GRED Answer: Double slit with fast lensless video screen

[RJN]

Guess the Result of the Experiment of the Day (GRED): Double slit with fast video camera

A classic double slit experiment is done with light (photons) that creates an interference pattern on a distant image screen. The experiment is repeated, except now the image screen is replaced by an extremely high speed video sensor array, without a lens. The video sensors act just like the old image screen, except now each frame of the video is precisely time tagged. The time of release of single source photons is also recorded precisely. Adding all of the frames, what pattern accumulates on the video camera's screen?

Here is an ASCII schematic:

Code: Select all

                                                            
                               |                                |
     s                         |                                |
                               |                                |

    Photon                   Double                            Fast
    Source                    Slit                            Video 
                             Screen                           Screen

Aspect to consider: if the precise time-of-flight time for a photon is known, won't it be possible to compare this with the time-of-flight it would take for this photon to go through each slit, and therefore determine which slit this photon went through? And if such "which-path" information is known -- won't this destroy the interference pattern?

I have now posted what I believe to be the answer here: http://asterisk.apod.com/vie ... 50#p125040 . Still, please continue to post other answers, comments, and discussion below.

The initial poll, where spoilers were not allowed, can be found here: http://asterisk.apod.com/vie ... 30&t=19825 . If you are new to this GRED and want to ponder this question without seeing spoilers, please go there now instead of scrolling down.

- RJN

[RJN]

I have just updated the above GRED text, adding an "Aspect to consider" paragraph under the ASCII schematic. - RJN

[djmuk]

Surely the interference pattern is independent of the means of observation - it is function of the photon properties so the video array should see the 'standard' interference bands. As for 'which slit' the photon passed through, the answer surely is 'both of them'...?

[Wayne]

Even if the photon passes through only one slit (e.g. experiments done with single photons at a time), it still produces an interference pattern as we can consider it to be interfering with virtual photons.

This is simply a high-tech take on the one photon at a time experiment which has been done and did produce an interference pattern.

[alter-ego]

Even if the photon passes through only one slit (e.g. experiments done with single photons at a time), it still produces an interference pattern as we can consider it to be interfering with virtual photons.

Actually the interference pattern is only explained if the photon does in fact go through both slits. If the photon only goes through a single slit, the intensity pattern would instead be the filled-in diffraction pattern (as if one slit were blocked)

This is simply a high-tech take on the one photon at a time experiment which has been done and did produce an interference pattern.

As I've interpreted the problem, it poses a deeper more thought provoking question. The problem presents you with a timing capability of arbitrarily high precision for both source and camera, which along with positional (pixel location) information, gives you the potential to determine which slit every photon goes through. If this is true, then we know the interference pattern will not be visible.

So the question still is, will you see the intereference pattern or not?

FYI, more recent exotic double-slit experiments have yielded a "which-way" determination for the single photons. Interestingly, the results still show an interference pattern albeit one having reduced fringe contrast, but not totally lost which historically has been the case when attempting to acquire photon pre- and post-slit positional information.

[ryan]

Ok, am i missing something? It appears as if it is stated that all of the frames would be added together, in which case, there would be no difference between this experiment and a photographic plate.

[alter-ego]

Ok, am i missing something? It appears as if it is stated that all of the frames would be added together, in which case, there would be no difference between this experiment and a photographic plate.

Good question, I'm actually not sure. If your saying that precise single-photon timing makes no difference, i.e. summed timed frames = integrated un-timed viewing screen, period, end of story, than that's your answer. On the other hand, if you don't understand why timing single photons was suggested, or how timing can give postional information, or how positional information could help, then yes, you are missing something.

[ryan]

Ok, am i missing something? It appears as if it is stated that all of the frames would be added together, in which case, there would be no difference between this experiment and a photographic plate.

Good question, I'm actually not sure. If your saying that precise single-photon timing makes no difference, i.e. summed timed frames = integrated un-timed viewing screen, period, end of story, than that's your answer. On the other hand, if you don't understand why timing single photons was suggested, or how timing can give postional information, or how positional information could help, then yes, you are missing something.

