The Double Slit Experiment

[Alex Andrews]

I would like to ask a question about (Eggert's?) Double Slit Experiment, but first I would like to check my understanding of the current interpretation.

 

My understanding is that when electrons are fired individually at a double slit, the observed result is an inteference pattern similar to that observed when a wave passes through a double-slit. The conclusion inferred from this observed pattern is that the electron is actually in two places simultaneously (ie it passes through both slits at the same time) and consequently interferes with itself to produce the observed pattern. This is then used as the basis for Quantum Theory.

 

Is my understanding correct?

 

Thanks very much,

 

Alex

 

[Sensei]

If you emit single photon, photon by photon, with any delays between them, result after some time, is diffraction or interference pattern.

Energy/frequency/wavelength of photon is used in (diffraction/interference) calcs.

 

[math]E=h*f[/math]

[math]f=\frac{E}{h}[/math]

 

[math]f=\frac{c}{\lambda}[/math]

 

[math]E=\frac{h*c}{\lambda}[/math]

[math]\lambda=\frac{h*c}{E}[/math]

 

Photons could be red-shifted or blue-shifted because of Relativistic Doppler Effect:

[math]f=f_0*(1-v)*\gamma=f_0*\sqrt{\frac{1-v}{1+v}}[/math]

 

[math]f=f_0*(1+v)*\gamma=f_0*\sqrt{\frac{1+v}{1-v}}[/math]

 

If you emit single electron, electron by electron, with any delays between them, result after some time, is diffraction or interference pattern.

Kinetic energy/momentum/velocity of electron is used in calcs.

 

[math]E.K.=m_ec^2*\gamma-m_ec^2[/math]

 

[math]p=m_e*v*\gamma[/math]

 

where

[math]h=6.62607004*10^{-34}J*s[/math]

 

[math]c=299792458 \frac{m}{s}[/math]

 

[math]\gamma =\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/math]

Edited May 4, 2016 by Sensei

[Strange]

Is my understanding correct?

 

I would say your understanding is correct, apart from: "This is then used as the basis for Quantum Theory."

 

Quantum theory was developed manly on the basis of Planck's work on the black body spectrum and Einstein's work on the photoelectric effect. I think the results of the double slit experiment were predicted by theory before the experiment was first performed (but I could be wrong about that).

[Klaynos]

It's probably also worth noteing that larger things than electrons have also been observed to have wave-like properties. Buckyballs jump to mind.

It's probably also worth noteing that larger things than electrons have also been observed to have wave-like properties. Buckyballs jump to mind.

[swansont]

Single electrons were not an early observation, so QM was not based on that. Electron diffraction through Nickel (Davisson-Germer) was, but electron interference was much later — in the 1950s. Electrons with a Young's double-slit was in 1961, and single-electron wasn't until the late 80s.

http://www.physics.rutgers.edu/~steves/501/links/double_slit_experiment.pdf (pdf)

[Alex Andrews]

Hi,

 

Thanks all for your replies. As you can probably tell, my knowledge in this area is fairly superficial.

 

OK, so the reason I wanted to check my understanding is as follows:

 

If, as is observed, single electrons fired through a double-slit produce an intereference pattern, it does not follow logically to infer that the electron passes through both slits and somehow intereferes with itself. I believe that when detectors are placed at the slits (a) the electron is detected passing through only one of the slits, and (b) the interference pattern is dampened down. However, the resultant interference pattern cannot be disputed, so what has caused it? Would it not make more sense (both instinctively and logically) if it were the case that while the electron passed through one of the slits, a wave also passed through both slits? The resultant two wave fronts would then interfere with each other as you would expect and in turn the electron, causing the electron's path to deviate as observed. After all, (again as I understand it!), it is only the path of the electron that suffers the "interference", not its speed or energy level or any other characteristic. I liken this to a boat travelling on water: as it moves forward it produces a bow-wave. Something similar could happen with electrons (or any particle) moving through space, whereby it produces some sort of bow-wave which I guess we currently can't detect. If a moving particle has some sort of associated bow-wave, then wouldn't that also chime rather well with the wave-particle duality principle? It would certainly explain why the electron is detected passing through only one slit, and possibly why the presence of the detectors dampens the result (the detectors absorbs some of the wave energy).

