Some very basic questions around the double slit experiment

In summary: The underlying math is Fourier analysis -- decomposing a function into sine waves. A very, very important tool in many branches of science and technology; wonderful videos aplenty on the net. Worth investigating !In summary, the conversation discusses various aspects of the double slit experiment including the distance between the slits, the orientation of the slits, and the distribution of electrons when only one slit is used. It is mentioned that the interference pattern will always be perpendicular to the orientation of the slits and that the pattern can be rotated if the slits are rotated. The concept of beam
  • #1
rede96
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15
I have a few basic questions about the double slit experiment and was hoping someone might be able to answer them.

1) How far apart from each other would have I have to make the slits so effectively no detection took place? E.g. is there a limit to how far the wave function can spread and a detection still take place?

2) I am assuming that the orientation of the slits is irrelevant? E.g. I'd still see the same interference pattern if the slits were horizontal or even at some angle?

3) If I removed the screen with two slits and just fired electrons one at a time at a target area, what sort of distribution would I see? E.g. would I I see a circular distribution around the target point? Would there be less electron being detected further away from the target point?

4) Has the experiment ever been done with two sets of slits? Say with the second set of slits at some distance away from the first and at a different distance apart? I was just trying to understand if there has to be a direct line of sight between the source and the detection point for a detection to take place or if the wave like property would still lead to a detection even if there was no direct line of sight?

Thanks
 
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  • #2
rede96 said:
2) I am assuming that the orientation of the slits is irrelevant? E.g. I'd still see the same interference pattern if the slits were horizontal or even at some angle?
The interference pattern, that is, the "line of dots", will always be perpendicular to the orientation of the slits. So if you rotate the slits, the pattern will also be rotated.
 
  • #3
rede96 said:
4) Has the experiment ever been done with two sets of slits? Say with the second set of slits at some distance away from the first and at a different distance apart? I was just trying to understand if there has to be a direct line of sight between the source and the detection point for a detection to take place or if the wave like property would still lead to a detection even if there was no direct line of sight?
You could do such a thing but wouldn't learn anything new. Note that even with one single slit, you already don't have the direct line of sight from the source, only from the slit. See the nice animations here
 
  • #4
rede96 said:
1) How far apart from each other would have I have to make the slits so effectively no detection took place? E.g. is there a limit to how far the wave function can spread and a detection still take place?
If you have a flat wave front (as in those animations), the double slit pattern can be pretty far apart. Of course the interference peaks would crawl ever closer together. There is no theoretical limit but intensities go down rapidly for large angles of diffraction.
 
  • #5
rede96 said:
3) If I removed the screen with two slits and just fired electrons one at a time at a target area, what sort of distribution would I see? E.g. would I I see a circular distribution around the target point? Would there be less electron being detected further away from the target point?
Depends on how you generate the beam. Google 'electron beam collimaton' or 'beam collimaton'
 
  • #6
rede96 said:
I have a few basic questions about the double slit experiment
You could save yourself just a ton of grief by learning how to solve the double slit for ordinary classical electromagnetic waves. There's a reason why that problem appears in the undergraduate physics curriculum before introductory QM.
 
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  • #7
DennisN said:
The interference pattern, that is, the "line of dots", will always be perpendicular to the orientation of the slits. So if you rotate the slits, the pattern will also be rotated.

I thought was the case but just wanted to check. Thanks for the reply.
 
  • #8
BvU said:
You could do such a thing but wouldn't learn anything new. Note that even with one single slit, you already don't have the direct line of sight from the source, only from the slit. See the nice animations here

BvU said:
If you have a flat wave front (as in those animations), the double slit pattern can be pretty far apart. Of course the interference peaks would crawl ever closer together. There is no theoretical limit but intensities go down rapidly for large angles of diffraction.

BvU said:
Depends on how you generate the beam. Google 'electron beam collimaton' or 'beam collimaton'
That's great info, thanks for that. I'll have to read and digest as I'm just an interested layman and not great with math side of things. But that's what I was looking to understand more.
 
  • #9
Nugatory said:
You could save yourself just a ton of grief by learning how to solve the double slit for ordinary classical electromagnetic waves. There's a reason why that problem appears in the undergraduate physics curriculum before introductory QM.
Thanks for the reply. Unfortunately at 52 years old and just basic high school math I can usually only aim to understand things conceptually. I really wish I had more time to learn all this properly!

But I'll definitely have a look for some video lectures on classical em waves.
 
  • #10
rede96 said:
Thanks for the reply. Unfortunately at 52 years old and just basic high school math I can usually only aim to understand things conceptually.
Kudos !

Conceptually the things to pick up are:
narrow slits give wide diffraction patterns
peaks are closer if wavelengths are smaller​

and, more broadly:
with smaller wavelengths you can 'see' (observe) smaller things -- the reason an electron microscope can explore where a light microscope can not; and the reason these particle physicists need ever bigger machines to study ever smaller structures​

The underlying math is Fourier analysis -- decomposing a function into sine waves. A very, very important tool in many branches of science and technology; wonderful videos aplenty on the net. Worth investigating !
 
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  • #11
BvU said:
Kudos !