Yeah, ok, so i guess I missed why the timing was mentioned...please forgive my mean tone and my lack of knowledge of the most recent developments in slit expts. However, the statement that all frames are added leaves this conundrum open to the simple conclusion that it is no different than the classical experiment.

[biddie67]

It seems to me that the interference pattern will still be recorded on the video frames. The big difference would seem to be the frame speed of the video recorder relative to the emission rate of the photons. It the video recorder frame speed is faster than the emission rate of the photons, then it should take more frames added together to display the interference pattern. If the video recorder frame speed is less than the emission rate of the photons, then it would take less frames to display the interference pattern.

Our eyes seem like they "see" at a much slower rate than the emission rate of photons so that we can "see" the interference pattern reflected off the flat screen as a steady or continuous effect. If we "saw" at a faster rate, then I don't think that we could see the same continuous effect.

[alter-ego]

Yeah, ok, so i guess I missed why the timing was mentioned...please forgive my mean tone and my lack of knowledge of the most recent developments in slit expts.

Hi ryan - I sensed no mean tone, no worries.

[Scottopoly]

Here's my stab at it:

An interference pattern would appear.

Reasons:

- Blocking one slit or "detecting" the photon passing through one of the slits fundementally changes the system. Once the photon gets to the slits it can be affected by the reality of what's going on at the silts. In our experiment here it can't be affected until it gets to the video screen. This is a causality argument. No signals are being sent from the video screen (it doesn't emit photons or anything) so the photon wave packet *can't* be affected by it until it reaches it. By then, the wave packet already has its interference-shaped distribution.
- Measuring the precise time a photon takes to travel is not equivalent to measuring which slit it went through. In principle, a photon could take a path that is not a straight line from the source to the target, travelling at the speed of light and taking the corresponding time to do so, though anything but the most direct path will be highly unlikely.
- You could solve the problem via thought-experiment like so: at the photon's conception it is represented by a focused wave-packet at its origin. Now evolve that wave packet in time, it will float forward, spreading out a bit, hit the slits, then get all wobbly and interference-shaped. I imagine it would be spread out "front to back" wise, not just sideways spreading-out, or vertical spreading-out. This would represent the uncertainty in the time that the photon will take to reach the screen. As soon as the wave packet begins overlapping the video screen with any significant probability-density, it would have a chance of becoming "detected" at any given instant once that happens. Of course then it *is* detected, and God chooses a point in that wave packet where The Photon Shall Be. He reaches down with his Finger of Determinability and Makes It So. The scientists detect the photon and everyone is happy. I don't think the different screen would affect the outcome of the spacial distribution of photons in any way, but I could be wrong.

(You would get extra data from many trials: the "depth" distribution of the wave-packet when the wave-packet intersects the screen. This third dimension is lost in the conventional experiment.)

[djmiller]

I think I may have this one...

In accordance with the traditional case of the double slit experiment you should see the diffraction pattern as you continue to detect photons at different positions on your detector. The image below demonstrates how this pattern builds up as the photon count increases.

Detection of electrons through a double slit through different exposure times. (From the Double Slit Wikipedia article)

---

As for the measurement of time of travel I believe that the uncertainty in position which causes us to be incapable of measuring which slit the photon moves through will be similarly translated into a temporal uncertainty. The energy-time uncertainty principle should similarly then make it impossible for the observer to determine the time of flight to a resolution or accuracy that would allow them to decide which slit the particle came through. Because of this the time of travel difference between each slit will be below uncertainty and thus your data would yield an fundamentally uncertain result.

[The_Duck]

I answered that you should see an interference pattern but now I think the opposite. I think that the energy-time uncertainty relation implies that if you time the departure of the photon very precisely you must produce some uncertainty in the energy/frequency of the photon (for example femtosecond laser pulses have a rather wide frequency spread). This means an uncertainty in the wavelength, too, which controls the spacing of the interference fringes. If your timing precision gets down to the same order as the period of the electromagnetic oscillations (which is what you need to determine which slit the photon went through) then the wavelength uncertainty will be very large, leading to very washed out fringes. Thus as your timing gets more precise the interference pattern should go away.

