Why is there no single slit interference when one slit is closed in a double slit experiment?

[elou]

TL;DR Summary

Why is there no single slit interference when one slit is closed in a double slit experiment?

When two slits produce an interference pattern, and one slit is closed, then the interference pattern disappears. But one slit interference should still be possible. What should be the measurements of each slit for this to occur? That is, that, starting with a double slit, closing one slit does not eliminate the interference pattern.

 

[BvU]

Why is there no single slit interference when one slit is closed in a double slit

Says who ?

Check out hyperphysics single slit and
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c1

 

[elou]

I admit that it is not clear to me, even if I understand the principle as explained in your link. Every article and video I have consulted agrees that closing one slit eliminates the interference pattern. Would you mind elaborating on your reply?

 

[Nugatory]

I admit that it is not clear to me, even if I understand the principle as explained in your link. Every article and video I have consulted agrees that closing one slit eliminates the interference pattern. Would you mind elaborating on your reply?

Chances are that the articles and videos you’ve been reading have oversimplified - most non-serious presentations of QM do this. There is a single-slit pattern (usually called a “diffraction” pattern instead of an “interference” pattern) and a more thorough explanation will include and make clear that was is eliminated is not “the” interference pattern but instead the two-slit pattern.

 

[elou]

First there is the article by Thomas Young himself where he presents his famous double slit experiment.(Can be found on the web). A second example is with the use of the Michelson interferometer by a M.I.T professor which can be found at

 

[BvU]

The single slit envelope is very present!

$\$

 

[elou]

I'm afraid I don't understand your position. If the single/double slit interference pattern never disappeared Quantum Mechanics would not exist.

 

[BvU]

Can be found on the web

I found Lecture II (Nov 12, 1801) and Lecture I (Nov 18, 1803 !?!?) . Are you referring to Table I in the latter ?

but this is single slit, so probably not ?

I admit that it is not clear to me, even if I understand the principle as explained in your link. Every article and video I have consulted agrees that closing one slit eliminates the interference pattern. Would you mind elaborating on your reply?

@Nugatory gave it a shot. I find it hard to improve on hyperphysics. Perhaps a clarification: they distinguish diffraction (single slit) and interference (double or more slit) for . The first doesn't go away when more slits are present:

and you can play with the check boxes

.

When you learn about Fourier transforms:
A double slit aperture is the convolution of a single slit and two delta functions. The pattern on the screen for the first is a a sinc ($\ ={\sin x\over x }\ )\$ and for the second it's a sine. The pattern for the convolution (a double slit) is then the product of a sine and a sinc. Since the width of a slit is necessarily less than the distance between the delta functions, the peaks in the sine are closer together than the peaks in the sinc. Sheets 25, 29 and especially 30 here .

Does that help ?

$\$

 

[Nugatory]

First there is the article by Thomas Young himself where he presents his famous double slit experiment.(Can be found on the web). A second example is with the use of the Michelson interferometer by a M.I.T professor which can be found at….

Those are electromagnetic wave phenomena that have little to do with quantum mechanics and were understood and explained by classical mechanics a century before QM.

To see quantum mechanical effects in single or double slit experiments we have to either
A) use a single-photon source so that the pattern builds up one dot at a time. The one dot at a time behavior cannot be explained classically, and the pattern created by the dots shows interference between the different paths available to a single photon, also a uniquely quantum phenomenon.
B) use a beam of massive particles instead of light. Here the dot at a time behavior is expected and consistent with classical mechanics; the interference and diffraction patterns that appear are not.

Whichever we do, we will find a single-slit pattern when one slit is open and a double-slit pattern when two slits are open.

 

[elou]

No it does not. The whole "weirdness" of Quantum Mechanic resides in the fact that when we "look at" (in fact, observe, detect, measure, etc.) where the interference pattern comes from, which is also considered as trying to find out which way the photon(s) went, the interference pattern disappears. The 2023 Nobel prize has been attributed for this very problem. Now you tell me that the interference pattern is different from the more general phenomenon of diffraction. Which I am most ready to accept, but that still does not explain what that means: does the interference pattern, as meant by Young and everyone, disappear when it is measured (and closing one slit is considered a form of measurement), or not?
I don't feel compelled to defend Quantum Theory, I juist want to understand what is going on. And right now, I am totally confused.

