important thing is that the light source matters. One might picture a simple single electronic transition as a single determined cause for photon emission, but the important thing is, that just having a lot of such transitions does not produce coherent light. Coherent light is different. If you have a look at how a laser works, you will notice, that the main source of photon emission is stimulated emission. So you have some atom/molecule/quantum dot or whatever your active medium is in an excited state. Another photon, which was emitted by some other atom/molecule/quantum dot and is resonant with the electronic transition comes along and triggers stimulated emission. The atom/molecule/quantum dot is back in its ground state again and you do now have two photons with equal phase, wavelength and direction. Can you tell, which one was emitted in the process of stimulated emission and which was the stimulating photon?

 

[Robert Noel]

Heh heh, which unveils yet another mystery: How a photon can stimulate the emission of another photon with the same properties (interact with another atom) without having its own properties changed.

But one mystery at a time is quite enough...I'll be spending a lot of time trying to understand all you've revealed to me in this thread.

I can't thank you enough Cthugha. Your input, and your patience, is much appreciated...as is everyone else's!

 

[dkv]

Yes how can a photon emit another photon?

 

[Nick666]

So are there any experiments where the effect is preceding its cause ?

 

[Cthugha]

Yes how can a photon emit another photon?

It doesn't. It just stimulates another atom to emit another photon.

 

[dkv]

How can the emitted photon have the same properties?

 

[Phrak]

How can the emitted photon have the same properties?

http://en.wikipedia.org/wiki/Stimulated_emission" if you want to read about it

 

[dkv]

The incident photon interacts with excited atom which means it must loose some of its original properties to do so... I mean how can some thing interact without interacting at all!