[alter-ego]

...I think that the energy-time uncertainty relation implies that if you time the departure of the photon very precisely you must produce some uncertainty in the energy/frequency of the photon (for example femtosecond laser pulses have a rather wide frequency spread). This means an uncertainty in the wavelength, too, which controls the spacing of the interference fringes.

It is true that more precise timings can be obtained with light sources having shorter pulse lengths and subsequently broader bandwidths (a consequence of the uncertainty prinicple). And it follows that interference patterns using these sources would be washed out because of the broader bandwidth similar to chromatic aberrations and imaging. And similarly for such a situation, narrow-band spectral filters would help extract fringe information.

If your timing precision gets down to the same order as the period of the electromagnetic oscillations (which is what you need to determine which slit the photon went through) then the wavelength uncertainty will be very large, leading to very washed out fringes. Thus as your timing gets more precise the interference pattern should go away

However, in this problem, the source is not being changed. We are only adding the ability to measure photon timings of this source (which before the timing equipment we could see an interference pattern), so the energy / bandwidth uncertainties remain unchanged. The important point here (for this ideal case) is the limits dictated by the uncertainty principle are driven by the source NOT the diagnostic equipment. Although the euipment may provide a suitable precision of measurement, the accuracy (or certainty) may not be attainable. In practice, diagnostic limitations certainly do apply.

[The_Duck]

However, in this problem, the source is not being changed. We are only adding the ability to measure photon timings of this source (which before the timing equipment we could see an interference pattern), so the energy / bandwidth uncertainties remain unchanged.

OK. But how do you time the departure of photons from this source? I don't really know about the quantum mechanics of EM fields but I'm imagining the photon source emitting wave packets. These wave packets have some length, so they take some amount of time to pass by a point. I don't think you can measure (or define) their departure time more precisely than that timescale. This timescale is also inversely proportional to the frequency bandwidth of the wave packet. That is, I think if it's possible to measure photon departure time with some level of precision then that ensures some level of frequency variation between photons, so I think my statements above apply.

[alter-ego]

However, in this problem, the source is not being changed. We are only adding the ability to measure photon timings of this source (which before the timing equipment we could see an interference pattern), so the energy / bandwidth uncertainties remain unchanged.

OK. But how do you time the departure of photons from this source? I don't really know about the quantum mechanics of EM fields but I'm imagining the photon source emitting wave packets. These wave packets have some length, so they take some amount of time to pass by a point. I don't think you can measure (or define) their departure time more precisely than that timescale. This timescale is also inversely proportional to the frequency bandwidth of the wave packet. That is, I think if it's possible to measure photon departure time with some level of precision then that ensures some level of frequency variation between photons, so I think my statements above apply.

Your statements here are true, and we are in agreement. Yes, to obtain a photon timing to a high degree of certainty (precision + accuracy) favors a broader bandwidth. No problem. What I'm saying is we are stuck with whatever certainty physics lets us have in measuring photon departure and arrival times, and whatever fringe visibility we had before implementing the timing equipment, we have after implementing the timing equipment (no matter how fast our video acquisition, photodiodes, O-scopes, etc) Unless I misunderstood your previous post, I interpreted you as saying that the resultant fringe patterns will change just by virtue of our timing equipment. This won't happen here. In this problem, the photon departure time is indirectly made, i.e. we cannot use a partial reflector to "sample" one photon. We must rely on another signal (e.g. "simultaneous" 2nd photon) to get the departure timing. The arrival time is made at, or as, the probability wave function collapses, so whatever the intensity distribution, the pattern is set when "detection" is made. Except for the slits, the propagating photon is not perturbed between the source to the camera/screen. Therefore, we cannot change the nature of the intensity distribution just by measuring photon times. Only if we try to "interrogate" the specific photon that ultimately is incident on the camera, will we change the intensity distribution. Again, I have assumed this problem was defined that way - not to probe the specific launched photon.