 

This explanation makes much more sense to me, but then I'm far from an expert in this area and maybe this idea has been considered and dismissed previously.

 

Any thoughts?

 

Alex

Edited May 4, 2016 by Alex Andrews

[swansont]

Hi,

 

Thanks all for your replies. As you can probably tell, my knowledge in this area is fairly superficial.

 

OK, so the reason I wanted to check my understanding is as follows:

 

If, as is observed, single electrons fired through a double-slit produce an intereference pattern, it does not follow logically to infer that the electron passes through both slits and somehow intereferes with itself. I believe that when detectors are placed at the slits (a) the electron is detected passing through only one of the slits, and (b) the interference pattern is dampened down. However, the resultant interference pattern cannot be disputed, so what has caused it? Would it not make more sense (both instinctively and logically) if it were the case that while the electron passed through one of the slits, a wave also passed through both slits? The resultant two wave fronts would then interfere with each other as you would expect and in turn the electron, causing the electron's path to deviate as observed. After all, (again as I understand it!), it is only the path of the electron that suffers the "interference", not its speed or energy level or any other characteristic. I liken this to a boat travelling on water: as it moves forward it produces a bow-wave. Something similar could happen with electrons (or any particle) moving through space, whereby it produces some sort of bow-wave which I guess we currently can't detect. If a moving particle has some sort of associated bow-wave, then wouldn't that also chime rather well with the wave-particle duality principle? It would certainly explain why the electron is detected passing through only one slit, and possibly why the presence of the detectors dampens the result (the detectors absorbs some of the wave energy).

 

This explanation makes much more sense to me, but then I'm far from an expert in this area and maybe this idea has been considered and dismissed previously.

 

Any thoughts?

 

Alex

 

 

 

A separate wave that undergoes interference sounds like the deBroglie-Bohm pilot wave. The problem is it's a hidden variable, and local hidden variables are forbidden. So for this to work, it has to be nonlocal.

 

https://en.wikipedia.org/wiki/Pilot_wave

[Alex Andrews]

 

 

 

A separate wave that undergoes interference sounds like the deBroglie-Bohm pilot wave. The problem is it's a hidden variable, and local hidden variables are forbidden. So for this to work, it has to be nonlocal.

 

https://en.wikipedia.org/wiki/Pilot_wave

 

OK, thanks I shall have a read and try to get my head around that.

So, I've had a quick read up on pilot waves and inelastic scattering. I might have misunderstood pilot waves, but the theory seems to be that a particle intrinsically has an associated wave:

 

 

Initially, de Broglie proposed a double solution approach, in which the quantum object consists of a physical wave (u-wave) in real space which has a spherical singular region that gives rise to particle-like behaviour... He later formulated it as a theory in which a particle is accompanied by a pilot wave... A collection of particles has an associated matter wave, which evolves according to the Schrödinger equation.

 

So, my understanding of this is that particles have an associated wave which I guess goes hand-in-hand with wave-particle duality. That is not what I am suggesting. My proposal is that a moving particle creates some sort of bow-wave: in my analogy, a moving boat creates a bow-wave in the water in front of it. I am not suggesting that the boat itself is some sort of wave or that it has some sort of wave intrinsically associated with it; it is its motion through the water which creates the bow-wave in the water and similarly the electron moving through space.

 

With regards to inelastic scattering:

 

 

In an inelastic scattering process, some of the energy of the incident particle is lost or increased.

 

Interaction between the bow-wave and the particle (or in my analogy, the bow-wave and the boat) could easily influence the speed of the particle (boat) to some greater or lesser degree when the bow-wave itself is interfered with by other waves.

 

Have I misunderstood?

 

Alex

Edited May 4, 2016 by Alex Andrews

[swansont]

 

Have I misunderstood?

 

Alex

 

 

I don't know.

 

I don't see how calling it a bow wave leads to any distinction — it's a wave associated with a particle. Does it lead to different predictions than we already have in QM? That's the only way to test it.

[Alex Andrews]

I don't see how calling it a bow wave leads to any distinction — it's a wave associated with a particle. Does it lead to different predictions than we already have in QM? That's the only way to test it.

 

Because the wave is not intrinsically associated with the particle, it is created by the motion of the particle. It is completely distinct from the particle itself. And it is completely beyond my ken to test it which is why I have come here to discuss it.

