# Double-Slit Questions

zoobyshoe
1.)I'm wondering to what extent Young's and other double-slit experiments depend on "slit" geometry. Does the same effect show up with two pinholes? I read a brief mention of G.I. Taylor having used a pinpoint somehow, but the description wasn't expanded enough for me to understand the set up.

2.) Young, obviously, did his experiment in air. Has anyone tried the double-slit with light in a vaccuum?

3.) With electron double-slit demonstrations the electrons have to be set in motion by electric potentials. I think this means they are accelerating as they go through the slits, unlike light. If so, does this create any signifigant differences from light demonstrations that have to be accounted for?

rayveldkamp
The double slit experiments, similar to Feynman's thought experiments, illustrate the distributions of particles, or waves as they enter the double slit apparatus, so the shape of the slits will not affect the experiment, neither does the fact it is in a vacuum or not.
If we fire particles at the slit, with one slit closed we get a distribution P, then close the other slit and open the other slit we get another distribution Q. Now leave both open we get a distribution equal to P+Q.
Now if the experiment is repeated with waves emitted from a source, we get the usual diffraction with distributions X and Y, however the ditribution corresponding to two open slits is not equal to the sum, this due to interference.
Now suppose we do it with a beam of electrons (acceleration does not affect this), we get distributions A and B, however the distribution corresponding to two open slits is not equal to A+B, this illustrates the essence of quantum mechanical behaviour - we do not know with certainty the electron's position until we measure it, thus "knocking" it into a position eigenstate. Mathematically this comes from the fact that (x+y)^2 is not equal to x^2 + y^2.

Hope this helps

Ray

Gold Member
zoobyshoe said:
1.)I'm wondering to what extent Young's and other double-slit experiments depend on "slit" geometry. Does the same effect show up with two pinholes? I read a brief mention of G.I. Taylor having used a pinpoint somehow, but the description wasn't expanded enough for me to understand the set up.

Not meaning to disagree with rayveldkamp's answer, as I think what was said is correct. The interference effects are still present with different shapes.

However, the slit shapes definitely alter the shape of the resulting interference pattern. For example, a diamond slit shape leads to a slightly different pattern (more like a diamond) than the traditional bar slits do. Ultimately, the interference pattern is a function of all possible paths that the light can take in its journey to the screen. The universe of such paths is therefore affected by the shape, even to some small extent by the texture of the slit edge. Usually, slit geometry is simply ignored because interference occurs anyway and that was the purpose of the experiment.

zoobyshoe
Mathematically this comes from the fact that (x+y)^2 is not equal to x^2 + y^2.
In terms of Feynman's "adding arrows" I'm assuming that the dark lines in an interference pattern represent areas where the probability amplitudes of a photon from one slit arriving 180 out of phase with a photon from the other slit are greatest. However, I don't know if that is right since he doesn't specifically talk about double slit interference in the chapters on photons in QED.

He discusses a single slit, and explains why the smaller the slit the more the light seems to spread out, which is that the narrower slit increases the probability of photons with the same bias (phase) arriving adjacently everywhere. The narrow slit selects out a group of adjacent paths, which, all being similar in time, are similar in bias. Being similar in bias, they don't interfere, don't cancel each other out. The apparent spreading, he seems to be saying, is not actually new behaviour, light is always doing this, it's just that now the impediment to seeing it (canceling by out of phase photons) has been removed. (This is all roughly, on pages 53-56 of the paperback edition of QED)

Imagine a horizontal slit in a vertical piece of flat metal parallel to a wall. Light comes through the slit and shines on the wall. My thinking about what happens next (Feynman doesn't explicitly say) is that, as all the selected 'in phase" light fans out from the slit, the arrows (that designate where the stopwatch pointer would be pointing when they hit the wall) are pointing in a slighly more advanced position for each bit of distance you go vertically up the wall, or down the wall from a horizontal line on the wall level with the slit in the metal through which the light is coming.
Each unit distance up or down the wall from the reference line represents a longer path, and the stopwatch will turn a little farther before the photon hits. And what we end up with is a very neat, smooth gradation of phase up and down from the original stopwatch position to the final one. Any given photon will be pretty much exactly in phase with the others on the same horizontal line, and will be only slightly out of phase with the ones that are, say, a thousandth of an inch above or below it. The ones an inch away, above and below are much more out of phase, and so on.