[The_Duck]

It does sound like we are in agreement. I guess it comes down to the ambiguity of the statement, "The time of release of single source photons is also recorded precisely."

[alter-ego]

It does sound like we are in agreement. I guess it comes down to the ambiguity of the statement, "The time of release of single source photons is also recorded precisely."

That's right. What does "precisely" really imply? I take it the following way: I think of measurement "precision" as a parameter resolution of the instrumentation, whereas I think of "accuracy" as how uncertain a collection of measurements are. So we might determine a single result to an amazing 25 places, but after a collection of results we find we can't predict the next result to 10 places. Bottom line, our measurement precision doesn't necessarily equal our prediction accuracy.

I hope this was somewhat clear

[alter-ego]

It does sound like we are in agreement. I guess it comes down to the ambiguity of the statement, "The time of release of single source photons is also recorded precisely."

That's right. What does "precisely" really imply? I take it the following way: I think of measurement "precision" as a parameter resolution of the instrumentation, whereas I think of "accuracy" as how uncertain a collection of measurements are. So we might determine a single result to an amazing 25 places, but after a collection of results we find we can't predict the next result to 10 places. Bottom line, our measurement precision doesn't necessarily equal our prediction accuracy.

I hope this was somewhat clear

A general comment about my experience with GRED: I have seen only a few of the problems presented, and sometimes it appears Robert poses a problem that, on the surface, seems to violate physics. When it comes to the solution, though, everything seems right in the world, and the laws of physics hold true. Robert leaves it up to us to find the truth as best we can. In that light, it seemed proper for light source in this GRED to remain a constant. IF the problem explicitly stated that the source was changed to a short-pulsed laser (or something like that) to help with timing measurements (in some way), then the solution would have to account for that change. It was not stated, so I think Robert was couching the problem for us to realise that "precise" timing cannot violate the uncertainty principle even though we went in to it with super high-tech equipment. In this GRED, one cannot determine the photon timing within a wavelength, which is the optical path difference between interference fringes.

Those are my thoughts. Kind of feels like science to me - you go in expecting one thing, and often you find out something else.

[alter-ego]

Something has been bugging me from the start. It has to do with the premise that accurately timing the photons can tell all about which slit a photon goes through. In fact, I was initially on board with this concept and assumed it could work. I thought that the idea was as solid as the simple geometrical approach to describing the 2-slit interference process itself. Until I realized the following failure point: There exists an axis of uncertainty which is parallel to the slits and intersects a line midway between and perpendicular to the slits (in the propagation direction). Along this axis, photon timings CANNOT be distinguished. The problem is suspicious to me because, if one assumes the timing model, it means that interference can happen ONLY along this axis. It then follows that the intensity on this axis can be 2x greater (by virtue of interference) than the rest of the intensity distribution! Let's say we can resolve timing distances = wavelength, then this central region will be about the width of a normal fringe. If the timing description is correct, what you would see is a normal diffraction pattern (no fringes) with a central intensity spike 2x brighter than the adjacent intensity regions. Do you see why this outcome seems hoky to me? In my opinion, this is a non-physical result and is a mathematical artifact of applying a photon timing model. I believe that any method used to track/interrogate a photon can result in three possible outcomes:

1. No light at all. This is the simplest outcome because it means that our method of measuring the launched photon departure time was poorly done. The photons are annihilated because we perturbed them (too much) and therefore no photons make it to the slits, and no light reaches the camera.
2. Intereference pattern preserved. To me, this outcome is more likely given a "good" timing setup, but we do not perturb the launch photon. Our indirect methods are based on a 2nd "simultaneous" photon, or an accurately calibrated electronic signal/trigger. The reason why is pretty simple - even if we had a "perfect" timing technique, we cannot violate the uncertainty principle, so therefore our timing measurements are really academic only. I believe we can't make good enough timing measurements. An unchanged interference pattern tells us so.
3. Degraded interference pattern overlaid on a diffraction pattern. This has been demonstrated (Wiki + other links). However, these setups are more sophisticated and I didn't think Robert was intending this outcome.