 

[Nugatory]

Now you tell me that the interference pattern is different from the more general phenomenon of diffraction.

If you’re replying to me, I’m trying to say the exact opposite: the general diffraction phenomenon (as described by @BvU link to hyperphysics) is always present; “double-slit interference pattern” is the label that is often and confusingly applied to this phenomenon in one particular case.

I just want to understand what is going on. And right now, I am totally confused.

That should be a very strong hint that the sources you’re trying to understand from are confusing and incomplete. Every time someone says “…. the interference pattern goes away when we close one slit” they should have said something like “…the two-slit pattern predicted by diffraction math, which we’re calling the ‘interference pattern’ goes away when we close one slit but of course we still have the single slit pattern also predicted by that same math“.

 

[Nugatory]

does the interference pattern, as meant by Young and everyone, disappear when it is measured (and closing one slit is considered a form of measurement), or not?

”Young and everyone” aren’t describing any quantum mechanical phenomenon. With two slits open, light waves form a two slit pattern, with one slit open they form a one slit pattern, and this has nothing to do with quantum mechanics (except perhaps by analogy, and as you are discovering much confusion results from pop-sci sources not making this clear).

If you do a quantum mechanical double slit experiment, such as the ones I described in #9, it will behave as you describe (with the caveat that the interference pattern isn’t something that “disappears” because we can only observe it by watching multiple particle impacts over time).

 

[elou]

If you’re replying to me, I’m trying to say the exact opposite: the general diffraction phenomenon (as described by @BvU link to hyperphysics) is always present; “double-slit interference pattern” is the label that is often and confusingly applied to this phenomenon in one particular case.
That should be a very strong hint that the sources you’re trying to understand from are confusing and incomplete. Every time someone says “…. the interference pattern goes away when we close one slit” they should have said something like “…the two-slit pattern predicted by diffraction math, which we’re calling the ‘interference pattern’ goes away when we close one slit but of course we still have the single slit pattern also predicted by that same math“.

You should publish your view. I am sure it will receive a lot of attention, because, if I understood you correctly, you are saying that whatever anybody thinks of the disappearance of the so-called interference pattern in a double slit or in a which-way experiment, is wrong because mathematics say differently.
Since the people taking this position include Feynman, Bohr, Einstein, and others, controversy is guaranteed.
It looks like my question will not be answered because it has already been deemed meaningless. Too bad.
btw: I have no problem with your view, and I would not mind hearing more of it. The reference given is I'm afraid not enough.

 

[Lord Jestocost]

A note regarding the terminology:

“We should point out that there is not much of a difference between the phenomena of interference and diffraction, indeed, interference corresponds to the situation when we consider the superposition of waves coming out from a number of point (or line) sources and diffraction corresponds to the situation when we consider waves coming out from an area source like a circular or rectangular aperture or even a large number of rectangular apertures (like the diffraction grating).”

from the book “Optics” by AJOY GHATAK

 

[DrChinese]

It looks like my question will not be answered because it has already been deemed meaningless. Too bad.
btw: I have no problem with your view, and I would not mind hearing more of it. The reference given is I'm afraid not enough.

Here is an experimental realization of the double slit with photons which should hopefully allow you to reconcile your questions with the (correct) answers that have already been provided. Some of the issues are in the words being used, but this experiment will focus precisely on the interference effects of 2 slits - with the element of diffraction present at all times.

You don't need to close off a slit to eliminate the double slit interference. And in fact you don't need to know the which-path information to eliminate the double slit interference either. You can encode which-path information (via polarizers) as a photon passes through the slits, but never perform the step necessary to decode it. The double slit interference pattern will disappear and only the base diffraction pattern remains. This is what some of the answers above are saying, and here are the pictures to show this:

Young's double-slit experiment with single photons and quantum eraser (2013)
"An apparatus for a double-slit interference experiment in the single-photon regime is described. The apparatus includes a which-path marker that destroys the [double slit] interference as well as a quantum eraser that restores it."

