Does the double-slit experiment depend on the observer knowing how many slits there are?

I know the answer is probably the obvious, but results of the double-slit experiment are so counterintuitive that…well, maybe it isn’t obvious—particularly since the interference pattern disappears when an observer knows which slit a photon went through. That raises the question in my mind, “What if the observer doesn’t know how many slits there are in the screen?”

First of all, the question is based on a couple of assumptions I have about the experiment, because I’ve only read about it being performed with two slits in the screen:
[li]Photons fired through a single slit would hit the detector only in the area behind the slit.[/li][li]Photons fired through a screen with three slits would form an interference pattern similar to but distinct from a screen with two slits.[/li][/ol]

Say a carpenter constructs a box around “double” slit experiment so that it’s impossible for anyone to observe it in action. Inside the box there are three screens: the first with one slit, the next with two slits and the last with three slits. The screen placed between the photon gun and the detector is selected at random, and no one has any way of knowing which screen is being used during any single experiment.

Would the pattern on the detector correlate with the corresponding screen so the experimenter could accurately tell which one was randomly selected?

The answer is yes they could tell. See for example various descriptions of three-slit experiments:

The point about the observer knowing which slit the photon went through is that there is no way of knowing without disturbing the state of the experiment. The obvious way of knowing is by closing one slit. But that changes the experiment. Alternatively you need some sort of detector in the slits. But this doesn’t work either. You have to interact with the photon, and that changes its state. Even if that interaction is by putting a detector in the slit it doesn’t “pass through”.

The “observer” need not be a conscious entity*. The question seems to be slightly confusing the observer of the overall experiment and the detector-observer, from the Copenhagen viewpoint. Copenhagen is only one viewpoint. You get the same results from pilot wave, many worlds, and don’t need to worry about the observer in quite the same way.

  • At least in some views. Some take the view that the ultimate collapse of the entire system state vector is that that is done by a conscious being. That seems to be were the OP is coming from in some ways.

yes the experimenter could tell.

The result is not influenced by the experimenters knowledge.

The experiment shows the wave size is the size given by the uncertainty principle.
If you lock it in to a more precise location, its not acting like a wave any more.

I don’t like using the word “knows” for this. A person can know what a particle detector tells him, but I think “knowing” implies a thinking brain. For the double-slit experiment, you just need a detector, which is a physical device, no thinking required.

I’m trying to remember a readable-by-laymen paper I think I myself once cited by a famous (?) Israeli theoretical physicist with a Russian name on his proposal for a I’m-not-looking-at-you “observational” kludge to monitor the two slit experiment.

Ring a bell with anyone here?

I’m afraid that that description is far too vague for me to know, off the top of my head, what physicist or paper you’re referring to. But I can echo what others have said, that consciousness is in no way relevant, and that measurements count even if no person is paying attention to them.

The OP seems to be in the same spirit as the delayed choice eraser experiments which I would love for someone to help me understand. So you have a detector, you find out which path, you get a particle pattern, but if, after the detector detects, you erase that info, you again get an interference pattern. So you set it up so that the choice of whether or not to erase the information happens randomly, and after the original particle completes it’s journey and hits the screen. Still, erase the path info you get an interference pattern and vice versa. WTF?! The particle already hit the screen! How can the choice you make after this happens affect what it does? (this all assuming I’m understanding this experiments correctly, which I’m probably not).

Back in Physics lab, I could easily tell a 1-slit diffraction pattern from a 2-slit one.

Here’s a page showing what various multiple slit diffraction patterns look like.

It looks like the little in-between peaks between the central main peaks would allow one to clearly separate a 2-slit from a 3-slit pattern.

Re-reading the OP I wonder about the use of “pattern” here. A pattern as shown in the linked page may not be exactly what the OP is getting at.

The difference in behavior between large number of photons and single photons is a curious matter. People can send individual (or paired quantum-entangled photons) at the screen. How the photon behaves is individually different from classic optics. But to get usuable results you have to repeat the experiment over and over and the standard pattern appears from the individual result.

A single experiment sending one photon thru and seeing where it lands tells you nothing. That photon could have landed anywhere regardless of the number of slits. (Well, at least one slit.) Look at the building of the pattern in the series of pics for electron diffraction here.

One particle does not a pattern make.

It’s intriguing how many options come to mind with ‘Russian-Israeli physicist doing something weird with measurements’: there’s Lev Vaidman, whose name doesn’t sound Russian, but who’s Russian-born, who’s proposed the interaction-free measurement scheme in a thought experiment together with Avshalom Elitzur (whose name maybe kinda sounds Russian), popularized as the Elitzur-Vaidman bomb tester.

