GRED Answer: Double slit with fast lensless video screen

[kirkpatrick]

@wavefunction:
I understand you to be saying that (1) there is an interference pattern being displayed (at least if there's an ordinary screen) AND (2) there is the ability to determine time-of-flight accurately enough to distinguish slit identity.
Now, (2) is possible only if the source is pulsed more briefly than the difference in time-of-flights. But, as I showed quantitatively, and then Henning showed in a nice verbal display (at his paragraph 4), this makes (1) impossible.

But I'm beginning to see that for you, and some others, the question has to do with something about detectors and knowledge.

the difference to ponder here is the effect of knowing the slit identity.

The answer to that question is trivial -- there is no effect. Knowledge has nothing to do with loss of coherence/interference. It isn't an issue of the precise time-of-flight being known, but being in principle knowable.

The nicest illustration of this that I've seen is in some experiments from Mandel, particularly Zou, Wang, and Mandel PRL 67, 318 (1991). Here, two coherently pumped downconversion crystals send their signal photons on the two arms of an interferometer, with the correlated idler photons leaving the apparatus on defined paths. If an idler photon were detected, it would tell which interferometer arm (path) were taken, hence no interference. But in this experiment the idler photons are not detected. If they are directed by reflections to leave on the same path, there is interference of the signal photons in the interferometer. If the idlers leave on divergent paths, there is no such interference. In neither case is there detection of the idlers. It has nothing to do with "knowing" anything; rather, it is entirely a matter of there being a distinguishing difference somewhere in the universe. (I hope it's obvious that, if the idler photons leave on the same path, the detection of a photon on that path gives no signal path information, because they can not be labeled "idler 1" and "idler 2".)

Of course, given such a distinguishing difference, an experimenter might measure it, and then know. But that is entirely a secondary, derivative result, not the "cause" of the loss of interference.

Relating this to the current question, then: The nature of the detecting screen, whether a photographic film integrating over time, or a video screen giving many instantaneous records, has no effect whatsoever on the existence of an interference pattern.

Turning now to the issue of numbers. (I've been a physicist for more than fifty years, and I believe I've never seen such resistance from physicists to dealing with physical reality. Gedankenexperimenten are not arbitrary fantasies; if you want to violate fundamental laws, you need to propose that up front.)

If we place the detector at the first minimum, we must pulse the source into a packet less than a half-wavelength long. The will create such a broadband signal that there will be no interference pattern possible, regardless of distinguishability issues. So instead let's place the detector at the 10th minimum, so the distinguishing pulse can be as much as 8 or 9 wavelengths long. This isn't monochromatic by any means, but it would allow a fuzzy pattern to exist. In this case, we have an interference pattern in the center, becoming less and less sharp as we go out, and vanishing by the 10th minimum, as the temporal overlap of the waves at the screen becomes less and less.

So we see that if you don't consider numbers at all, you could be dealing with a trivialized situation -- everything is smeared out. And if you do think a bit quantitatively, you come up with interesting results like this -- the gradual vanishing of the interference pattern with distance from the central axis.

Finally, wavefunction, your last post (appearing just as I'm finishing this) is correct. That it is possible to distinguish the paths is everything; whether anyone has bothered to do so is irrelevant. So I don't understand why you seem to treat this issue of knowledge in the opposite fashion in your immediately previous post.

[chull]

What do you mean, "In a few days I will post what I believe to be the correct answer."? Has this experiment been done or not? I would love to hear the _real_ answer because I swear I have wondered about this kind of experiment but never heard of it being done.

[alter-ego]

What do you mean, "In a few days I will post what I believe to be the correct answer."? Has this experiment been done or not? I would love to hear the _real_ answer because I swear I have wondered about this kind of experiment but never heard of it being done.

Single-photon interference experiments have been conducted, typically at near-IR or IR wavelengths. However, I highly doubt actual timings to the wavelength accuracy have been conducted because of technological limits. On the surface, it does seem feasable that timings at microwave frequencies are testable (λ ~ 10's of centimeters, timing resolution ~1ns, 300MHz BW). To my knowledge, this experiment has not been tried, but I'm not sure.

[RJN]

I believe the best answer is "An interference pattern." Now this was a tough one for me and I may well be wrong in whole or in part of my brief explanation, but here goes.

