Effect Preceding Cause: A Quantum Physics Thought Experiment on Usenet

[Phrak]

Maybe I am just to dumb to understand: "The coherency length of a laser is equal to its length, ..."

Which length do you mean by "its length"?

It goes something like this, with my limited understanding. There's a narrow, but finite bandwidth of frequencies when the electron 'falls' from it's metastable state to a lower energy state. The laser is a resonant cavity that will only amplify the frequencies withing this bandwidth that that meet the boundry conditions imposed by the size and shape of the cavity. In the case of a lazer, it's just two mirrored surfaces. So the length between the two mirrored surfaces accommodates something like one trillion, one trillion and one, one trillion and two, etc. wavelengths.

Additionally, the phase of the wave at the mirrored surface is fixed for all frequencies. So, at the mirrors, they're in phase. Anywhere else, they will not be in phase. Check me on this.

Addtionally, how and where all the transverse components of the fields add-up has something to do with the TEM(x,x) specification. Maybe someone else, fresher on this material, can clarify.

 

[Phrak]

Robert-

An etalon is something new to me. Care to share?

 

[Robert Noel]

An etalon is a Fabry-Perot interferometer, either solid or air-spaced (but solid in laser cavities), and when it is used in the cavity of a laser, the beam enters it and is reflected back and forth by the reflective surfaces...the end result being that when angled properly, only the desired frequency is allowed to pass through while others interfere destructively, allowing the plasma (or whatever medium) to only amplify that single frequency, resulting in an extremely long coherence length. When I attended a holography course in Toronto, the large 50mw HeNe laser they had was equipped with an etalon, which allowed them to ignore the length differences between reference and object beam paths in the recording setup (I had to take care to keep beam paths as equal as possible on my table with my little 5mw HeNe in order to record 8"x10" holograms with a lot of depth, but I did it).

An etalon-equipped laser is standard in professional holography labs, where extremely monochromatic/temporally-coherent light is required.

From Wikipedia (under applications):

"Etalons are used to construct single-mode lasers. Without an etalon, a laser will generally produce light over a wavelength range corresponding to a number of cavity modes, which are similar to Fabry-Pérot modes. Inserting an etalon into the laser cavity, with well-chosen finesse and free-spectral range, can suppress all cavity modes except for one, thus changing the operation of the laser from multi-mode to single-mode. "

They are talking about longitudinal mode (temporal coherence/monochromacity) and not transverse mode (spatial coherence...ie. TEM OO)

Edit: I never really thought about it before, but it's funny how all holography texts I've read refer to the temporal coherence of a laser as the coherence-length (instead of coherence-time).

 

[dkv]

The interference is realized when and only when the paths are available to interfere.
blocking one of paths does not produce any interference.
In other words the intereference can be seen only after 45ns and not 5ns.
If path B is blocked the interfernce then the experiment is equivalent to the single slit experiment.
Is this correct?

 

[Phrak]

dkv, and all.
Here's an interesting factoid regaurding the experiment in question that will show that the analysis of this is not as simple as expected. A continuous wave sent to a shutter that's open for a short time, say, will modify the spectral components of the wave. (The same occurs with the 'half shutter' under question.)

Now you have a lot of different frequencies that have non-zero amplitudes on the down-stream side of the shutter before the shutter is opened--or did someone already mention this?

 

[Robert Noel]

The interference is realized when and only when the paths are available to interfere.
blocking one of paths does not produce any interference.
In other words the intereference can be seen only after 45ns and not 5ns.
If path B is blocked the interfernce then the experiment is equivalent to the single slit experiment.
Is this correct?

That is correct. I'm talking about the interference pattern disappearing after 5ns. I'm also talking about a single-frequency laser. Somehow I assumed most physics labs performing such an experiment would use an etalon-equipped single-frequency CW laser (hence the extremely long coherence length.

Again, I think the second image I posted should make it much clearer what I'm thinking. The interference is already occurring and we purposely destroy the interference, thereby (I assumed), determining the paths/locations of all photons, making all quantum weirdness suddenly irrellevant (or so I thought...I'm still struggling to understand why this isn't so).

Edit: I'll repost the image here with one gross error in phrasing corrected:

 

[Cthugha]

It goes something like this, with my limited understanding. There's a narrow, but finite bandwidth of frequencies when the electron 'falls' from it's metastable state to a lower energy state. The laser is a resonant cavity that will only amplify the frequencies withing this bandwidth that that meet the boundry conditions imposed by the size and shape of the cavity. In the case of a lazer, it's just two mirrored surfaces. So the length between the two mirrored surfaces accommodates something like one trillion, one trillion and one, one trillion and two, etc. wavelengths.

Additionally, the phase of the wave at the mirrored surface is fixed for all frequencies. So, at the mirrors, they're in phase. Anywhere else, they will not be in phase. Check me on this.

Roughly speaking this is correct, but it depends of course on the kind of laser you are using. For pulsed lasers you also may have designs, where you want to have lots of different modes in phase at a certain point of time (mode locking) or to detune the cavity (Q-switching).

