Effect Preceding Cause: A Quantum Physics Thought Experiment on Usenet

[Robert Noel]

Ten years ago, I posted a long rambling post concluding with a thought-experiment on Usenet, and got no useful feedback. I'd like to try again here. I'd like to post a link to the original post, as it includes details on how I'd go about measuring the effect that I predict, but I don't seem to be allowed to post urls yet. Instead, I'll include a simple drawing that will preclude any need to even read the original post. It involves a simple interferometer using any long-coherence CW laser. Forgive my primitive drawing skills and terminology. If you find quantum physics at all interesting though, I hope you'll have fun considering my thoughts and correcting them as necessary. In the image below, nothing is to scale, and I pulled my distances out of a hat so to speak, but that should not affect the principle I'm trying to understand. If the text looks blurry, maximizing the page should fix it.
Thanks!

 

[AzonicZeniths]

I read your attachment, and you seem to have a mixed understanding of interference. For the interference pattern to happen you must have some kind of slit, because without that slit, you will not get the wave pattern from the photons. I have a pretty solid understand of wave-quantum-particle mechanics but I might not be understanding your experiment much yet. Explain how your beam splitters work and I might understand a little better. But, what you were saying about sending a signal that goes backwards through time, what would this do? How could it be applied for anything?

 

[ZapperZ]

Ten years ago, I posted a long rambling post concluding with a thought-experiment on Usenet, and got no useful feedback. I'd like to try again here. I'd like to post a link to the original post, as it includes details on how I'd go about measuring the effect that I predict, but I don't seem to be allowed to post urls yet. Instead, I'll include a simple drawing that will preclude any need to even read the original post. It involves a simple interferometer using any long-coherence CW laser. Forgive my primitive drawing skills and terminology. If you find quantum physics at all interesting though, I hope you'll have fun considering my thoughts and correcting them as necessary. In the image below, nothing is to scale, and I pulled my distances out of a hat so to speak, but that should not affect the principle I'm trying to understand. If the text looks blurry, maximizing the page should fix it.
Thanks!

I don't get it.

First of all, what is a "long-coherence CW laser"?

Secondly, why is this any different than the many Mach-Zehnder-type interferometer experiments that have been done? See, for example, T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

Zz.

 

[Robert Noel]

Hi ZapperZ. I thought CW was a pretty standard laser term. It means "continuous-wave", as in "not pulsed", like a standard HeNe. "Long-Coherence" means the waves remain in phase over a long distance, allowing interference to occur with large path-length differences. Perhaps I should have been more specific and said "long coherence length", but I though it was obvious.

And the drawing does not depict the experiment per se (though, I did state my original post on usenet contained an idea as to how to measure when the pattern disappears vs when we actually block path B). It is, as stated, a typical Mach-Zehnder interferometer. My question was, if we block the beam in path B 45ns into the light's journey, when does the pattern disappear at the screens (considering that path A's journey is only 5ns total and that the light in path A cannot interfere with it's path B counterpart because we block path B...40ns after the path A light reaches its target)?

 

[Robert Noel]

I read your attachment, and you seem to have a mixed understanding of interference. For the interference pattern to happen you must have some kind of slit, because without that slit, you will not get the wave pattern from the photons. I have a pretty solid understand of wave-quantum-particle mechanics but I might not be understanding your experiment much yet. Explain how your beam splitters work and I might understand a little better. But, what you were saying about sending a signal that goes backwards through time, what would this do? How could it be applied for anything?

Hi AzonicZeniths. The beamsplitters are standard cubes. You certainly can get wave patterns with cube beamsplitters (and plate beamslitters for that matter) as I've recorded holograms with them. What would this do?! Proving that the pattern disappears before we actually block path B would shatter beliefs about cause necessarily preceding effect on the macroscopic scale for one thing (and that's good enough for me). And if it were possible, creating chain reactions of such signals would change the world in more ways than I can imagine, but I'll wait until I find out if it's possible before I go speculating about that, heh heh.

 

[DrChinese]

If you find quantum physics at all interesting though, I hope you'll have fun considering my thoughts and correcting them as necessary. In the image below, nothing is to scale, and I pulled my distances out of a hat so to speak, but that should not affect the principle I'm trying to understand.