I think a key is that the timing information indicated would not be specific enough to give which-path information that would destroy the interference pattern. Now perhaps the wording of the question was deceptive with the phrase "The time of release of single source photons is also recorded precisely", but then again the only thing that was replaced since the appearance of the interference pattern was the image screen, meaning that source photons could still create an interference pattern. Adding time-resolution to the image screen should not affect the interference pattern.

What could affect the interference pattern is increased time-resolution of the source emission. Consider, for example, that the source photons are emitted through a slit that rotates into a position where a source photon may be released. I believe this timing mechanism is general enough to explore all relevant possibilities. Now this source slit has some width, and so a photon may escape just as the leading side of the slit aligns with an opening, or as the trailing side aligns with the opening. There will be some time difference inherent in this. I could call it "dt" but I consider it a challenge to explain this only using words!

Now one could create a map for how long it takes photons to go from the source to any point on the image screen, through one slit, and then another map for the other slit. One could hope to find "which path" information by measuring photon flight time and comparing it to this map. But this map does not take into account the range of possible starting times for each source photon.

OK, so this might mask "which path" information near the image screen center, but what about photons that land far from the center? This was a key to my understanding of this thought experiment. Originally, I had thought that photons that landed increasingly far out from the image screen center would be increasingly easy to tell which slit they went through. But even for these distant photons, there is only a slight time difference between arriving though each slit in the slit screen. The largest time difference is approximately the time it takes for a photon to go directly from one slit to the other. This is not a very big time difference!

As one might now guess, for interference to occur initially, the timing of photon release from the source can not be resolved better than this length of time. It is not a matter of knowing this information and discarding it -- the apparatus cited was not capable of determining this information.

If the source slit rotates so fast that which-path information becomes discernible, then the interference pattern will disappear. Why? Well in quantum mechanics it seems that just the possibility of measuring "which path" information wipes out interference patterns, even is the measurement does not itself affect anything at all.

Nevertheless, in this case, it does appear to me that the time measurement at the source will create a disturbing effect. Specifically, forcing even monochromatic laser-created photons through such a small time window will fan them out over many energies, as indicated by the energy-time uncertainty principle. The equivalent case for the position-momentum uncertainty principle is a straight-line laser being fanned out by going through a very narrow slit.

Much of this answer is just a rehash of much of what has been posted above by several knowledgeable posters. Still, my understanding continues to evolve, and if I am incorrect in whole or in part in this answer, I will update it at a future time.

To the best of my present knowledge, this experiment has not been done, nor even analyzed in mathematical detail. If anyone knows of such an experiment or analysis, I would be interested to know the reference(s). Alternatively, if anyone does this experiment, I would also be interested to know the result. Additionally, if anyone wants to analyze this in physical and mathematical detail, I would be interested to see the result at the least, and collaborate at the most.

- RJN

[thescotsgosling]

This strikes me as the same question as a photon coming from a distant quasar around a gravity lens. Does the photon come around the right or left side as a particle or does it come around both sides as a wave. When we test for particle nature we see it come around a side but if we test for wave nature we see it come around both sides. The paradox, "How does it know?" Presumably it was emited from the Quazar a few billion years ago.

Here is my responce to the above "paradox" and your thought expermiment. Become the photon. Photons are generated by quantum changes which happen across our preceived bounderies with out crossing them and in an instant. Traveling at the speed of light the photon's time contracts to infinitly short. By becoming the photon your creation, your start time and your arrival time are all in the same instant. By becoming the photon you, are present at the quasar and detection point on Earth in the same instant. In you thought experiment you are present at the source and screen in the same instant The notion of measuring the time delay is meaning less to the behaviour of the photon in either case.

This simple direct interpretaion of Relativity also seems to account for the tied twin experiments.

Instant is an infinitly short period of time. Whether an infinitly short anything has duration or lenght is another topic.

[kirkpatrick]

@RJN
In your statement of the problem, the only mention of existing interference is prior to, and the only mention of photon time-of-release is after, the phrase "the experiment is repeated, except now..." The only reasonable, literate interpretation of your statement is that the time measurement is added, along with the video screen, at the repetition of the experiment, and (as is to be expected) does not occur in the initial experiment.

I presume, however, that the interpretation you've stated is the problem you meant to pose. So my question to you is: Why the timing data? What purpose is served by adding a factor which, by definition, has no effect? Why the "Aspect to consider," misleadingly emphasizing the timing data?