Furthermore, Vaidman has, together with the more Russian-sounding Yakir Aharonov (and David Z. Albert, who doesn’t really sound Russian), proposed the scheme of weak measurements, where you try to disturb the system as little as possible, and then do it a lot of times to get out some information.

Aharonov, together with David Bohm, has also shown that an electromagnetic potential can have an influence on an interference pattern even if the particle never traverses a region with a nonzero electromagnetic field, the so-called Aharonov-Bohm effect.

Finally (and even though the nationality doesn’t quite fit, I think this is the most likely candidate for what you’re thinking of), there’s Iranian-American Shahriar Afshar, who’s proposed an experiment (aptly named Afshar experiment) that he claims violates the impossibility of simultaneously obtaining information about which path the photon has taken, while retaining the interference fringe (it doesn’t).

In flipping through my collection of the bibliography of Aharonov (:), thanks, Half Man) I found this:
Time and the Quantum: Erasing the Past and Impacting the Future
Yakir Aharonov, M. Suhail Zubairy

Science 11 Feb 2005:
Vol. 307, Issue 5711, pp. 875-879
DOI: 10.1126/science.1107787

The quantum eraser effect of Scully and Drühl dramatically underscores the difference between our classical conceptions of time and how quantum processes can unfold in time. Such eyebrow-raising features of time in quantum mechanics have been labeled “the fallacy of delayed choice and quantum eraser” on the one hand and described “as one of the most intriguing effects in quantum mechanics” on the other.

In the present paper, we discuss how the availability or erasure of information generated in the past can affect how we interpret data in the present. The quantum eraser concept has been studied and extended in many different experiments and scenarios, for example, the entanglement quantum eraser, the kaon quantum eraser, and the use of quantum eraser entanglement to improve microscopic resolution.

Take it away, smart guys! If you want. I got nuttin’.

The thing to keep in mind with this sort of experiment is that without any additional information, what you see on the screen never shows any interference pattern. It’s only if you condition the detection events on additional information obtained, say, from some ‘far away’ detector that the interference pattern becomes visible—by allowing you to select a subset of detection events that does show interference.

Somewhat long-ish discussion of the experiment and its implications (or lack thereof) follows:

[spoiler]The typical layout of the delayed-choice experiment is that after the double slit, the photons are ‘split in half’ using a non-linear crystal; this creates two entangled photons for every photon going in. One of each pair—the signal—is transmitted to a detector D[sub]0[/sub]. Using only the detections made there, no interference pattern will be visible—ever.

The other half of the pair is then sent through a complicated array of beamsplitters, prisms, and mirrors that we’ll completely ignore here to focus on the only salient fact: in the end, it will be detected on either of four detectors D[sub]1[/sub], D[sub]2[/sub], D[sub]3[/sub] or D[sub]4[/sub], such that which-path information is unavailable if it is detected either at D[sub]1[/sub] or D[sub]2[/sub], while which path information is conserved if it is detected at one of the other detectors (say, if it is detected at D[sub]3[/sub], it came from slit A, and if it is detected at D[sub]4[/sub], it came from slit B).

You can view this as two separate experiments: one in which you preserve, and one in which you delete which-path information, by randomly inserting an element that causes the photons to either be detected at D[sub]1[/sub] or D[sub]2[/sub], deleting which-path information, or at D[sub]3[/sub] or D[sub]4[/sub], preserving it instead. Since this choice can, in principle, be made long after the signal has been detected at D[sub]0[/sub], that’s where the delayed choice erasure comes in. In practice, however, this choice is just made by a beamsplitter, where photons either pass or are reflected with 50% probability.

Now, the crucial point is that only if you look at the detections made on the detector D[sub]0[/sub] conditioned on the detections made of the other half of the pair at one of the other detectors that an interference pattern has any chance of appearing. So, only if you look at, say, those detections where one half of a pair was registered at D[sub]0[/sub] and the other half at D[sub]1[/sub], then you see an interference pattern (and likewise with D[sub]2[/sub]); if you look at coincidences with either of the other detectors, you see no pattern. Consequently, you need to know which choice was made in order to see the interference pattern; it’s not that you can make that choice three years into the future and then have an interference pattern magically appear in the past. Only after the choice is made can you use the joint information in order to make the interference come out.