As ZapperZ points out, there are recent experiments that address the basic idea here: that effects can precede a cause. However, there are some major caveats: a) No FTL communication possibilities; b)The actual "effect" is still random and therefore the cause-effect connection is not deterministic; c) The predictions of QM are supported even though it appears to lead to logical contradictions.

There are plenty of head-scratching issues in QM, if you choose to think in "everyday" terms. For example, the issue you identify - effect preceding cause - is not a problem if the laws of physics are time-symmetric (particles can go either direction in time). I am not advocating this position particularly, merely stating that the contradictions are in our minds more than in the physics.

 

[Robert Noel]

As ZapperZ points out, there are recent experiments that address the basic idea here: that effects can precede a cause. However, there are some major caveats: a) No FTL communication possibilities; b)The actual "effect" is still random and therefore the cause-effect connection is not deterministic; c) The predictions of QM are supported even though it appears to lead to logical contradictions.

There are plenty of head-scratching issues in QM, if you choose to think in "everyday" terms. For example, the issue you identify - effect preceding cause - is not a problem if the laws of physics are time-symmetric (particles can go either direction in time). I am not advocating this position particularly, merely stating that the contradictions are in our minds more than in the physics.

Thanks for the reply DrChinese! I'll try to look up those references (assuming I can access them), but if it can be proven that the pattern would disappear a full 40ns (in this case) before we actually block path B, then we should be able to create a system whereby the process repeats itself (a chain reaction backwards through time via a feedback loop), in which case I can think of no argument that would negate the possibility of sending a binary signal (on/off or yes/no) as far back through time as the device was active, wether a few milliseconds or a few years!

 

[Robert Noel]

If anyone is interested, I have to go out for the day, but later tonight, I intend to post pictures depicting how I would go about measuring the timing between the disappearance of the pattern vs the blocking of path B (so someone can tell me how it compares to experiments already performed) as well as exactly how I would go about creating the "feedback loop" I mentioned. It's not as sci-fi as you might think...the signal (or lack thereof) would be present the moment the device was activated, that is, it's not as though we would experience one reality and then do something in the future to change that reality and create a new past or anything like that. The reaction would appear to be occurring in a forward through time direction, even though it's not...you'll see.

Wether my thought processes are faulty or not, I think you'll find it amusing since we all obviously find this stuff fascinating. At the very least, you'll have a good laugh at my expense.

Cheers!

Rob

PS: @AzonicZeniths: I was thinking about what you were saying about slits. To clarify, under ideal circumstances, in a Mach-Zehnder interferometer, light would interfere destructively at one exit port of the recombining beamsplitter and constructively at the other exit port. Just so you know, I consider the total absense of light at one exit port due to interference as a "pattern"...that is, I'm not expecting the classic double-slit pattern, though a slight shift in angular geometry of the setup can bring about such a pattern...but I know what you mean, and I know my terminology leaves much to be desired.

 

[Cthugha]

I'll try to look up those references (assuming I can access them), but if it can be proven that the pattern would disappear a full 40ns (in this case) before we actually block path B, then we should be able to create a system whereby the process repeats itself (a chain reaction backwards through time via a feedback loop), in which case I can think of no argument that would negate the possibility of sending a binary signal (on/off or yes/no) as far back through time as the device was active, wether a few milliseconds or a few years!

Ehm, no. I do not see, why the pattern should disappear before you block the path. You quoted Dirac in the picture, but I suppose you misunderstood his famous "each photon interferes only with itself". This statement aims at a situation with low light intensity down to the level of for example one photon passing a double slit at a time. Each photon interferes only with itself in this case as the interference of several photons would mean, that there are sometimes 2 photons, sometimes none and so one. In terms of conservation of energy this is impossible.

Now consider a situation where there are several photons present at a time. Let's start with 2. There have been experiments showing two photon interference, but they emphasized, that 2-photon interference is not the result of 2 photons interfering, but of the superposition of two indistinguishable two-photon amplitudes. If two photons are indistinguishable you can't even in principle tell, whether interference is a result of just one photon interfering with itself.

Going to even more photons - for example a CW laser - one might ask, whether these photons are distinguishable or not. Mandel once showed, that the degree of coherence corresponds with the degree of indistinguishability, so using a laser with long coherence time should not allow you to see an effect before blocking a a path.