• Fig. 8 shows results with no polarizers in place: a typical double slit interference pattern.
• Fig. 9 shows results with polarizers (which-path markers) in place: no double slit interference pattern.
• Fig. 10 shows results with polarizers in place, plus the which-path eraser: double slit interference pattern but not as well formed.

I hope this helps.

 

[elou]

Here is an experimental realization of the double slit with photons which should hopefully allow you to reconcile your questions with the (correct) answers that have already been provided. Some of the issues are in the words being used, but this experiment will focus precisely on the interference effects of 2 slits - with the element of diffraction present at all times.

You don't need to close off a slit to eliminate the double slit interference. And in fact you don't need to know the which-path information to eliminate the double slit interference either. You can encode which-path information (via polarizers) as a photon passes through the slits, but never perform the step necessary to decode it. The double slit interference pattern will disappear and only the base diffraction pattern remains. This is what some of the answers above are saying, and here are the pictures to show this:

Young's double-slit experiment with single photons and quantum eraser (2013)
"An apparatus for a double-slit interference experiment in the single-photon regime is described. The apparatus includes a which-path marker that destroys the [double slit] interference as well as a quantum eraser that restores it."

• Fig. 8 shows results with no polarizers in place: a typical double slit interference pattern.
• Fig. 9 shows results with polarizers (which-path markers) in place: no double slit interference pattern.
• Fig. 10 shows results with polarizers in place, plus the which-path eraser: double slit interference pattern but not as well formed.

I hope this helps.

I am afraid that this discussion is not what I had in mind when I asked my question. I am not interested in diffraction in general, but the special case that is called everywhere else an interference pattern, and that involves so-called bright and dark fringes. It is this pattern that is supposed to disappear. Another "who" who thinks so is

This is the problem I am referring to and hope to find an answer to my question.

edit: I know of the eraser experiment in this context, or the delayed choice experiment, for the moment, the "classical" version of the double slit clearly shows and states that the interference pattern disappears. I do not believe in the interference model and I think that it is possible to build a setup where two different photons reach the same detector and create an interference pattern, without having taken the same path. But that is another story for another day.

 

[elou]

I found Lecture II (Nov 12, 1801) and Lecture I (Nov 18, 1803 !?!?) . Are you referring to Table I in the latter ?

View attachment 341017
but this is single slit, so probably not ?



@Nugatory gave it a shot. I find it hard to improve on hyperphysics. Perhaps a clarification: they distinguish diffraction (single slit) and interference (double or more slit) for . The first doesn't go away when more slits are present: View attachment 341018 and you can play with the check boxes View attachment 341019.

When you learn about Fourier transforms:
A double slit aperture is the convolution of a single slit and two delta functions. The pattern on the screen for the first is a a sinc ($\ ={\sin x\over x }\ )\$ and for the second it's a sine. The pattern for the convolution (a double slit) is then the product of a sine and a sinc. Since the width of a slit is necessarily less than the distance between the delta functions, the peaks in the sine are closer together than the peaks in the sinc. Sheets 25, 29 and especially 30 here .

Does that help ?

$\$

Yes, it is one of the articles I was referring to, not that I was referring to the tabel, only to the fact that when a card is inserted in the path of the beam, an interference pattern appears. And disappears when another card is pushed against one of the sides, effectively blocking it.
Concerning the single slit, I agree that the interference pattern does not disappear. And that is exactly the reason why I asked the question.

 

[Nugatory]

You should publish your view.

It's been published many times over the past two and half centuries (not by me of course) and you'll find it in any textbook treatment of waves. Crawford's "Waves" is volume 3 of the Berkeley Physics series, a standard textbook for the third semester of a undergraduate physics program and a good starting point - I'm partial to it because it's the one my professor used so I have a copy on my bookshelf.