(Even if you always choose not to erase the information, no interference pattern will be visible at D[sub]0[/sub]: the reason for this is that the interference patterns generated using the data of D[sub]0[/sub] conditioned on that of D[sub]1[/sub] will be phase-shifted as compared to the interference pattern generated by taking the coincidence counts of D[sub]0[/sub] and D[sub]2[/sub], such that the respective ‘peaks’ and ‘valleys’ cancel each other out.)

Now, should you be astonished by that? Well, it depends: on the one hand, I think the description above makes it clear that there are no violations of causality—indeed, one can prove that there never will be. Nevertheless, it certainly seems like what happens at the arbitrarily far away (in time and space) detectors D[sub]1[/sub]-D[sub]4[/sub], in some sense, holds an influence over what occurs at D[sub]0[/sub]: if we make the choice of deleting which-path information, and if the photon is detected, say, at D[sub]1[/sub], then there are certain areas on the screen of D[sub]0[/sub] where the signal photon can’t have been detected. There seems to be some tension with, if not an outright violation of, usual ideas of causality.

It’s sometimes claimed (also in the wikipedia article) that the fact that one can just as well phrase things in a causal way—i.e. that where the photon was detected on D[sub]0[/sub] influenced on which of the other detectors a detection will be made—solves the mystery. But I think this doesn’t quite work: one could causally isolate all of the detectors from one another, such that no signal from D[sub]0[/sub] could influence what happens at D[sub]1[/sub]-D[sub]4[/sub], just like the other way around.

So I think there is some weirdness there—but it’s really just the usual quantum weirdness, not anything fundamentally new, not anything that fundamentally differs from the question of how single photons can cause interference patterns in the first place. There’s ways to get that weirdness out of the way, at the expense of interpretational extravagance: thus, in the Many Worlds-picture, you only discover which ‘world’ you’re in once you have the full information from both detectors; and in Bohmian mechanics, everything is really all nice and determinate at all times, but there are superluminal influences between quantum objects.

These are ultimately all attempts to rescue pre-quantum intuitions about how the world works. I think, however, that the real lesson is that well, the world just doesn’t work that way; and really, it never had any reason to conform to our expectations.[/spoiler]

Regarding the difference between 2- and 3-slit patterns, in quantum mechanics, in some sense, ‘nothing new’ enters the picture when you add more slits—that is, while the pattern you get if you have two slits is not the sum of the patterns from two single slits (that’s interference), the pattern you get from having three (or more) slits is just the sum of all two-slit patterns (for those with some training in QM, this follows directly from the fact that the probability of observing an event is given by the square of the wave function)—i.e. there’s no higher-order interference. But yes, three-slit patterns are readily distinguishable from two-slit patterns, and the observer need not know anything about the number of slits.

In fact, extensions to quantum theory showing higher-order interference have been proposed, but so far, experimental results are all perfectly in keeping with ordinary vanilla QM. So there is something of interest in doing experiments with multiple slits; but it’s got nothing to do with what the observer knows or not.

Interesting thread. I’ll just add that Einstein worried about these sorts of things, and wondered what would constitute an “observation” – “What about a sidelong glance from a mouse?,” he asked.

I know this question has been (more or less) answered, but I thought that was funny and well put.

Thanks for that explanation, the delayed-choice eraser experiments make a lot more sense to me now. It seems not nearly so “spooky”, either.

In fact I don’t really see how anyone could interpret it as information being sent back in time: surely you can only isolate the coincidental photons (ie coincident between D[sub]0[/sub] and D[sub]1[/sub]-D[sub]4[/sub]) once you have detected the photon at D[sub]1[/sub]-D[sub]4[/sub]? So nothing is being transmitted to the past at all.

Well, the intuition here is that first the signal photon impinges on D[sub]0[/sub], and then the idler reaches (say) D[sub]1[/sub]; but given the fact that the idler reaches D[sub]1[/sub], there are certain areas on D[sub]0[/sub] that are forbidden (or nearly so) for the signal, and others that are preferred—the dark and bright interference bands. But how did the signal ‘know’ to preferentially land on a bright spot, given that the detection of the idler at D[sub]1[/sub] might not happen for years to come (theoretically)?

So while you can only isolate the right events once you have the data from the far-away detectors, it seems that where individual photons land (on D[sub]0[/sub]) does depend on where their counterparts will eventually be detected.

I don’t think this is a whoosh, so the inevitable: cite? It might even sound better in German.

(Cf. Shroedinger’s “smeared” cat (original English translation), which makes me, with correct NY/Yiddish/German pronunciation, answer bagels and lox whenever someone poses the “is it dead or alive” question [not a common occurrence, admittedly]; I can’t get my hands on the original German, but it’s got to be on line, but no joy for me. Where the hell did it go?)