Adding a second slit, by this reasoning, superimposes a similar fan of photons, precisely graduated by phase, onto the first. The stopwatch pointers of alternate bands of them will naturally fall into "in phase" and "out of phase" categories. The out of phase ones cancel each other out, and the in phase ones reinforce each other. Since all horizontal lines from each individual slit are in phase, the net result is "bands" of light and dark.

Feynman, however, doesn't explicitly say anything about what happens when you put a second slit next to the first, so I'm not sure if I've reasoned this out correctly.

zoobyshoe
DrChinese said:
The interference effects are still present with different shapes.

However, the slit shapes definitely alter the shape of the resulting interference pattern. For example, a diamond slit shape leads to a slightly different pattern (more like a diamond) than the traditional bar slits do.

Ultimately, the interference pattern is a function of all possible paths that the light can take in its journey to the screen. The universe of such paths is therefore affected by the shape, even to some small extent by the texture of the slit edge. Usually, slit geometry is simply ignored because interference occurs anyway and that was the purpose of the experiment.
What prompted the question was the thought that Nature must be full of double slit situations, like the branches of trees, or tall grass, but you don't see all kinds of interference patterns everywhere.

I was wondering about the maximum and minimum parameters that have to be in place for this effect to be visible. As near as I can tell very narrow slits are superior to all other configurations for making this effect apparent.

Staff Emeritus
zoobyshoe said:
What prompted the question was the thought that Nature must be full of double slit situations, like the branches of trees, or tall grass, but you don't see all kinds of interference patterns everywhere.

How do "branches of trees" and "tall grass" the same as "interference pattern", which is nothing more than an illustration of superposition principle? The interference pattern is the result of the same phenomenon as the Schrodinger Cat.

Zz.

Staff Emeritus
Gold Member
Dearly Missed
zoobyshoe said:
What prompted the question was the thought that Nature must be full of double slit situations, like the branches of trees, or tall grass, but you don't see all kinds of interference patterns everywhere.

I was wondering about the maximum and minimum parameters that have to be in place for this effect to be visible. As near as I can tell very narrow slits are superior to all other configurations for making this effect apparent.

The slits or pinholes and their spacing have to be on the millimeter scale for light. Diffraction is a form of interference and feathers do produce colors by diffraction.

DaTario
Nature of the slits

I have heard of studies in which the interference pattern is generated by (or can be also explained by) the tunneling effect of the traveling wave-particle through the solid stuff which constitutes the slit borders. look up in Nuovo Cimento - Moyses Nussenzveig.

Staff Emeritus
DaTario said:
I have heard of studies in which the interference pattern is generated by (or can be also explained by) the tunneling effect of the traveling wave-particle through the solid stuff which constitutes the slit borders. look up in Nuovo Cimento - Moyses Nussenzveig.

Then I'd like to see THAT being used to explained the SQUID interference pattern.

You need to give a more exact citation than that.

Zz.

DaTario
references

Sorry for not being so exact.

But once discussing with Prof. Moyses Nussezveig, researcher with works on quantum optics , microspheres and rainbow theory, he told me that he had once written a paper i Nuovo Cimento where he attempted to derive interference effect in double slit experiment through the use of tunneling.

I, as a matter o fact, have not looked up, but naturally I trust him.

Staff Emeritus
DaTario said:
Sorry for not being so exact.

But once discussing with Prof. Moyses Nussezveig, researcher with works on quantum optics , microspheres and rainbow theory, he told me that he had once written a paper i Nuovo Cimento where he attempted to derive interference effect in double slit experiment through the use of tunneling.