However I am still puzzled on the connection to the coherence length. The longitudinal coherence length is related to the coherence time and is in easy cases usually determined via the decay of the autocorrelation, which is in easy cases the Fourier transform of the power spectrum.

 

[dkv]

if the obstruction of path B is dependent on a random outcome of another experiment then
your experiment suggests that the random outcome is deterministic in time which is not possible unless there is nothing random in the definition of randomness.(i.e the interfernce pattern disappears even before the random experiment is performed!)
therefore ,
I don't think that interference can be seen before 45ns.That is if interference can be seen only after 45ns then there is no question of the interference disappearence after 5ns and before 45ns.

 

[Robert Noel]

if the obstruction of path B is dependent on a random outcome of another experiment then
your experiment suggests that the random outcome is deterministic in time which is not possible unless there is nothing random in the definition of randomness.(i.e the interfernce pattern disappears even before the random experiment is performed!)
therefore ,
I don't think that interference can be seen before 45ns.That is if interference can be seen only after 45ns then there is no question of the interference disappearence after 5ns and before 45ns.

There is no randomness involved. We swith the laser on and see the interference occurring, and we then press a button that causes the shutter (or whatever obstruction we are using) to suddenly block the long path, stopping the already-occuring interference.

In the case of the second image (see post #41 above), the polarization of the linearly-polarized beam is rotated, causing it to be diverted away from the recombining beamsplitter to the long-path detector by the polarizing cube beamsplitter, causing interference (which has been occurring before we even start the experiment by diverting the long-path beam) to stop at the recombining beamsplitter and allowing light to reach the short-path detector. The beam is monochromatic (one single wavelength) and I'm confused as to why the subject of wavelengths has been discussed...I assumed that it is taken for granted that an etalon is used in a laser where such long beam-path length differences exist, and that etalon-equipped lasers can produce photons of only one single wavelength (or frequency, whichever you prefer) if desired, in other words, purely monochromatic light.

If I take the definition of photons as "discrete packets of energy" as I've read, I can't understand how interference can keep happening until we puposely divert the long-path beam. To me, it should logically disappear before we divert the beam, but if what Cthugha says is correct, apparently I've got some studying to do.

And for the record Cthugha, I never imagine photons as "bullets" traveling anywhere, or even waves travelling...I find it hard to imagine photons existing at any point between emission and absorption...but that's another matter entirely and is irrellevant in this experiment. When I say "the photon takes the short path or the long path", I'm just using easy to understand language that is commonly used.

 

[dkv]

the effects can precede cause but not in a deterministic way as you are suggesting.
I read the main diagram and not the second one.
Anyways ,
photons do not interfere with themselves...
We can understand the photon self-interference using different concepts.
"Deterministically" ,Effect is realized only after the causes become available.


(wavelength discussion is irrellevant and also the bullet or wave debate)

 

[Cthugha]

And for the record Cthugha, I never imagine photons as "bullets" traveling anywhere, or even waves travelling...I find it hard to imagine photons existing at any point between emission and absorption...but that's another matter entirely and is irrellevant in this experiment. When I say "the photon takes the short path or the long path", I'm just using easy to understand language that is commonly used.

Ok, I did not mean to sound like I "accused" you of thinking so. I just met a lot of people jumping to wrong conclusions from using commonly used language.

If I take the definition of photons as "discrete packets of energy" as I've read, I can't understand how interference can keep happening until we puposely divert the long-path beam.

Hmm, I am not sure, I get you here, but I would like to understand what you mean. Why does discreteness of the energy prevent interference right before one diverts the long path, from your point of view?

Anyways ,
photons do not interfere with themselves...
We can understand the photon self-interference using different concepts.

Photons do not self-interfere, but we can understand this interference, which is not happening with different concepts? That does not make any sense.
How do you explain single photon interference experiments, if photons do not interfere with themselves?

(wavelength discussion is irrellevant and also the bullet or wave debate)

Did you even bother to read the rest of this thread? As your first two posts already show, obviously not, there even was no "bullet or wave debate". I just commented about what one has to keep in mind, when dealing with photons and beam splitters on timescales shorter than the coherence length in post #24.

 

[dkv]

Anyone who has even a bit of the understanding of physics will not bother to discuss the non-commutativity of cause and effect becuase it will lead to contradiction to its very core as I said like introducing the non-probabilistic physics based on which we can not discuss the question of interference from quantum mechanical point of view.

 

[Cthugha]

Anyone who has even a bit of the understanding of physics will not bother to discuss the non-commutativity of cause and effect becuase it will lead to contradiction to its very core as I said like introducing the non-probabilistic physics based on which we can not discuss the question of interference from quantum mechanical point of view.

I strongly disagree. Finding flaws in thought experiments is usually very educative, especially if they are well put. Bohr and Einstein were very successful in doing so. For example one needs a severe understanding of coherence in order to find the flaw in the experiment presented here. As another example delayed choice quantum erasers also do not violate the principle of cause and effect, but it is very educative to find out, why.