 

[Robert Noel]

Ehm, no. I do not see, why the pattern should disappear before you block the path. You quoted Dirac in the picture, but I suppose you misunderstood his famous "each photon interferes only with itself". This statement aims at a situation with low light intensity down to the level of for example one photon passing a double slit at a time. Each photon interferes only with itself in this case as the interference of several photons would mean, that there are sometimes 2 photons, sometimes none and so one. In terms of conservation of energy this is impossible.

Now consider a situation where there are several photons present at a time. Let's start with 2. There have been experiments showing two photon interference, but they emphasized, that 2-photon interference is not the result of 2 photons interfering, but of the superposition of two indistinguishable two-photon amplitudes. If two photons are indistinguishable you can't even in principle tell, whether interference is a result of just one photon interfering with itself.

Going to even more photons - for example a CW laser - one might ask, whether these photons are distinguishable or not. Mandel once showed, that the degree of coherence corresponds with the degree of indistinguishability, so using a laser with long coherence time should not allow you to see an effect before blocking a a path.

Hmmm...I've obviously got some more research to do before I waste my time with more illustrations, but I'm not quite buying it. If two separate photons could combine their effects to contribute to the interference pattern, then you could combine single beams from two separate lasers with the same single longitudinal mode and obtain an interference pattern...you can't...at least everything I've read about holography,(a hobby of mine) suggests that it is not possible. But I'm taking you seriously enough to concede that I've got some more reading to do. Thanks for the reply.

 

[Cthugha]

If two separate photons could combine their effects to contribute to the interference pattern, then you could combine single beams from two separate lasers with the same single longitudinal mode and obtain an interference pattern...you can't...at least everything I've read about holography,(a hobby of mine) suggests that it is not possible.

That's right. You can't just combine single beams and expect an interference pattern to arise. It is at least not that simple. In most cases different light pulses are easily distinguishable.

I am not good at explaining, especially not in English. Maybe this paper might hint at what I mean:

Quantum interference by two temporally distinguishable pulses (Phys. Rev. A 60, R37 - R40 (1999)) (also available on arXiv)

You might also want to have a look at the Hong-Ou-Mandel experiment, but I must admit I do not know, which paper it was reported in. But I suppose, you might find a brief review of it in:

L. Mandel:Quantum effects in one-photon and two-photon interference; Reviews of
Modern Physics 71; 1999

 

[ZapperZ]

Hmmm...I've obviously got some more research to do before I waste my time with more illustrations, but I'm not quite buying it. If two separate photons could combine their effects to contribute to the interference pattern, then you could combine single beams from two separate lasers with the same single longitudinal mode and obtain an interference pattern...

This is incorrect. The interference pattern that we are all familiar with is the single-photon interference! 2-photon interference almost never, ever occur, and when it does, it isn't the interference pattern that you are familiar with. Refer to the Mendel paper that has been cited.

Zz.

 

[Robert Noel]

This is incorrect. The interference pattern that we are all familiar with is the single-photon interference! 2-photon interference almost never, ever occur, and when it does, it isn't the interference pattern that you are familiar with. Refer to the Mendel paper that has been cited.

Zz.

So...you're agreeing with me then? That's exactly what I was hinting at...that all the photons, even in a CW beam, interfere only with themselves and not each other, which is why I believe the pattern must disappear before beam B is blocked. But I'm going to have to research this concept of indistiguishability Cthugha has mentioned. I just can't imagine what difference it can make wether one photon or a billion photons strike the detector at once where the destruction of the pattern is concerned if each photon can only interfere with itself. I'll look up those references and see if I can convince myself to give this up.

You people are a gold-mine!

 

[Robert Noel]

From a brief search for these references (interference involving pulses/photons from different sources), I still can't understand how they relate to my interpretation, but I will continue to research.

As far as I can intuit, when we block the beam near the end of path B, all the corresponding photons that have reached the target via path A had nothing to interfere with, no matter how many were striking the target, period. If it takes the photons leaving the laser cavity 45ns to reach the point where we decide to obstruct path B, and only 5ns to reach the target via path A, I cannot see how the interference pattern can possibly continue to exist until after we block path B since the photons that took 5ns to reach the target via path A are the same photons that would have also taken over 45ns to reach the target via path B to interfere with themselves.