I, as a matter o fact, have not looked up, but naturally I trust him.

There are two separate issues here that would pop up immediately, especially if you know a bit more about what "tunneling" is.

1. Is the explanation only SPECIFIC to the standard 2-slit interference effect from light? Or is this a GENERIC 2-slit interference effect, meaning it could be applied to anything with a superposition of 2 separate path? That's why I said I would like to see it being applied to the SQUID case. I'd like to see what exactly is "tunneling" through and where.

2. "Tunneling" phenomenon produces no "interference". In fact, if you look at it closely enough, a ballistic tunneling phenomenon is nothing more than a "handshaking" between the states on either side of the tunneling barrier, with the tunneling matrix as the "mediator". So if the slit and the slit material act as "barriers", this STILL produces no explanation for any interference effect.

Zz.

P.S. Not to mention, Il Nuovo Cimento website SUCKS. There's no way to do an author search. So unless you have an exact citation to the paper, bringing this up is not exactly helpful.

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zoobyshoe
The slits or pinholes and their spacing have to be on the millimeter scale for light.
That's the kind of parameter I was wondering about.
Diffraction is a form of interference and feathers do produce colors by diffraction.
In this manifestation, there's a fair amount of it around in Nature, then. Also in oily mud puddles after it rains.

DaTario
tunneling and interference

My guess, regarding the observations you have made, is that the tunneling was used to explain the process of pattern formation on a screen, using the slit wall as a specific and well defined potential, which causes deflections in an electron path, for example. Some Statistics on this ballistic experimente also must have took place. I know that , without the explicit reference to Mr. Nussenzveig, this conversation lose much of its scientifical character.

I will quit bothering in this specific question. But I would like to aknowledge you so much for the attention.

Sincerely yous,

DaTario

DaTario
ZapperZ said:
2. "Tunneling" phenomenon produces no "interference".

Just commenting: I believe tunneling is also a manifestation of interference.

Staff Emeritus
DaTario said:
Just commenting: I believe tunneling is also a manifestation of interference.

You "believe"?

Derive it. After you think you have shown this, then explain the tunneling density of states obtained from conventional superconductors. Show me where the "manifestation of interference" is.

Zz.

DaTario
Even deriving, I believe faith is still present in my argument. But let me try to better arrange my argument.

In quantum mechanics of a material particle in one dimension, potential barriers are provided in such a way that, sometimes, the presence of a particle at a given locallity, as classically predicted, is an impossible event. However, with the use of a wave function representation, Schroedinger equation is used to propagate the probability amplitude wave and, after the calculation, as resulting from the action of a wave propagator, non zero amplitudes of position are found in these classically forbiden regions.

I have no other word to present in order to justify this effect but interference.

DaTario
you may remember those results in Fabry-Perot or Mach-Zhender interferometers where multiple beams interferece formalism were used. It is something like this I am referring to.

Staff Emeritus
DaTario said:
Even deriving, I believe faith is still present in my argument. But let me try to better arrange my argument.

In quantum mechanics of a material particle in one dimension, potential barriers are provided in such a way that, sometimes, the presence of a particle at a given locallity, as classically predicted, is an impossible event. However, with the use of a wave function representation, Schroedinger equation is used to propagate the probability amplitude wave and, after the calculation, as resulting from the action of a wave propagator, non zero amplitudes of position are found in these classically forbiden regions.

I have no other word to present in order to justify this effect but interference.

You have simply described is the "wavefunction". This isn't interference, and it isn't interference from tunneling. Why don't you actually LOOK at tunneling phenomena in solids, such as from Ed Wolf's text. Then point out to me where is this "interference" phenomena coming from that.

Zz.

Staff Emeritus
DaTario said:
you may remember those results in Fabry-Perot or Mach-Zhender interferometers where multiple beams interferece formalism were used. It is something like this I am referring to.