At the end of your answer, you wonder if the experiment has been done. I ask, Why would anyone do it? Under the circumstance that the timing information is too imprecise to be of interest, there can be no result of interest. You are really only wondering if anyone has looked at an interference pattern with a high-shutter-speed videocam. What result of interest, or null result of interest, could be looked for?

Let me explain my evident irritation with your problem and answer -- after all, why should I care? Well, this is a topic that is often badly handled, even in textbooks, so it is confusing to many who read about quantum mechanics. This discussion was an opportunity to clarify the ways of handling complementarity correctly. But your answer failed to do so -- it failed to integrate, or to improve upon, what had been presented, and your answer leaves the incorrect impression that the subject is confusing and not well understood. Nothing about the loss of coherence due to distinguishability is an open physics question, and the answer should make this clear.

[neufer]

Einstein's thought experiment of 1930 as designed by Bohr. Einstein's box was supposed to prove the violation of the indeterminacy relation between time and energy.

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George Gamow's make-believe experimental apparatus for validating the thought experiment at the Niels Bohr Institute in Copenhagen.

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<<At the sixth Congress of Solvay in 1930, the indeterminacy relation just discussed was Einstein's target of criticism. His idea contemplates the existence of an experimental apparatus which was subsequently designed by Bohr in such a way as to emphasize the essential elements and the key points which he would use in his response.

Einstein considers a box (called Einstein's box; see figure =>) containing electromagnetic radiation and a clock which controls the opening of a shutter which covers a hole made in one of the walls of the box. The shutter uncovers the hole for a time Δt which can be chosen arbitrarily. During the opening, we are to suppose that a photon, from among those inside the box, escapes through the hole. In this way a wave of limited spatial extension has been created, following the explanation given above. In order to challenge the indeterminacy relation between time and energy, it is necessary to find a way to determine with an adequate precision the energy that the photon has brought with it. At this point, Einstein turns to his celebrated relation between mass and energy of special relativity: E=mc². From this it follows that knowledge of the mass of an object provides a precise indication about its energy. The argument is therefore very simple: if one weighs the box before and after the opening of the shutter and if a certain amount of energy has escaped from the box, the box will be lighter. The variation in mass multiplied by c², will provide precise knowledge of the energy emitted. Moreover, the clock will indicate the precise time at which the event of the particle’s emission took place. Since, in principle, the mass of the box can be determined to an arbitrary degree of accuracy, the energy emitted can be determined with a precision ΔE as accurate as one desires. Therefore, the product ΔEΔt can be rendered less than what is implied by the principle of indeterminacy.

The idea is particularly acute and the argument seemed unassailable. It's important to consider the impact of all of these exchanges on the people involved at the time. Leon Rosenfeld, a scientist who had participated in the Congress, described the event several years later: "It was a real shock for Bohr...who, at first, could not think of a solution. For the entire evening he was extremely agitated, and he continued passing from one scientist to another, seeking to persuade them that it could not be the case, that it would have been the end of physics if Einstein were right; but he couldn't come up with any way to resolve the paradox. I will never forget the image of the two antagonists as they left the club: Einstein, with his tall and commanding figure, who walked tranquilly, with a mildly ironic smile, and Bohr who trotted along beside him, full of excitement...The morning after saw the triumph of Bohr.">>

<<The "triumph of Bohr" consisted in his demonstrating, once again, that Einstein's subtle argument was not conclusive, but even more so in the way that he arrived at this conclusion by appealing precisely to one of the great ideas of Einstein: the principle of equivalence between gravitational mass and inertial mass. Bohr showed that, in order for Einstein's experiment to function, the box would have to be suspended on a spring in the middle of a gravitational field. In order to obtain a measurement of weight, a pointer would have to be attached to the box which corresponded with the index on a scale. After the release of a photon, weights could be added to the box to restore it to its original position and this would allow us to determine the weight. But in order to return the box to its original position, the box itself would have to be measured. The inevitable uncertainty of the position of the box translates into an uncertainty in the position of the pointer and of the determination of weight and therefore of energy. On the other hand, since the system is immersed in a gravitational field which varies with the position, according to the principle of equivalence the uncertainty in the position of the clock implies an uncertainty with respect to its measurement of time and therefore of the value of the interval Δt. A precise evaluation of this effect leads to the conclusion that the relation ΔE Δt ≥ h, cannot be violated.>>