Conceptually the things to pick up are:
narrow slits give wide diffraction patterns
peaks are closer if wavelengths are smaller​

and, more broadly:
with smaller wavelengths you can 'see' (observe) smaller things -- the reason an electron microscope can explore where a light microscope can not; and the reason these particle physicists need ever bigger machines to study ever smaller structures​

The underlying math is Fourier analysis -- decomposing a function into sine waves. A very, very important tool in many branches of science and technology; wonderful videos aplenty on the net. Worth investigating !

Thanks for the link, I'll have a good search around.
BvU said:
Depends on how you generate the beam. Google 'electron beam collimaton' or 'beam collimaton'

All I was trying to understand here is if I simply fire electrons one at a time from a source to a screen that detects them, what pattern would I see?

I would image I would see the particle nature of the electron hitting the screen and causing a 'dot' but it would be the wave function that would decide where the electron hit the screen. So although there is some randomness as to where the electron will hit the screen, if I allowed the pattern to build up I'd start to see circles forming on the screen that detects the electrons. The inner circles would have more 'dots' and the outer circles fewer.

Does that make sense in very broad terms?
 
  • #12
rede96 said:
if I simply fire electrons one at a time from a source to a screen that detects them
Whhat source do you have in mind (see #5) ?

A screen that lights up when an electron hits it is a good detector. There is no reason for circles to become visible; you would just see a blob if you took a long exposure time picture -- but perhaps I interpret your terminology wrongly ?

Things become different when you use a small circular hole in the beam path. The you do get a 2D 'equivalent' of the single slit pattern again as shown here
 
  • #13
BvU said:
Whhat source do you have in mind (see #5) ?

If you'll excuse my ignorance, what difference does the source make? An electron is an electron. I didn't think it would behave differently depending on the source? But I haven't had time to look up the different sources yet, but was thinking of one that just fired a single electron at a time.

BvU said:
A screen that lights up when an electron hits it is a good detector. There is no reason for circles to become visible; you would just see a blob if you took a long exposure time picture -- but perhaps I interpret your terminology wrongly ?

Sorry, I can be pretty crap at explaining myself so thanks for being patient with me. What I was trying to visualize was the pattern that would be generated over time by electrons being fired one at a time at the screen. Obviously each electron will not hit the screen in exactly the same position. I would imagine there would be some variance just because the electron generated may leave the source at a slightly different angle wrt to the screen each time it is generated.

But ignoring that process variation for a moment, even if the electrons trajectory was exactly the same each time, I thought that where the electrons hit the screen would be probabilistic due to the wave function. But if I observed enough electrons, over time I'd see a pattern (assuming I could measure to enough resolution) and I thought that pattern would be circular with more electrons detected near the center of the patter and less so further away.

Does that make sense?
 
  • #14
rede96 said:
If you'll excuse my ignorance, what difference does the source make? An electron is an electron. I didn't think it would behave differently depending on the source? But I haven't had time to look up the different sources yet, but was thinking of one that just fired a single electron at a time.
Sorry, I can be pretty crap at explaining myself so thanks for being patient with me. What I was trying to visualize was the pattern that would be generated over time by electrons being fired one at a time at the screen. Obviously each electron will not hit the screen in exactly the same position. I would imagine there would be some variance just because the electron generated may leave the source at a slightly different angle wrt to the screen each time it is generated.

But ignoring that process variation for a moment, even if the electrons trajectory was exactly the same each time, I thought that where the electrons hit the screen would be probabilistic due to the wave function. But if I observed enough electrons, over time I'd see a pattern (assuming I could measure to enough resolution) and I thought that pattern would be circular with more electrons detected near the center of the patter and less so further away.

Does that make sense?
If the electrons are represented by wave packets you'll get a bivariate Gaussian with zero correlation. Which looks like what you expect.

https://en.wikipedia.org/wiki/Multivariate_normal_distribution
 
  • #15
Makes perfect sense. But making a beam of electrons is a complicated business in itself. You can have a cloud of electrons around e.g. a cathode but then you still need to give them a momentum along the beam axis (cathode ray tube -- ignore the deflection plates) while limiting the variance in transverse momentum (by using a small aperture in the positive anode, at the cost of lower beam intensity). You can imagine that the size of the aperture determines the size of the blob on the screen. With very, very small aperture sizes we are back to diffraction patterns again -- but those sizes are really very small: an aperture of one nanometer is of the order of six wavelengths of e.g. a 50 eV electron .
 

1. What is the double slit experiment?

The double slit experiment is a classic scientific experiment that demonstrates the wave-particle duality of light. It involves shining a beam of light through two slits and observing the interference pattern that is created on a screen behind the slits.

2. How does the double slit experiment work?

The experiment involves a source of light, two slits, and a screen. The light is shined through the slits and creates an interference pattern on the screen, which is a result of the waves from the two slits overlapping and creating areas of constructive and destructive interference.

3. What does the double slit experiment prove?

The double slit experiment proves that light exhibits both particle-like and wave-like properties. This is known as wave-particle duality and is a fundamental concept in quantum mechanics.

4. What are the implications of the double slit experiment?

The double slit experiment has many implications, including the understanding that particles can exhibit wave-like behavior and that our observation of a system can affect its behavior. It also supports the idea that the behavior of particles at the quantum level is inherently probabilistic.

5. How is the double slit experiment used in other fields of science?

The double slit experiment is not only used in physics, but also in other fields such as chemistry and biology. It has been used to study the behavior of particles in various systems, as well as to understand the properties of light and how it interacts with matter.

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