Edited May 4, 2016 by Alex Andrews

[Strange]

So, my understanding of this is that particles have an associated wave which I guess goes hand-in-hand with wave-particle duality. That is not what I am suggesting. My proposal is that a moving particle creates some sort of bow-wave: in my analogy, a moving boat creates a bow-wave in the water in front of it. I am not suggesting that the boat itself is some sort of wave or that it has some sort of wave intrinsically associated with it; it is its motion through the water which creates the bow-wave in the water and similarly the electron moving through space.

 

If you look at how the double slit experiment is done, to allow the "which slit" information to be obtained without destroying the photon they use entangled pairs of particles. So you have to figure out a way for the bow wave to be affected by the measurement of a remote photon - which might be so remote that it would require faster than light communication. (Which is impossible.)

 

And then look at the quantum eraser, and the delayed choice quantum eraser versions of the experiment. These demonstrate that the non-locality that creates the interference pattern (by allowing the particle to go through both holes) is also non-locality in time.

 

If you try and stick with a "mechanical" explanation of the experiment, then I think you have to imagine that your "bow waves" can also go back in time. (Which is really impossible.)

[swansont]

 

Because the wave is not intrinsically associated with the particle, it is created by the motion of the particle. It is completely distinct from the particle itself. And it is completely beyond my ken to test it which is why I have come here to discuss it.

 

 

I still don't see the distinction between the two cases. You simply have suggested a detail regarding how the wave is made.

The deBroglie wavelength of an electron is dependent on its momentum, so if this is some separate wave, it also depends on the motion.

[elfmotat]

And it is completely beyond my ken to test it which is why I have come here to discuss it.

The issue is that there isn't a way to test it, even in principle. De Broglie-Bohm's predictions are completely equivalent to those of any other interpretation of QM.

[Alex Andrews]

 

If you look at how the double slit experiment is done, to allow the "which slit" information to be obtained without destroying the photon they use entangled pairs of particles. So you have to figure out a way for the bow wave to be affected by the measurement of a remote photon - which might be so remote that it would require faster than light communication. (Which is impossible.)

 

And then look at the quantum eraser, and the delayed choice quantum eraser versions of the experiment. These demonstrate that the non-locality that creates the interference pattern (by allowing the particle to go through both holes) is also non-locality in time.

 

If you try and stick with a "mechanical" explanation of the experiment, then I think you have to imagine that your "bow waves" can also go back in time. (Which is really impossible.)

 

OK, well I don't pretend to understand even half of what you have said, but I am happy to accept that you know what you're talking about! I'll see if I can get my head around some of it at least.

 

 

I still don't see the distinction between the two cases. You simply have suggested a detail regarding how the wave is made.

The deBroglie wavelength of an electron is dependent on its momentum, so if this is some separate wave, it also depends on the motion.

 

Then maybe I have misunderstood because I thought that de Broglie's pilot wave was in essence the wave part of wave-particle duality. In retrospect, I think it was a mistake to bring up wave-particle duality as now I don't think it's really relevant.

The issue is that there isn't a way to test it, even in principle. De Broglie-Bohm's predictions are completely equivalent to those of any other interpretation of QM.

 

I guess what I'm trying to say is that the observed results of the double slit experiment (with single electrons) do not appear (to me) to be consistent with the electron passing through both slits but do appear consistent with a wave front passing through both slits and as a consequence causing the path of the electron to deviate from its original course (Occam's Razor springs to mind). What exactly that wave is I have no idea but I suggested the possibility of a bow wave as a real-world analogy.

 

Out of interest, suppose the experiment is conducted with slits A and B and the electrons are fired through slit B. If slit A is covered up, presumably the electrons pass straight through without any sort of deviation? And if slit B is instead covered up, do electrons still "go through" slit A?

 

Thanks,

 

Alex

Edited May 5, 2016 by Alex Andrews

[Strange]

 

OK, well I don't pretend to understand even half of what you have said, but I am happy to accept that you know what you're talking about!

 

 

That may not be a safe assumption! (But luckily there are others around who do.)

 

I guess what I'm trying to say is that the observed results of the double slit experiment (with single electrons) do not appear (to me) to be consistent with the electron passing through both slits but do appear consistent with a wave front passing through both slits and as a consequence causing the path of the electron to deviate from its original course (Occam's Razor springs to mind). What exactly that wave is I have no idea but I suggested the possibility of a bow wave as a real-world analogy.