What are the photons taking path A interfering with if the pattern doesn't disappear 40ns before we block path B? Certainly not themselves, since we have prevented that (or more accurately, WILL have prevented that) by blocking path B!

 

[Cthugha]

As far as I can intuit, when we block the beam near the end of path B, all the corresponding photons that have reached the target via path A had nothing to interfere with, no matter how many were striking the target, period. If it takes the photons leaving the laser cavity 45ns to reach the point where we decide to obstruct path B, and only 5ns to reach the target via path A, I cannot see how the interference pattern can possibly continue to exist until after we block path B since the photons that took 5ns to reach the target via path A are the same photons that would have also taken over 45ns to reach the target via path B to interfere with themselves.

That is exactly, why I think the term single photon interference is badly chosen. A laser beam consists of a lot of photons, which are intrinsically indistinguishable during coherence time or stated more precisely if coming from the same coherence volume. So due to indistinguishability one could say at most that only photons from the same coherence volume can interfere. At first you can't tell, whether they do so with themselves or each other. So if you block the long path, taking your terminology there are still photons taking path B, which have already passed the blocking point and came from the same coherence volume as photons arriving at the same time, which took path A and therefore there should be interference.

However, this sounds pretty odd in particle description. It sounds much better, if you take the underlying field and possible paths into account.

Anyway I have to leave this discussion for a while as I am off to NOEKS 9 now. I hope to read some interesting posts, when I return end of the week.

 

[Robert Noel]

Wow! I just looked up NOEKS 9...Nonlinear optics is what I've been hoping would ultimately make my experiment (not the timing measurement but rather the chain reaction) possible -a two-wave mixing scenario using the right material, if it exists. I look forward to continuing this discussion with you! Have fun over there!

 

[Robert Noel]

This indistinguishability concept has me baffled. A photon leaving the laser cavity can only travel at one speed: "The speed of light". I can't understand how anything can circumvent the fact that after 45ns of leaving the laser cavity, a photon can only be at one specific distance along its path (assuming we force it to choose only one path). Therefore, I cannot see how our inability to distinguish which photon is interfering with which photon can have any bearing on the destruction of the pattern, how it can allow a photon to sneak past our barrier before we block it, wether we are thinking waves or particles, single photons or many photons. The constancy of the speed of light (of a photon) in a given medium is what makes me doubt that the pattern can continue to exist after the path A photons reach the target if we block path B 40ns later, preventing those same photons from reaching the target via path B (I hope I'm making sense here...I'm giving myself a headache).

I guess what I'm saying is that I don't understand why individual photons should care if we cannot distinguish them from other photons. Each travels at exactly the same speed and if we know the ones at our obtruction in path B would have taken 40ns less to reach path A, then the path A photons from 40ns ago could not have had anything to interfere with. I feel like an idiot for not "getting it", but my primitive brain just refuses to digest what it's being told, but I'll keep trying.

 

[muppet]

There's another Dirac quote that may be of relevance here. Someone once asked him what he thought happened when a wavefunction collapses. His reply was: "Nature makes a choice". In this experiment, nature is free to consider her options right up until the barrier is implemented.
It's difficult for me to sharpen this argument up much because I haven't studied QFT; I'm not sure if the idea of a "wavefunction" means anything when particle numbers aren't necessarily conserved. But conceptually (and very roughly speaking), it might be worthwhile remembering that wavefunctions commonly aren't strictly localised? A wavefunction assigns to each point in space the probability that a localised particle will be found there. Even though we talk about a hydrogen atom as having a radius of a couple of angstroms, the radial distribution function isn't zero a metre way from the proton; it's just extremely small. A free particle can only be completely localised to any finite region of space if it's described by a superposition of infinitely many plane waves (in which case all talk of it taking one path or the other is meaningless as the uncertainty in its momentum blows up in your face). The best way I could hope to understand this experiment without a knowledge of QFT would be to say that when the barrier is put in place the contribution to the wavefunction from eigenstates traversing that path is reduced to zero, so the interference pattern of the wavfunction vanishes. The "actual location" of the photon (by which it is meant a small region of high probability density of finding the electron) doesn't actually have a great deal to do with it. People who actually know something about the QM description of light please feel free to shoot me down if that's hideously inapplicable?