But, repeating myself, this is not quantum mechanics. It is classical wave behavior and a prerequisite to quantum mechanics (which started for me in the fourth semester). The quantum mechanical double slit experiment works more like:

The probability of a photon landing at any given point on the screen is calculated by considering all possible paths between the photon source and that point. Each path makes either a positive or a negative contribution to that probability, and we sum all of these to get the total probability (the actual probability is the square of this sum).
When two slits are open a photon can pass through either slit. There will be some areas of the screen where the contribution from paths through one slit will be positive while that from the other is negative and they cancel; in others both will have the same sign and they reinforce one another; and we get the alternating regions of high and low probability that make an interference pattern after enough photons have made their dots on the screen.

But when we close a one slit, or place a detector at a slit, then any given photon can only have gone through one slit or the other, so we only have the contributions from the path through that one slit. There’s no opposite sign contribution from the other slit to cancel or reinforce it, so no interference pattern. There still is a bit of pattern, usually called a “diffraction pattern”, that comes from having some paths through the left-hand side of the single slit and others through the right-hand side.

The connection to classical electromagnetic waves, Young's double-slit experiment, and other "let's make an interference pattern with laser light" demonstrations is that the probability amplitudes in the quantum mechanical experiments obey a wave equation similar to the classical wave equation. Thus we need the mathematical techniques of Crawford's book or equivalent before we can start in on the quantum mechanical problem, and we can use our intuition from the classical waves as an analogy to get a feel for how the quantum mechanical probabilities behave. And if we're trying for a layman-friendly math-free explanation, that analogy is all we have.... but it leads to confusion when people hear it, mistake the analogy for the real thing, and come away believing that Young and subsequent optical demonstrations are showing quantum mechanical behavior.

Feynman’s non-serious layman-friendly book “QED: The strange theory of light and matter” is worth reading. It is no substitute for learning the math, but it goes into more interesting examples of this “contributions from all paths” model.

 

[sophiecentaur]

There is a great danger of assuming that "this is reality" when discussing the idea of matter as waves. It so happens that the same Maths can predict how both matter and EM energy behave. That doesn't imply any a common nature of the two, any more than the fact that the basic rules of school arithmetic work over Physics as a whole.

Also, it would be a great help if students were taught that 'Interference' is just a coarse description of the diffraction pattern for simplified systems. It's the difference between Σ and ∫. A simple sum and a formal integral can sometimes give the same answer.

 

[PeroK]

I am afraid that this discussion is not what I had in mind when I asked my question. I am not interested in diffraction in general, but the special case that is called everywhere else an interference pattern, and that involves so-called bright and dark fringes. It is this pattern that is supposed to disappear. Another "who" who thinks so is

This is the problem I am referring to and hope to find an answer to my question.

The presentation by al-Khalili is clearly wrong. This is a problem with signifcantly dumbed down popular science.

In principle:

If a position on the screen has a nonzero probability/intensity in the double-slit experiment, then it must have a nonzero probability/intensity in at least one of the single slit experiments.

The distinctively QM behaviour is that a position on the screen which has a nonzero probability in both single slit experiments may have a reduced or even zero probability in the double slit.

To show I'm not making this up, here a post of mine from a while back.

https://www.physicsforums.com/threa...n-that-needs-to-be-asked.1055646/post-6932256

 

[elou]

The presentation by al-Khalili is clearly wrong. This is a problem with signifcantly dumbed down popular science.

In principle:

If a position on the screen has a nonzero probability/intensity in the double-slit experiment, then it must have a nonzero probability/intensity in at least one of the single slit experiments.

The distinctively QM behaviour is that a position on the screen which has a nonzero probability in both single slit experiments may have a reduced or even zero probability in the double slit.

To show I'm not making this up, here a post of mine from a while back.

https://www.physicsforums.com/threa...n-that-needs-to-be-asked.1055646/post-6932256

Just like you, I am interested in the behavior of photons/electrons in a double slit. I have the impression that all of you are trying to convince me that observation does not change reality. Please do not preach to the choir. I have never believed in that nonsense. Still, in your linked post, you say that electrons do not behave as classical particles. I will let that stand, even if I don't believe it either. But I cannot prove it otherwise (yet, hopefully, improbably?).
That still does not answer my question: why does not the interference pattern we see appear after one slit is closed? I am even willing to accept that it does not happen in reality. But what makes all those people believe it? even if wrongly?