 

That wave is the electron. The key point to get your head round is that an electron is not like a little bullet. You can think of it as spread out through space (with a probability of being at any particular location). It is the evolution of that non-localised nature of the electron that is described by the wave equations. And that is what allows it to be affected by the presence of the two slits: they change its probability of ending up at any particular location.

See if you can find the videos of the QED lectures by Feynman on line. He was explaining this to a non-technical audience, so it is quite easy to follow. He describes it in terms of the electron taking every possible path through space (and time) with different probabilities. You sum all those probabilities to get the final result. So things that are not directly in the path can have affect.

Out of interest, suppose the experiment is conducted with slits A and B and the electrons are fired through slit B. If slit A is covered up, presumably the electrons pass straight through without any sort of deviation? And if slit B is instead covered up, do electrons still "go through" slit A?

 

 

I think the problem with that is that you can't guarantee to send the electrons through only one slit. Unless the slits are very wide and/or very far apart. In which case you won't get an interference pattern anyway. In which case covering the other slit will have zero (or minimal) effect.

p.s. Here's the the Feynman videos. He talks in terms of photons, but most of it applies equally to electrons.

http://www.vega.org.uk/video/subseries/8

[Alex Andrews]

 

That wave is the electron. The key point to get your head round is that an electron is not like a little bullet. You can think of it as spread out through space (with a probability of being at any particular location). It is the evolution of that non-localised nature of the electron that is described by the wave equations. And that is what allows it to be affected by the presence of the two slits: they change its probability of ending up at any particular location.

See if you can find the videos of the QED lectures by Feynman on line. He was explaining this to a non-technical audience, so it is quite easy to follow. He describes it in terms of the electron taking every possible path through space (and time) with different probabilities. You sum all those probabilities to get the final result. So things that are not directly in the path can have affect.

 

I think the problem with that is that you can't guarantee to send the electrons through only one slit. Unless the slits are very wide and/or very far apart. In which case you won't get an interference pattern anyway. In which case covering the other slit will have zero (or minimal) effect.

p.s. Here's the the Feynman videos. He talks in terms of photons, but most of it applies equally to electrons.

http://www.vega.org.uk/video/subseries/8

 

OK, thanks very much, I will definitely have a watch. I can understand how such an explanation would predict the oberved result, but it still just seems an inordinately complex one hence my citing of Occam's Razor. Also, when you say that it is not possible to guarantee which slit the electron would pass through, what if you were to build a "corridor" from the electron source to one of the slits so that the electron could only pass through the one slit, would you still get the observed interference pattern? And why is this effect only observable for small objects (as I understand it)? Surely size shouldn't be a factor if an object is being interfered with by a copy of itself?

 

Sorry - so many questions!

[Strange]

 

OK, thanks very much, I will definitely have a watch. I can understand how such an explanation would predict the oberved result, but it still just seems an inordinately complex one hence my citing of Occam's Razor.

 

 

The thing is, Occam's razor is not about complexity. It is about not including unnecessary things. No one has managed to come up with a simpler model that works. So it seems the complexity is necessary (there is no reason the universe should be simple enough for us to understand it).

 

Also, when you say that it is not possible to guarantee which slit the electron would pass through, what if you were to build a "corridor" from the electron source to one of the slits so that the electron could only pass through the one slit, would you still get the observed interference pattern?

 

If you force the electrons to go through a single slit, that is the same as having the "which way" information that breaks the interference pattern.

 

And why is this effect only observable for small objects (as I understand it)? Surely size shouldn't be a factor if an object is being interfered with by a copy of itself?

 

Because the size of the wave is (roughly) inversely proportional to size. So the experiment has been done with C₆₀ "buckyball" molecules (and some even bigger, I think). But it becomes increasingly difficult to do the experiment.

[swansont]

And why is this effect only observable for small objects (as I understand it)? Surely size shouldn't be a factor if an object is being interfered with by a copy of itself?

 

 

The effect scales with wavelength, which is h/p, where p is the momentum. It's really hard to have more massive objects have a small enough momentum where this can be observed. If size didn't matter, you would diffract when you walked through a doorway.