 

[Robert Noel]

But when photons reach the end of one path (detector or obstruction), the wavefunction collapses, the photon is localized, and since we know the exact length of each path, is it not determined exactly when they would have reached the end of the other path had they taken it? It's not like the speed of light is going to change in one path in order to preserve the pattern so we can't make effect precede cause...Or are we back to the indistinguishability thing again? It feels like we're supposed to believe nature actually cares what we know, like some program designed to foil our every attempt to tamper with it. I don't want to believe it, heh heh!

 

[muppet]

Well... by that reasoning you could time how long the photon took to be detected and work out which path it took without ever actually measuring the position at an intermediate point.

Would anyone care to explain why you can't do this?

 

[Robert Noel]

Well, because there's no way to tell when the photon was emitted or left the laser cavity unless you could trigger the emission of a single photon and measure the timing between triggering and absorption, which by itself, couldn't really be considered an interference pattern. We could, I suppose, do this many many times and see if a pattern still emerges though. Not quite as dramatic as what I'm proposing (trying to make the pattern disappear before we block path B), but I do wonder if it's possible.

 

[Robert Noel]

Here's an image depicting how I'd try to measure the timing if it helps. Again, maximize the image if the text is blurry. I hope I didn't leave out anything obvious. Again, the laser is a continuous wave laser with a long coherence length, but importantly, is also linearly polarized (pretty standard fare...a typical HeNe could fit the bill).

 

[Phrak]

Well, because there's no way to tell when the photon was emitted or left the laser cavity unless you could trigger the emission of a single photon and measure the timing between triggering and absorption, which by itself, couldn't really be considered an interference pattern. We could, I suppose, do this many many times and see if a pattern still emerges though. Not quite as dramatic as what I'm proposing (trying to make the pattern disappear before we block path B), but I do wonder if it's possible.

There are picosecond pulse lasers. A lot of filtering could bring the average photon density down to 1 per pulse. It's feasible, if not practicle.

 

[Cthugha]

This indistinguishability concept has me baffled. A photon leaving the laser cavity can only travel at one speed: "The speed of light". I can't understand how anything can circumvent the fact that after 45ns of leaving the laser cavity, a photon can only be at one specific distance along its path (assuming we force it to choose only one path). Therefore, I cannot see how our inability to distinguish which photon is interfering with which photon can have any bearing on the destruction of the pattern, how it can allow a photon to sneak past our barrier before we block it, wether we are thinking waves or particles, single photons or many photons. The constancy of the speed of light (of a photon) in a given medium is what makes me doubt that the pattern can continue to exist after the path A photons reach the target if we block path B 40ns later, preventing those same photons from reaching the target via path B (I hope I'm making sense here...I'm giving myself a headache).

I guess what I'm saying is that I don't understand why individual photons should care if we cannot distinguish them from other photons. Each travels at exactly the same speed and if we know the ones at our obtruction in path B would have taken 40ns less to reach path A, then the path A photons from 40ns ago could not have had anything to interfere with. I feel like an idiot for not "getting it", but my primitive brain just refuses to digest what it's being told, but I'll keep trying.

Ok, I see the problem here. Now it gets a bit complicated. I hope I manage to formulate my point of view in an understandable manner.

So what is a photon? It is the quantized analogon to the classical intensity of the light field. So in terms of fields it is second order, at a certain place and time it is something like

$$I(r,t)=E^*(r,t)E(r,t)$$

Now one can deconstruct the em-field at a certain point into a superposition of several fields. For example, you could have a superposition of a laser and several usual lamps or generally speaking just several sources. How does this superposition effect the intensity. Each field has an amplitude and a phase. Two different light sources do usually not show a fixed phase relationship, so it is pretty random, whether these fields add up (same phase) or cancel each other (phase shift of pi). So in average there will be no intensity created by the product of different light sources. The intensity is then created by the square of a single field.
Now consider the usual double slit. Here each of the two slits is a light source of its own, but as both are created by a single light beam, they show a fixed phase relationship. As you surely know, you will see an interference pattern at the screen. This is due to the fact, that now not only the squares of the fields from each slit contribute to the intensity, but also the product of the two fields, which does not have a random phase relationship and does therefore not cancel.
Moving on to a laser, the principle stays the same. Each atom (or molecule or quantum dot or whatever you use as the active medium) contributes to the final em-field. Due to the lasing processes all of these single fields show a fixed phase relationship.