 

[elou]

I am curious as to what this forum would tell people/students asking this kind of questions: do not listen to all those university professors, or your own teachers, listen to us?
I also think very often that all those university professors are wrong, but then I don't do homework help.

 

[PeroK]

But what makes all those people believe it? even if wrongly?

I doubt he does believe it. Instead, he probably thought it was simpler to present it that way. A little white lie to get people interested in physics by making it so simple it's actually wrong.

You could try contacting al-Khalili and see what he says.

If you learn QM from an undergraduate textbook, then you won't encounter these issues. Which is why the video you posted, strictly speaking, is not a valid reference for serious debate on PF.

That's why such videos are excluded according to the rules of this site.

 

[PeroK]

I am curious as to what this forum would tell people/students asking this kind of questions: do not listen to all those university professors, or your own teachers, listen to us?

The rules are clear: textbooks and peer-reviewed sources. Not popular science.

 

[PeterDonis]

why does not the interference pattern we see appear after one slit is closed?

Because the interference pattern (as opposed to the diffraction pattern) requires, um, interference between waves coming from both slits. The diffraction pattern only requires, um, diffraction by a single slit. That's why there are two different terms for these two different things.

I am even willing to accept that it does not happen in reality. But what makes all those people believe it? even if wrongly?

I don't think any reputable sources "believe" anything except what I said above.

I am curious as to what this forum would tell people/students asking this kind of questions: do not listen to all those university professors, or your own teachers, listen to us?

Even university professors will say things in informal contexts that are, strictly speaking, not justified by the actual peer-reviewed science. They might be doing it because they think oversimplifying things is better for their intended audience. Or they might be doing it just to sell more books or get more views on their videos.

In any case, they won't say such things in peer-reviewed papers (or at least it's a lot harder), because other experts reviewing the papers will call out such misstatements.

I am afraid that this discussion is not what I had in mind when I asked my question. I am not interested in diffraction in general, but the special case that is called everywhere else an interference pattern, and that involves so-called bright and dark fringes. It is this pattern that is supposed to disappear.

When you close one slit, this pattern, the interference pattern (as opposed to the difraction pattern) does disappear. Nobody has said otherwise.

 

[DrChinese]

1. I am afraid that this discussion is not what I had in mind when I asked my question. I am not interested in diffraction in general, but the special case that is called everywhere else an interference pattern, and that involves so-called bright and dark fringes. It is this pattern that is supposed to disappear.

2. edit: I know of the eraser experiment in this context, or the delayed choice experiment, for the moment, the "classical" version of the double slit clearly shows and states that the interference pattern disappears. I do not believe in the interference model and I think that it is possible to build a setup where two different photons reach the same detector and create an interference pattern, without having taken the same path. But that is another story for another day.

1. My post reference shows exactly this. You can see the change from interference to no interference with a single photon at a time buildup. Dark and light fringes, as requested. Peer reviewed and published article on the exact thing you ask. Did you consider reading it? It proves that photon self-interference depends on the photon having the opportunity to go through BOTH slits.

2. This experiment has nothing to do with delayed choice, that is a completely difference setup using entangled photons. Not sure why you mentioned it.

Not sure how you don't believe in the "interference model" which has been around, as mentioned by several, for hundreds of years. The quantum version, maybe only 75-100 years.

As to whether two photons can interference with each other: that is a very different subject and very complex to discuss. Certainly contains speculative elements and would be something for a different thread - probably in Quantum Foundations subforum.

 

[elou]

Because the interference pattern (as opposed to the diffraction pattern) requires, um, interference between waves coming from both slits. The diffraction pattern only requires, um, diffraction by a single slit. That's why there are two different terms for these two different things.


I don't think any reputable sources "believe" anything except what I said above.