And where exactly is the TUNNELING phenomenon in these setups? Interferometer has no tunneling barrier.

This line of discussion is getting to be VERY strange.

Zz.

DaTario
Mentioning the interferometers I was only trying to refer to multi beam interference formalism. But I agree with you on the strangeness of this discussion. My tendency is to look for interference in everything which concerns waves and departs from pure plane wave propagation.

I would like to acknowledge you for the attention as well as congratulate you for doing this task of replying with attention and kindness.

Thank you

DaTario

Staff Emeritus
DaTario said:
Mentioning the interferometers I was only trying to refer to multi beam interference formalism. But I agree with you on the strangeness of this discussion. My tendency is to look for interference in everything which concerns waves and departs from pure plane wave propagation.

But you still keep doing it. You appear to have the habit of throwing things out without either the obligation to back them up, or having the necessary understanding to justify what you are trying to connect. This is just one of the most recent example. You CLAIM (it wasn't a question from you) that tunneling is an "interference". When I asked you to prove it, you then, strangely enough, brought in interferometers as the explanation. This one of those big "HUH?" moment. What do interferometers have anything to do with explaning interference in tunneling?

Question 1: Have you EVER done any tunneling measurement?

Question 2: Have you ever looked at tunneling spectroscopy (such as the I-V curve and dI/dV curve) from a tunneling measurement such as those in Ref. 1?

If you have, then I would suggest you come up with an explanation using your "interference" scenario and obtain the identical theoretical results to match those types of experiments. Untill you do that, I would suggest you hold off on throwing things like this out here.

Zz.

[1] Q. Huang et al., Nature v.347, p.369 (1990).

DaTario
when you set up a fabry-Perot interferometer, for some particular wave length the two mirrors system appears as a completelly transparent medium. This result come out through the use of multi beam analysis, which makes use of the interference of these waves yielding the perfect transmission condition. Tunneling, as I understand it, of course I may be wrong, is based on the properties of difusion an anti-difusion processes through potential barriers, wells, etc implied by Schroedinger equation. Evanescent waves are ultimately caused to exist by the way a wave function propagates and interferes. What is tunneling without evanescent waves? So, what is tunneling without interference.

I agree that, when dealing with tunneling in solids, superconductors, the situation may get very complicated, and to find the interference in this context may be a difficult task. But I would suggest you to force yourself to look for it. It is there. It is my sincere belief.

Best regards

DaTario

zoobyshoe
ZapperZ said:
How do "branches of trees" and "tall grass" the same as "interference pattern", which is nothing more than an illustration of superposition principle?
You left a word out of this question, or something, because I can't understand what you're asking.
The interference pattern is the result of the same phenomenon as the Schrodinger Cat.
I'm not sure in what sense you mean this. Because they are both macroscopic results of quantum level events?

Staff Emeritus
zoobyshoe said:
You left a word out of this question, or something, because I can't understand what you're asking.

You earlier said:

zoobyshoe said:
What prompted the question was the thought that Nature must be full of double slit situations, like the branches of trees, or tall grass, but you don't see all kinds of interference patterns everywhere.

I was wondering about the maximum and minimum parameters that have to be in place for this effect to be visible. As near as I can tell very narrow slits are superior to all other configurations for making this effect apparent.

So I was curious as to how "branches of trees" is of the same "situation" as double slits.

I'm not sure in what sense you mean this. Because they are both macroscopic results of quantum level events?

No, they ARE macroscopic quantum events. The double slit is an illustration of superposition of paths, the same way Schrodinger's thought experiment tried to macroscopically illustrate QM's superposition principle.

Zz.

Staff Emeritus
DaTario said:
when you set up a fabry-Perot interferometer, for some particular wave length the two mirrors system appears as a completelly transparent medium. This result come out through the use of multi beam analysis, which makes use of the interference of these waves yielding the perfect transmission condition. Tunneling, as I understand it, of course I may be wrong, is based on the properties of difusion an anti-difusion processes through potential barriers, wells, etc implied by Schroedinger equation. Evanescent waves are ultimately caused to exist by the way a wave function propagates and interferes. What is tunneling without evanescent waves? So, what is tunneling without interference.