Now the definition of coherence time is simply speaking a measure of how long there is a fixed phase relationship of the emission of a light source. So roughly speaking, coherence time determines the timespan inside which there are also contributions of products of different fields to the intensity, whereas outside of the coherence time there are just contributions of the squared single fields.

So inside coherence time, you can't just map each photon to a single source (which would be distinguishability), but have to take the whole superposition of all fields into account. If you introduce some delay (like you do) you even have to take the products of the fields at different times into account (inside coherence time) and all of the products of these fields contribute to the intensity, which is at the heart of indistinguishability. You just can't imagine the photon as a bullet traveling from the emitter to the detector anymore.

However, this was a rather classical explanation. To get to the quantum point of view, you just replace the fields with adequate operators.

 

[scjphysicist]

I pretty much agree with the other replies to this question, but let me give a little different viewpoint.

I think the main difficulty in interpretting your proposed experiment is with the energy-time uncertainty relation, often written as $$\Delta E \Delta t > \hbar$$. When you regard the time that a photon is launched into your apparatus as being very well-localized, say, to within a nanosecond, you are giving it a small delta t. But saying that it has a very long coherence length means, among other things, that it has a very small uncertainty in its energy, a small delta E. The energy-time uncertainty relation says that you can't meet both of those conditions in the same experiment. What I think this will mean is that if you have a laser with a coherence length of 50 light-nanoseconds, you won't be able to say when a photon is emittited with better than 50 nanosecond precision. My guess for what would happen if you ran this experiment is that as you changed the time that the shutter is switched, the contrast you would see in your fringes would change, gradually disappearing as you blocked the interference for a greater fraction of the time when the photon is in the apparatus.

 

[f95toli]

There are picosecond pulse lasers. A lot of filtering could bring the average photon density down to 1 per pulse. It's feasible, if not practicle.

There are some pretty good single photon sources around, they are not completely deterministic and the fidelity isn't 100%, but they are getting there. Quantum cryptography actually requires deterministic single photon sources in order to be completely secure, so there is a lot of money being spent on R&D in this field at the moment.

 

[Fredrik]

Thanks for starting this thread Robert. I really like this experiment. It's a fun problem that really shows how weird QM can be.

By carefully adjusting the length of the longer beam, we can choose what fraction of the photons will be detected by the lower detector. Let's say that we set it up so that the lower detector never clicks. By inserting the obstacle (permanently) we destroy the interference, and the result is that the lower detector clicks 50% of the time.

Now let's assume that the intensity of the beam is so low that only one photon at a time is emitted. This doesn't change any part of what I just said. With the obstacle in place, the lower detector clicks 50% of the time. Without the obstacle, the lower detector never clicks. This can be explained using path integral methods. (The simple kind that's described in Feynman's QED book). The amplitude associated with the longer path to the lower detector is -1 times the amplitude associated with the shorter path to the lower detector, so the amplitudes add up to zero.

Now we're getting to the fun part. Let's start with the obstacle in place and wait until the lower detector clicks. Now we quickly remove the obstacle. If the photon "takes both paths", moving at speed c, it isn't going to hit the obstacle, so how could the lower detector click?

The only answer I can think of is that the obstacle blocks some of the superluminal paths through space-time. Apparently that's enough to get the detector to click some percentage of the time. (We're not just supposed to add up amplitudes associated with paths through space, we're supposed to add up amplitudes associated with paths through space-time. We can often ignore paths with the "wrong" velocity, but this isn't one of those times).

Now let's do it a bit differently. Let's say that we instead remove the obstacle exactly 10 ns after each time a photon is emitted. (We'd have to change the setup a little bit, but it can be done). This situation is only slightly different from the first. The obstacle still blocks only some of the superluminal paths, but that's enough to change what percentage of the photons will be detected by the lower detector.

Does it matter how long we leave the obstacle in place before we remove it? I think it makes a big difference. I think that if we remove it almost instantly, the result of the experiment will be close to what it would be with no obstacle (50% detected by the lower detector), and if we wait until the last nanosecond to remove it, the result of the experiment will be close to what it would be with a permanent obstacle (0% detected by the lower detector).

