Double slit - where do they aim?

[Vdtta]

I could not find any explanation or illustration where it is shown where do they actually aim electron gun (or something) in the version of the experiment where they shoot electrons one-by-one. I suppose this is how original setup looks like:

====================screen==

       \  /  \  /
_______   ___   __________mask__
   \                /
     \            /
       \        /
         \    /
         light

Here light beam is pretty wide and no doubt some photons will get to go through the slits, while still most of them would be stopped at the mask.But, what do they do when they shoot electrons one-by-one?

====================screen==_______   ___   __________mask__
           |
           |
           |
           |
         e-gun

My best guess is that they randomly change the angle or swivel the gun left-right so some electrons get to go through slits, but most of them would still get stopped at the mask.

Can someone provide some links with some illustrations of how is this done?Another question, what happens if the beam is not perpendicular to the mask, like this:

====================screen==_______   ___   __________mask__
          /   
        /     
      /       
    /         
  e-gun

 

[Bob_for_short]

The source of light or electrons is suficcienly far behind in order to provide a uniform flux of parallel particles covering well the area of two slots.

If the beam is not perpendicular, nothing special happens. Remember a pinhole camera. It "shows" everything . Some "images" are simply not at the center.

 

[Vdtta]

The source of light or electrons is suficcienly far behind in order to provide a uniform flux of parallel particles covering well the area of two slots.

Hi, thank you.

I can not imagine something so very precisely narrow like laser or electron beam to randomly fluctuate in width as to cover one inch separation between slits. I also can not imagine this fluctuation would result in somewhat parallel lines, unless the gun is like 10km away.

If someone can provide some links with these illustrations, or photos of real setup and some diagrams so I can picture this better.

If the beam is not perpendicular, nothing special happens. Remember a pinhole camera. It "shows" everything . Some "images" are simply not at the center.

Do you mean there will be no patterns or that patterns would be as usual?

 

[Bob_for_short]

...I can not imagine something so very precisely narrow like laser or electron beam to randomly fluctuate in width as to cover one inch separation between slits. I also can not imagine this fluctuation would result in somewhat parallel lines, unless the gun is like 10km away.

The particle source is not point-like itself. It is of finite width but put far enough. So the beam is of finite size too.

Do you mean there will be no patterns or that patterns would be as usual?

Patterns will be shifted aside and, maybe, slightly distorted (stretched).

 

[Vdtta]

The particle source is not point-like itself. It is of finite width but put far enough. So the beam is of finite size too.

Patterns will be shifted aside and, maybe, slightly distorted (stretched).

Thanks, that explains fully.


In the meantime I found this video in another thread here.


"This shows Thomas Young's double slit experiment using a laser pen and a couple of pencil leads. "

 

[Vdtta]

Yet another question, can we get interference pattern without slits, with just two intersecting cones of light, like this:

==========================================screen==
       \        \         /        /
         \        \     /        /
           \        \ /        /
             \      / \      /
               \  /     \  /
             light1   light2

This effectively models the double slit from the point after the mask, where light already has went through the slits, so I would expect interference pattern exactly match this situation:

==========================================screen==
       \        \         /        /
         \        \     /        /
           \        \ /        /
             \      / \      /
               \  /     \  /
________________  _______  _________________mask___
            \                  /
              \              /
                \          /
                  \      /    
                   light

If yes, why the need for double slit?

If no, why not?

 

[Bob_for_short]

Yet another question, can we get interference pattern without slits, with just two intersecting cones of light, like this:...

Yes, it is possible if the sources provide the coherent waves. Two lasers of the same frequency, for example.

If yes, why the need for double slit?

The double-slit system provides automatically coherent waves - from one source with two different paths. It is an old optical experiment. Only recently it became to be used in QM.

 

[Vdtta]

Thank you Bob, you're very helpful, and it's greatly appreciated.In the meantime I found some discussion on some other forum about it while Googling. There is a part there which makes sense, but sounds illogical, so could you/anyone comment on the sentence in bold, is that true?

http://lofi.forum.physorg.com/Composition-Of-Aether_16150-100.html - "Let's say I have two crossing broad coherent beams of single frequency light (say, at 45 degree angles to each other). Assume they are each shining on a linear photo detector array on a far wall. Where the beams cross, there are standing wave patterns produced, with nodes and anti nodes existing. If you blew smoke over the crossing areas, you should see bright and dark patterns, and if you put an obstruction across the intersection, you would see an interference pattern on the obstruction.

Now, assume you look at the signal power registered on the photo detectors for each beam. If you turn one beam on and off, the power reading will not change at the photo detector for the other beam. They in no way interfere with each other, other than to produce interesting mathematical patterns where they cross."
And yet another question, would we get interference pattern on the screen placed across the intersection of two light cones if we were to turn each light on and off in an alternating fashion, so they are never turned on in the same time? To me this sounds crazy, but possible, just as interference pattern produced by shooting electrons one-by-one, what are they interfering with?

 

[Bob_for_short]

... They in no way interfere with each other, other than to produce interesting mathematical patterns where they cross."?

Yes, they do not prevent each other from propagating farther that their cross area. It is OK. The electromagnetic wave just add where they are (principle of superposition). The volume energy is also conserved, it is just redistributed between maxima and minima. They do not hinder each other: the EM field equation are linear and we can add different solution together when they cross. The total filed is their sum, the intensity has an interference pattern followed from this sum.