As to the second part of your post, I do not get it. No one introduced non-probabilistic physics here, so I am very puzzled.

And I also still do not get, whether you think, that photons do or do not show self-interference. Your posts are not very clear.

 

[Robert Noel]

Ok, I did not mean to sound like I "accused" you of thinking so. I just met a lot of people jumping to wrong conclusions from using commonly used language.

No! Don't worry about that Cthugha! I did not take offense at all. I fully realize that the language I use makes it sound like that is how I think. I just wanted to let you know I don't think it's that simple. Hmmm...at the risk taking this thread way off-topic, here's an excerpt from something I wrote in another post about photons:

"But relativity states that for anything traveling at the "speed" of light, space would have to contract to a singularity in the direction of travel. I don't pretend to know what it's like to experience the knowable universe as a singularity, as I assume a photon must since it obviously "travels" at the speed of light, but I assume that in a singularity, all possible points along the path of the thing doing the traveling must overlap, that is, in some way, every place a photon can go (its knowable universe) exists in one place to the photon (even the term "place" would be meaningless in a singularity). I also assume that from relativity we can deduce that from the photons perspective, it's "journey" would be instantaneous (time dilation), which makes sense since if all possible points along its path overlap, it shouldn't take any time for it to get where it's going. So does it necessarily have to actually exist between emission and absorption? Is it possible that what we interpret as the wave-function is actually just an interpretation we make because we don't quite get what it's like inside a singularity. Could it be that the concept of existing in spacetime to a photon is as meaningless as the concept of existing in a singularity is to us?

I'm just having fun (I like to bend my mind around crap like this), but when thinking about relativity, I can't help but intuit that the photon's target is actually chosen the instant it is emitted...that an atom absorbing a photon has as much a causal effect on the atom emitting it (no matter how far back in time) as the emitting atom has on the absorber. Putting things like lenses in the path certainly affects the probabilities of where the photon can be absorbed, but who knows how a lens can be said to affect a photon when it exists as a part of a singularity? Does the photon actually have to exist between emission and absorption?"

My ideas are probably totally misguided, but that's how I see it at the moment. The main argument against this view is that particles that travel slower than the speed of light (ie. electrons) also have a wave-function, but then who knows how the bound-energy that constitutes an electron sees it's knowable universe? Does anyone know what an electron really is? We call it a "negative charge" but that's really a description based on what it does, not what it is (ie. it attracts particles that we call "positive charges", and changes direction in a magnetic field etc...). It seems that just about everything in nature is defined by what it does and not what it is. Same goes for gravity...some say it is warps in spacetime (I like that one), and some still try to define it by an exchange of hypothetical particles called "gravitons" (I groan whenever I read that one). Nobody knows what any of these things actually are...at least not that I'm aware of. Sorry to get so off-topic...I'll shut up now.

Hmm, I am not sure, I get you here, but I would like to understand what you mean. Why does discreteness of the energy prevent interference right before one diverts the long path, from your point of view?

Actually, it's more the term "packet" that I'm referring to...a small bundle of energy. It implies to me that it's something that can only be in one place (emitted or absorbed by one atom or particle). This concept of it taking multiple paths or existing as a spreading wave, to me, sounds more like an illusion or interpretation than an actual existing phenomenon. If I recall correctly (and I may not be), in one book by Richard Feynman, I was told to view this wave-function that we see depicted in interference diagrams as an abstraction that we use to calculate probabilities, and not an actual thing (I'm misquoting for sure as that particular book is back at the library..."QED" I think).

The concept that it matters wether or not we can distinguish photons in this thought experiment is incomprehensible to me. I have always considered that when we detect a photon (it is absorbed), we automatically determine exactly when it would have been absorbed at any other point in space (taking into account what we interpret as path changes via lenses, mirrors, gravity etc...). Likewise, I would think that we automatically determine exactly when any photon leaving the laser cavity (and again, "leaving the laser cavity", is just simplified language that I use) at the same time as the detected photon would be absorbed at any point in space. I can't seem to wrap my brain around the concept that, at least in this experiment, it matters if we can't distinguish which photon is which, but I'll keep trying.

Everything you're writing is going on my "try to understand" list...and I do appreciate your taking the time to reply!

Edit: The more I reread this post, the more I wonder if I'm making the slightest bit of sense...can you tell I'm confused? heh heh.

 

[Cthugha]

The concept that it matters wether or not we can distinguish photons in this thought experiment is incomprehensible to me. [...] I can't seem to wrap my brain around the concept that, at least in this experiment, it matters if we can't distinguish which photon is which, but I'll keep trying.

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.

I have always considered that when we detect a photon (it is absorbed), we automatically determine exactly when it would have been absorbed at any other point in space (taking into account what we interpret as path changes via lenses, mirrors, gravity etc...). Likewise, I would think that we automatically determine exactly when any photon leaving the laser cavity (and again, "leaving the laser cavity", is just simplified language that I use) at the same time as the detected photon would be absorbed at any point in space.

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?

 

[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!