Even university professors will say things in informal contexts that are, strictly speaking, not justified by the actual peer-reviewed science. They might be doing it because they think oversimplifying things is better for their intended audience. Or they might be doing it just to sell more books or get more views on their videos.


When you close one slit, this pattern, the interference pattern (as opposed to the difraction pattern) does disappear. Nobody has said otherwise.

Then I don't understand the purpose of this whole discussion. I asked about interference pattern, not diffraction. I should get an answer.
Besides, I do not rely on popular sources for my final judgement. I have no problem reading reputable and peer-reviewed articles.

 

[PeterDonis]

I don't understand the purpose of this whole discussion.

To clarify what, exactly, you are asking, and what sources PF considers to be valid sources.

I asked about interference pattern, not diffraction.

No, you didn't. Here is what you explicitly said in your OP:

When two slits produce an interference pattern, and one slit is closed, then the interference pattern disappears. But one slit interference should still be possible.

"One slit interference" is diffraction.

I should get an answer.

You have gotten multiple answers. But you keep talking as if you're still confused. So people keep trying to explain it to you.

I have no problem reading reputable and peer-reviewed articles.

Then you should go read some. @Nugatory referenced a textbook on waves.

 

[PeterDonis]

If the single/double slit interference pattern never disappeared Quantum Mechanics would not exist.

What do you mean by this? Under what circumstances do you think QM says the single/double slit interference pattern should "disappear"?

 

[PeroK]

I have no problem reading reputable and peer-reviewed articles.

I'm sorry to say I don't believe this. No serious student is going to watch an RI lecture other than from curiosity. And certainly not try to learn QM from such a source.

 

[Nugatory]

Still, in your linked post, you say that electrons do not behave as classical particles. I will let that stand, even if I don't believe it either.

There is an abundance of experimental evidence that electrons do not behave as classical particles:
- Double-slit interference and single-slit diffraction has been observed with electrons.
- Schrodinger’s equation accurately describes the observed non-classical behavior of bound electrons. Every chemical reaction depends on this.
- Tunneling is routinely demonstrated in undergraduate lab exercises.
- Superconductivity depends on non-classical electron behavior.
- Every electronic device in the world works because of the non-classical behavior of electrons in silicon and other semiconductors
….
And on and on and on…. also worth mentioning that if electrons did behave as classical particles then atoms would be unstable with decay times far less than a second. Indeed, the indisputable fact that atoms are stable was one of the medium-large mysteries of classical physics before the discovery of quantum mechanics.

 

[Nugatory]

I am curious as to what this forum would tell people/students asking this kind of questions: do not listen to all those university professors, or your own teachers, listen to us?

Listen to what the university professors and teachers say in their published textbooks and class notes, not the popular presentations that they do for the general public. The latter are for entertainment not education.

 

[PeroK]

Listen to what the university professors and teachers say in their published textbooks and class notes, not the popular presentations that they do for the general public. The latter are for entertainment not education.

BTW I've emailed Jim al-Khalili about this. Let's see if I get a response!

 

[elou]

There is an abundance of experimental evidence that electrons do not behave as classical particles:
- Double-slit interference and single-slit diffraction has been observed with electrons.
- Schrodinger’s equation accurately describes the observed non-classical behavior of bound electrons. Every chemical reaction depends on this.
- Tunneling is routinely demonstrated in undergraduate lab exercises.
- Superconductivity depends on non-classical electron behavior.
- Every electronic device in the world works because of the non-classical behavior of electrons in silicon and other semiconductors
….
And on and on and on…. also worth mentioning that if electrons did behave as classical particles then atoms would be unstable with decay times far less than a second. Indeed, the indisputable fact that atoms are stable was one of the medium-large mysteries of classical physics before the discovery of quantum mechanics.

Bad formulation from my part. I meant it very strictly with regard to the context. I think, I cannot prove it, that the behavior of photons/electrons in the double slit experiment will ultimately turn out to be classical. But then, like I said, I cannot prove it and would not stake my life on it.

edit: I wish we could back to my original question.

 

[PeterDonis]

I wish we could back to my original question.

Your original question has already been answered. Multiple times.