And yet another question, would we get interference pattern on the screen placed across the intersection of two light cones if we were to turn each light on and off in alternating fashion, so they are never turned on in the same time? To me this sounds crazy, but possible, just as interference pattern produced by shooting electrons one-by-one, what are they interfering with?

No. Interference needs two fields at the same time. This experiment has already been carried out - no interference pattern. If you listen to the radio in a MW diapason, there might be two stations at the same frequency. When they both are on, you hear interference noise. When one of them is off, you hear clearly another one. Same for the other radiostation.

The case with electrons is just similar to the photonic on-by-one case: you have one sourse on with splitted paths so two signals arrive at the "receiver". One point is a result of two wave signals in this case. Sometimes they say "A photon interferes with itself", not with other photons.

EDIT: Let me return to two lasers in one-by-one experiment. Our good sense tells us that it is two different photons interfere in the cross area. We think that they are different because they are from different sources. But in fact, according to the equations both lasers, turned on simultaneously, are one source providing different light paths, so in this case even one-by-one photon experiment will show an interference pattern at their beam intersection.

 

[Vdtta]

Thanks a lot.

The case with electrons is just similar to the photonic on-by-one case: you have one sourse on with splitted paths so two signals arrive at the "receiver". One point is a result of two wave signals in this case. Sometimes they say "A photon interferes with itself", not with other photons.

And there it is, I suppose this sums up the mystery of this experiment. And now, yet another question. I read somewhere this experiment can not only be done with photons, electrons and neutrons, but the patterns emerge even if they shoot the whole molecules. Now, molecules are very mach particles and very much unlike waves, so what in the world is going on there? One more... are there any similar effect going on with longitudinal waves, such as sound?I hope you enjoy answering as much as I enjoy asking, thanks again :-)

 

[Bob_for_short]

And now, yet another question. I read somewhere this experiment can not only be done with photons, electrons and neutrons, but the patterns emerge even if they shoot the whole molecules. Now, molecules are very mach particles and very much unlike waves, so what in the world is going on there?

In fact any system is a wave. When the wavelength is very short, we observe such a wave as a ray with a certain trajectory (geometrical optic limit). When the wavelength is large (comparable with the slit widths), it gives an interference picture. The wavelength is inversely proportional to the mass and velocity λ ∝ ћ/(mv). For heavy and fast objects it is rather short so we see them as particles. In order to observe an interference pattern we have to prepare very slow particles.

One more... are there any similar effect going on with longitudinal waves, such as sound?

Yes, all kind of waves may interfere, including sound waves. That is why there is a whole science about arranging speakers.

 

[jtbell]

I can not imagine something so very precisely narrow like laser or electron beam to randomly fluctuate in width as to cover one inch separation between slits.

One inch??

Who has done a two-slit electron interference experiment with a one-inch separation between the slits?

Students commonly do two-slit interference of light using a laser beam. The beam diameter is typically a couple of mm or so. If the slits are, say, a half mm apart, you can "cover" both of them with the beam and you get two-slit interference. If the slits are a couple of cm apart, the beam cannot cover both of them at once. If you "hit" one of the slits, you get single-slit diffraction, otherwise you don't get anything at all.

 

[Vdtta]

In fact any system is a wave. When the wavelength is very short, we observe such a wave as a ray with a certain trajectory (geometrical optic limit). When the wavelength is large (comparable with the slit widths), it gives an interference picture. The wavelength is inversely proportional to the mass and velocity λ ∝ ћ/(mv). For heavy and fast objects it is rather short so we see them as particles. In order to observe an interference pattern we have to prepare very slow particles.

Wow, amazing! It sounds mathematically logical, it makes as much sense to me as it can be shown experimentally and considering the fact everyone can easily witness it, and so have I, but other than that I'm scratching my head. Thanks again.


Another one:

====================screen==


_______   ___   __________mask__
           |      
           |     
           |  
           | 
         e-gun

In case we do use point source and if we do swivel the gun left-right, or aim directly through one of the slits, would there be interference pattern again? This situation reminds me of one-slit experiment and I'm guessing patterns might be there, probably more similar to one-slit than two-slit patterns, but on the other hand I would not be surprised if this situation does not produce patterns at all. And if so, in case point sources do not produce interference patterns, would that still make sense with the rest?

 

[Vdtta]

One inch??

Who has done a two-slit electron interference experiment with a one-inch separation between the slits?

Students commonly do two-slit interference of light using a laser beam. The beam diameter is typically a couple of mm or so. If the slits are, say, a half mm apart, you can "cover" both of them with the beam and you get two-slit interference. If the slits are a couple of cm apart, the beam cannot cover both of them at once. If you "hit" one of the slits, you get single-slit diffraction, otherwise you don't get anything at all.

Thanks, I did not know that at the time. I think I read it on Wikipedia some slits, in some experiments, were indeed one inch apart, but I also used it to exaggerate so to explain my confusion better. That video on YouTube from above link really got me a great perspective on the whole thing, I wish I saw something like that before.By the way, you see now why I started that thread about simulating electron beam with classical physics or special relativity... I'm trying to figure out if I can simulate double slit experiment as kinematic n-body simulation. It sounds impossible, but that's what makes it interesting.