I'm sorry, but did you understand what you just wrote? You have two separate things that somehow share some characteristics (both are "waves"?), and so they must also share the same properties? Whoa!

I agree that, when dealing with tunneling in solids, superconductors, the situation may get very complicated, and to find the interference in this context may be a difficult task. But I would suggest you to force yourself to look for it. It is there. It is my sincere belief.

And I would suggest you force yourself to understand tunneling principle. THEN we'll talk. I mean, DIFFUSION?

Zz.

DaTario
I am trying to force myself in this direction. Thank you for the collaboration.

zoobyshoe
ZapperZ said:
So I was curious as to how "branches of trees" is of the same "situation" as double slits.
They are the same in that narrow, elongated apertures are created through which light can shine. Obviously they are different in some important way, though, because you don't see interference patterns in shadows from tree branches or tall grass. This lead me to wonder about the minimum requirements for this effect to be seen.

Interference in water waves is visible with the crudest of set-ups: any old puddle, a breeze, a rock and a beer can will do. Or three rocks and two beer cans and a chunk of wood: you still can see the interference.

It struck me as funny that at least once in a while you don't run into naturally occurring interference lines with light. I decided that must be because the requirements for it to be visible must be more stringent than it sounds from the descriptions I read.

Staff Emeritus
zoobyshoe said:
They are the same in that narrow, elongated apertures are created through which light can shine. Obviously they are different in some important way, though, because you don't see interference patterns in shadows from tree branches or tall grass. This lead me to wonder about the minimum requirements for this effect to be seen.

Interference in water waves is visible with the crudest of set-ups: any old puddle, a breeze, a rock and a beer can will do. Or three rocks and two beer cans and a chunk of wood: you still can see the interference.

It struck me as funny that at least once in a while you don't run into naturally occurring interference lines with light. I decided that must be because the requirements for it to be visible must be more stringent than it sounds from the descriptions I read.

Ah, now I understand.

There are, however, two very important reasons why you don't see such things:

1. The "slit size" when compared to the wavelength of the waves involved. Visible light has wavelength of the order of hundreds of nanometers. I doubt that you could notice that kind of spacings in between branches leaves. I believe this point has been mentioned already in this thread.

2. You are also dealing with a whole spectrum of wavelenghts, not just a monochromatic source. So even if interference occurs, this will occur in a particular location for a particular wavelength, and most likely it will be wiped out by the non-interfering effects from other wavelengths within the visible spectrum.

Zz.

Staff Emeritus
Gold Member
Dearly Missed
Zapper, consider zooby's example of the oil film in the street, which I believe can be close to monomolecular, I think one could work up a simple demonstration in the spirit of QED (sum over paths) where the interference between the reflections from the top of the layer and that from its bottom produces the spectral colors we see.

Antiphon
A couple of comments about terminology. All the above ideas are essentially
right.

Diffraction is not an interference penomenon. It is a consequence of wave
action interacting with a geometrical discontniuity. Only if you generalize
your thinking all the way back to Huygens would this interpretation be correct.
That is, if you treat the motion of a plane wave as Huygens did
by assuming that each point of the front is a spherical source for the next
infinitesimal front then yes, even the motion of a plane wave through space
is an interference pheomenon. But while this is mathematically true, it is
not helpful for understanding what diffraction is. It is certainly not what
an engineer today working on an electromagnetic propagation problem would
consider to be diffraction.

The term diffraction is most properly applied the case of describing
the propogation of waves around obstacles with features of the order of a
wavelength or less.

This description relies on interferece in the larger sense that a "diffracted
wave" is mathematically added to say the "incident wave" and the correct
results are obtained through interference.

