Quantum effects in a single-slit experiment

[Uhtred]

The famous double-slit-experiment has been widely discussed just about everywhere, but I'm wondering about seeing wave-particle duality with a single-slit experiment. This experiment would consist of a source of particles, a screen with a single slit, and a second screen with some sort of particle detector that could determine the position of the particles as they hit.

1) If I shine a beam of particles (say, electrons) at the screen with the single-slit, then I would expect to see a diffraction pattern on the second screen (assuming that the electrons' energy and the slit width are appropriately selected).

2) If I modify the particle source to fire a single electron at a time, then I would still expect to see the diffraction pattern.

3) At this point, the experiment has shown wave-particle duality, correct? Each electron propagates through the slit as a wave, and is detected at the second screen as a definite particle.

OK, so here is my question: is there some sort of observation that could be made on the electrons in this experiment that would cause the diffraction pattern to disappear? For example, observing not only whether or not a particular electron made it through the single slit, but determining its position to arbitrary precision as it went through the slit?

Thanks for any insight into this question...

 

[soothsayer]

By measuring the position of the electron as it passes through the slit with significant precision should alter the diffraction pattern. My guess is that it would create a narrow slit of particles, such as one would expect to see classically, in keeping with results from similar measurements in the double slit experiment, but I don't know for sure.

 

[FedEx]

Yup, If you make an observation, you force the electron to collapse to one of the states. The e is in a superposition of two states
1) Go through slit 1
2) Go through slit 2.
So once you make an observation the e collapses either in 1 or 2. And hence no diffraction pattern. However naked eye obs will not work, get a smaller wavelength i guess.

 

[soothsayer]

get a smaller wavelength i guess.

If that.

 

[FedEx]

If that.

Sorry?

 

[soothsayer]

Oh, nothing, it's just that you had mentioned that naked eye observation would if anything make the wavelength a little bit smaller. I was just saying that I wasn't sure it would even do that, but the difference is inconsequential.

 

[Uhtred]

Well, it sounds like I'm on the right track. It seems that the diffraction pattern would disappear if sufficiently precise measurements were made of the position of the electrons as they go through the slit.

As the uncertainty of position is reduced, the uncertainty of the electrons' momentum is increased, with a corresponding increase in the uncertainty of the electrons' wavelength. As the uncertainty of the wavelength increases, the diffraction pattern will eventually be destroyed. At least, that's how I'm thinking about it now.

I'm reading John Gribbin's "In Search of Schrödinger's Cat" and I want to be solid on my understanding of the slit experiments (he's a bit light on what happens with a single slit) before going on to EPR.

The single-slit experiment seems to demonstrate the same quantum effects as the double-slit, so I wonder why the double-slit experiment is so commonly discussed? Perhaps because it's experimentally easier to see the effects with the double-slit? It's certainly easier to make a particle detector that can determine which of two slits the particle goes through as opposed to making a single-slit detector try to determine a very accurate position within the slit.

 

[FedEx]

As the uncertainty of position is reduced, the uncertainty of the electrons' momentum is increased, with a corresponding increase in the uncertainty of the electrons' wavelength. As the uncertainty of the wavelength increases, the diffraction pattern will eventually be destroyed. At least, that's how I'm thinking about it now.

Hmm.. I don't think that is true... Your observation forces the e to collapse into one of the states... I don't think it is a gradual process.. I haven't heard of any diminishing diffraction patterns..

 

[DGriffiths]

I think if the electron is not being 'watched' as it passes through the slits then no particular path is indistinguishable from any other path - in this case you add the quantum amplitudes of the individual paths before you take the modulus squared of the quantum amplitudes (that equates to the probability of finding the electron at a particular point on the screen) - the consequence of this is that when the modulus squared process is done there is an interference term that comes out of the maths - hence the observed interference.
However if the electrons path is measured then we have a distinguishable rather than an indistinguishable path - the consequence of now taking the modulus squared on the quantum amplitude of this 'known' path means that the interference term is now lost. The same weirdness I believe happens with diffraction gratings that if light is allowed to bounce of any part of the grating and a particular path is indistinguishable from others then the diffraction grating gives the orders of diffraction as you'd expect if however you block off a portion of the grating such that reflections occur of a tiny portion of it (i.e. with the uncertainty principle limitations you can pinpoint where the reflection must have occurred from) then the grating does not show the diffraction pattern.

Sorry not a great explanation - you'll have to read Feynman to get it explained properly

 

[DevilsAvocado]

This is what happens in a real experiment:

https://www.youtube.com/watch?v=<object width="640" height="505">
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<param name="allowFullScreen" value="true"></param>
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</object>



P.S. Welcome to Physics Forums Uhtred!

 

[DGriffiths]

Ah Professor Walter Lewin love him, thanks DevilsAvocado never seen that video before though.

 

[eaglelake]

See arXiv:quant-ph/0703126 where it is all explained.

 

[DevilsAvocado]

Ah Professor Walter Lewin love him, thanks DevilsAvocado never seen that video before though.

You are welcome. If you like educational videos, check out https://www.physicsforums.com/showthread.php?t=455473" with +126 hrs video (locked for some totally unknown reason everything is perfectly legal).

 

[Uhtred]

Thanks to all for the excellent information. I will look through the Cornell paper tonight - it looks to be an interesting read. And the video was great!

And I see you what you mean, FedEx... When I said "As the uncertainty of the wavelength increases, the diffraction pattern will eventually be destroyed" it sounded like I'm implying a gradual process for the destruction of the interference. I didn't word that very well, and I should have said something like "at some point" instead of "eventually".