One interesting point: Not one of the outcomes is purely a diffraction pattern! For us to generate that we would have to block a slit, which we don't do.

Based on what I know, I chose outcome #2 but other outcomes are possible based on Robert's intent and assumptions. It's late now, but maybe some clarification on photon departure timing is needed (Thanks The_Duck for your comments).

Lastly, if the answer really is the oddball intensity distribution, then the correct choice should be Waffles the Wonder Llama.
Robert, great problem! You think you spend too much time on these things? I don't know, I might have you beat!
Keep up the great work!

[science hack]

Greetings,

Remember that a photon exhibits both particle and wave properties. This really becomes simply a two point wave addition problem. Presuming continuous random timing of the photons, they will ultimately create a standard diffraction interference pattern.

[questionmark]

Wow. Well, in the extreme, the knowledge of travel times should degrade or eliminate the interference pattern when all those images are added. But what happens if a voltage spike suddenly damages the database -- after the data is collected but before anyone combines all those images -- so that we no longer can find out the travel times but the images remain unaffected? Talk about spooky action at a distance! Do the images then suddenly sum to an interference pattern again??

[alter-ego]

Greetings,

Remember that a photon exhibits both particle and wave properties. This really becomes simply a two point wave addition problem. Presuming continuous random timing of the photons, they will ultimately create a standard diffraction interference pattern.

Hi,
I might be missing something, but the dual nature of EM radiation is being considered here. It is demonstrated by the intereference pattern of photon detection points on a screen collected over time ("random timing of photons"). This intereference pattern occurs only when the slit of origin is not known. Only when the slit of origin is known will a standard diffraction pattern will occur.
What are you assuming about absolute timings? Are you simply assuming that we know all the photon timings to infinite accuracy?

[alter-ego]

Wow. Well, in the extreme, the knowledge of travel times should degrade or eliminate the interference pattern when all those images are added. But what happens if a voltage spike suddenly damages the database -- after the data is collected but before anyone combines all those images -- so that we no longer can find out the travel times but the images remain unaffected? Talk about spooky action at a distance! Do the images then suddenly sum to an interference pattern again??

Nice response questionmark. I appreciate your levity because there's a hint of truth at the same time. I've lost experimental data sets before and had doubts about their repeatabiltiy! Sounds like you might have had similar experiences.

[Henning Makholm]

However, in this problem, the source is not being changed. We are only adding the ability to measure photon timings of this source (which before the timing equipment we could see an interference pattern), so the energy / bandwidth uncertainties remain unchanged.

It appears that you assume that you can increase the precision of the timing measurement as much as you want. I'd question that assumption. If the source emits photons with a highly stable frequency, then there is an inherent limitation in how precisely you can measure the time of emission. As in so many other variations on this general theme, it's not a question of how well your measuring equipment works; it is that there simply is no more precise time to measure. In order for the photon to have a narrowly defined frequency, its wave packet must have a certain minimum length, which limits your precision. One might imagine pinpointing the "exact midpoint" of the wave packet, but that does not help you because you don't know when during the duration of the wave packet the detector chose to react to it (so still not precise time-of-flight information).

Alternatively, and arguably complementarily, any device capable of measuring the passage time of the photon precisely will cause the conjugate value of its frequency/energy to smear out and become uncertain, even if it was precisely known before you measured the time. I.e. the usual observation-affects-the-observed-system presentation of the uncertainty principle.

Until I realized the following failure point: There exists an axis of uncertainty which is parallel to the slits and intersects a line midway between and perpendicular to the slits (in the propagation direction). Along this axis, photon timings CANNOT be distinguished.

You can always imagine a double-pinhole experiment instead of a double-slit one. The classic formulation uses slits in order to get any practical fraction of the particles to pass through the screen at all, but since we're doing gedankenstuff anyway...