Finally,

Oily films get their color from interference (of the reflected [not diffracted])
waves between the oil-water-air interfaces. Window panes refract and
reflect. They aren't considered to diffract except perhaps at the edges
or at blemishes which are on the order of a wavelength or less in size.

Feathers get their color by a grating effect which is diffraction because
the geomtrical features of interest are smaller than a wavelength. The
multiple diffracted wavefronts do interefere mathematically, but the term
interference when referring to large-scale wavefronts like plane or
spherical waves implies something different from diffraction.

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zoobyshoe
ZapperZ said:
Visible light has wavelength of the order of hundreds of nanometers.
This suggests another, probably equally naive, question: do photons have anything that corresponds to width? Are shorter wavelength photons narrower than those with longer wavelengths?
2. You are also dealing with a whole spectrum of wavelenghts, not just a monochromatic source. So even if interference occurs, this will occur in a particular location for a particular wavelength, and most likely it will be wiped out by the non-interfering effects from other wavelengths within the visible spectrum.
This makes perfect sense to me. Just to be certain, let me ask: a given photon can only be interfered with by another photon of the same frequency, and it has to be exactly 180º of of phase, correct?

zoobyshoe
Antiphon said:
Oily films get their color from interference (of the reflected [not diffracted])
waves between the oil-water-air interfaces.
Does this mean that the colors which you don't see have been canceled by interference?

Staff Emeritus
zoobyshoe said:
This suggests another, probably equally naive, question: do photons have anything that corresponds to width? Are shorter wavelength photons narrower than those with longer wavelengths?

I don't know. Photons are not defined by its physical size. The wavelength are typically used as a characteris length. However, it would be wrong of me to say that yes, that's the size of a photon.

This makes perfect sense to me. Just to be certain, let me ask: a given photon can only be interfered with by another photon of the same frequency, and it has to be exactly 180º of of phase, correct?

Since you have started to use the "photon language", here is something you have to make sure you understand.

The interference pattern that you are familar with is the result of the interference of SINGLE photons. In a 2-slit experiment, ONE photon has a superposition of 2 different paths. In classical language, it means that it "interferes" with itself! This is what will result in the beloved interference pattern. 2-photon interference almost never happen. It is a higher order effect, and it also produces a remarkably different type of interference pattern.[1,2]

Thus, you can understand why your question above would sound a bit "strange" within the QM/photon picture.

Zz.

[1] T.B. Pittman et al., PRL v.77, p.1917 (1996).
[2] L. Mandel, Rev. Mod. Phys. v.71, p.274 (1999).

zoobyshoe
ZapperZ said:
The interference pattern that you are familar with is the result of the interference of SINGLE photons. In a 2-slit experiment, ONE photon has a superposition of 2 different paths. In classical language, it means that it "interferes" with itself! This is what will result in the beloved interference pattern. 2-photon interference almost never happen. It is a higher order effect, and it also produces a remarkably different type of interference pattern.[1,2]
I was going to ask how, with white light, all the different frequency photons would happen to end up with another of the same frequency to cancel out. Your explanation, however, neatly takes care of that problem.

However, your exlanation raises at least two more questions 1.) Do some of the photons somehow reinforce themselves by self interference? And, 2.) What happens to the the ones that cancel themselves out? Where does the energy end up?

Thus, you can understand why your question above would sound a bit "strange" within the QM/photon picture.
Same old problem: people who know enough to ask non-strange question usually don't need to ask at all.

[1] T.B. Pittman et al., PRL v.77, p.1917 (1996).
[2] L. Mandel, Rev. Mod. Phys. v.71, p.274 (1999).
If these are on line in a form I don't have to subscribe to something to read them, I'd be very interested to have a look at them.

Antiphon
zoobyshoe said:
Does this mean that the colors which you don't see have been canceled by interference?

No, it is likely that either the "color" (wavelength) is outside the range of
your vision or is a balence of red green and blue that appears as a shade
of grey.