Does this mean that the effect is preceding the cause? In a way, yes, because by removing the obstacle at t=10 ns, we're affecting the probability of the possible events at t=5 ns. Does this mean that we can send messages into the past? No, it doesn't. This should explain why:

Suppose that we choose the time to leave the obstacle in place so that the lower detector will click 25% of the time. By increasing the time a bit, we can get it to click 30% of the time. By decreasing the time a bit, we can get it to click 20% of the time. We can let 30% mean "1" and 20% mean "0", and send a binary code message by sometimes going for 30% and sometimes going for 20%. But to send even a single binary digit, we'd have to let many photons be detected. We are, in a way, "sending a message into the past", but there's no way to see what the message says until after we're done.

This is the reason why causality isn't really violated. The interference "pattern" is only present in the data from a large number of detection events. Nothing useful can be learned from a single detection event.

 

[Cthugha]

Now we're getting to the fun part. Let's start with the obstacle in place and wait until the lower detector clicks. Now we quickly remove the obstacle. If the photon "takes both paths", moving at speed c, it isn't going to hit the obstacle, so how could the lower detector click?

The only answer I can think of is that the obstacle blocks some of the superluminal paths through space-time. Apparently that's enough to get the detector to click some percentage of the time. (We're not just supposed to add up amplitudes associated with paths through space, we're supposed to add up amplitudes associated with paths through space-time. We can often ignore paths with the "wrong" velocity, but this isn't one of those times).

Ehm, no. This is quite some usual problem. Popular statements like "the photon takes both parts and moves at c" are ripped out of context and lead to wrong results. If you read post #24 again, you will notice, that the notion of a photon being a somewhat bulletlike entity moving at c is at most valid outside of coherence time. In fact the changes in the underlying fields are moving at c, which is a huge difference. There already is a field beyond the obstacle. You do not annihilate it instantly by putting the obstacle in.

 

[Robert Noel]

Wow...this is a lot to digest! I guess one of my problems is in terminology. I've gotten used to thinking in terms of "coherence lengths" (all holography books refer to coherence length of lasers) and "discrete packets" etc...

"Fields" and "coherence times" and "indistinguishability" are bending my mind, but I really, really appreciate all the input. I have to learn to think in these terms. I'll probably spend days (if not weeks) thinking about what you folks have been saying.

I really do wish I'd posted the image I uploaded in post #22 instead of the one I uploaded in post #1 though. It might not make any difference, but it might better depict where my thought processes went wrong. I think that where my thinking is flawed is in assuming that once the wave-function collapses for the photons in either path (eg. we divert path B to detector 2 in the second image), the time of emission of the photons in either path becomes irrellevant. Obviously I was wrong, and I have to spend some time trying to understand all of this.

I can't thank you people enough!

Edit: I did make major typo in the second image...where it says "at the same time" I should have said "as a result"...but hopefuly it was obvious.

 

[Fredrik]

If you read post #24 again, you will notice, that the notion of a photon being a somewhat bulletlike entity moving at c is at most valid outside of coherence time. In fact the changes in the underlying fields are moving at c, which is a huge difference. There already is a field beyond the obstacle. You do not annihilate it instantly by putting the obstacle in.

I didn't read #24 before, but I have read it now. I don't see how concerns about photons being indistinguishable are relevant when we can just lower the intensity so that the source emits (for example) an average of one photon per millisecond.

You're implying that there's something wrong with what I said, but you didn't say what. The only hint you gave me seems to be a misunderstanding on your part:

Popular statements like "the photon takes both parts and moves at c" are ripped out of context and lead to wrong results.

That was my conclusion too. I thought I made that clear enough in my post.

I have always felt that it's an extreme oversimplification to say that the photon takes both paths. I would rather say that each path through space-time from the emission event to a possible detection event contributes to the probability that the photon will be detected at that event. To calculate that probability, we would have to add up the probability amplitudes associated with N paths (chosen so we can get all the paths by letting N go to infinity), divide by N, take the square of the magnitude of the result, and then let N go to infinity. (That's just the definition of a path integral). Hm, that's quite a mouthful. Maybe that's why the phrase "the photon takes both paths" is used so often.