Questions about double slit experiments

[rede96]

TL;DR Summary

Just some basic questions around the double slit experiments to try and understand it better conceptually.

Firstly I’m just an interested layman who only started delving into QM and physics later on on life. So please forgive my ignorance.

One of the things I’m trying to understand better is the wave / particle duality nature of objects.

In the classical set up where single electrons are fired one at a time at a detector screen with the double slit filter in front of it:

a) Is every election fired at the detector screen detected? Or do some hit ‘in between’ the slits and don’t make it through? If so what percentage roughly are not detected?

b) What does the pattern of elections detected look like if just fired at a screen without the two slit filter in front of it? Is it just a circular blob?

c) If I had one slit positioned in a straight line from the electron gun, so the slit is in the centre of the electrons trajectory, and the second slit placed over to the right (or left) of centre, how far would right hand slit have to be from the centre slit before the interference pattern breaks down? (Was trying to understand the radius of the electron wave

Thanks :)

 

[PeroK]

Summary:: Just some basic questions around the double slit experiments to try and understand it better conceptually.

Firstly I’m just an interested layman who only started delving into QM and physics later on on life. So please forgive my ignorance.

One of the things I’m trying to understand better is the wave / particle duality nature of objects.

In the classical set up where single electrons are fired one at a time at a detector screen with the double slit filter in front of it:

a) Is every election fired at the detector screen detected? Or do some hit ‘in between’ the slits and don’t make it through? If so what percentage roughly are not detected?

b) What does the pattern of elections detected look like if just fired at a screen without the two slit filter in front of it? Is it just a circular blob?

c) If I had one slit positioned in a straight line from the electron gun, so the slit is in the centre of the electrons trajectory, and the second slit placed over to the right (or left) of centre, how far would right hand slit have to be from the centre slit before the interference pattern breaks down? (Was trying to understand the radius of the electron wave

Thanks :)

a) The narrower the slits, the fewer electrons make it through.

b) More or less.

c) Anything significant will spoil the experiment. I suspect you need a high-precision set-up to get a clear interference pattern.

 

[Nugatory]

One of the things I’m trying to understand better is the wave / particle duality nature of objects.

It would best to try to forget that you ever heard that phrase “wave/particle duality”. The idea dates from back when physicists first encountered quantum phenomena and were struggling to explain them, and was pretty much abandoned with the development of the modern theory in the late 1920s.

a) Is every election fired at the detector screen detected? Or do some hit ‘in between’ the slits and don’t make it through? If so what percentage roughly are not detected?

Many do not make it past the barrier to be detected at the screen. The exact percentage that get through will depend on the exact setup, but you’ll be reasonably close if you go with the ratio of the area of the slits to the total area of the barrier that is illuminated by the particle beam.

b) What does the pattern of elections detected look like if just fired at a screen without the two slit filter in front of it? Is it just a circular blob?

It’s a slit not a round aperture, so you get a bar not a circular blob, and there will be diffraction fringes at the edges - the same sort of pattern you’d get from shining coherent light through a slit.

c) If I had one slit positioned in a straight line from the electron gun, so the slit is in the centre of the electrons trajectory, and the second slit placed over to the right (or left) of centre, how far would right hand slit have to be from the centre slit before the interference pattern breaks down?

The beam has to illuminate both slits. As you move one slit farther away from the center of the beam the pattern becomes weaker and disappears altogether when it is out of the beam. The actual distance will depend on how well collimated the beam is.

 

[BvU]

a) if the slits are in between, some electrons do not make it to the detector screen. How big a fraction depends on dimensions.
b) usually just a blob, yes.
c) There is an interference pattern with an angular dependence, just as with light; see here. There is no sudden cutoff/break down.

For the wavelength, see de Broglie wavelength (or here)​

Read Feynman for an excellent treatment of the subject

 

[PeroK]

It’s a slit not a round aperture, so you get a bar not a circular blob, and there will be diffraction fringes at the edges - the same sort of pattern you’d get from shining coherent light through a slit.

I think for part b) there is no slit, no nothing between the gun and screen.

 

[Nugatory]

I think for part b) there is no slit, no nothing between the gun and screen.

Ah - yes, on rereading I think you’re right and I answered a different question - thank you.

 

[rede96]

Thanks for the replies. As a follow up, I am assuming there is a relationship between the area and position of the slits in a given set up to the number of electrons detected.

I am also assuming that given a set number of electrons were emitted in each experiment, if I was to repeat the experiment a number of times without changing the set up I would get the same amount of electrons detected, within a certain statistical variance of course.

So my question: If I create a second set up, where I replace the two slits with just a detector screen with no slits, but where the slit areas and position are drawn onto the detector screen so they are in exactly the same position as the original slits, would the number of electrons detected within the slit areas drawn on to this detector screen be equivalent to the number of electrons detected when the slits were in place in the first set up?

Hope that makes sense!

 

[PeroK]

So my question: If I create a second set up, where I replace the two slits with just a detector screen with no slits, but where the slit areas and position are drawn onto the detector screen so they are in exactly the same position as the original slits, would the number of electrons detected within the slit areas drawn on to this detector screen be equivalent to the number of electrons detected when the slits were in place in the first set up?

These questions are easier to answer if you understand what is happening. The original electron beam has an uncertainty in the position of the electron (in all three dimensions). The critical uncertainty is in the direction perpendicular to the slits. There must be uncertainty in position in this direction, otherwise every electron would do the same thing.

According to QM this uncertainty increases over time, so that the beam inevitably becomes more spread out as it travels. The pattern of a simple electron beam, therefore, will be a circular blob that increases with size the further away you put the detector screen.

It makes no difference whether you draw slits on the screen or not!

 

[rede96]

These questions are easier to answer if you understand what is happening. The original electron beam has an uncertainty in the position of the electron (in all three dimensions). The critical uncertainty is in the direction perpendicular to the slits. There must be uncertainty in position in this direction, otherwise every electron would do the same thing.

According to QM this uncertainty increases over time, so that the beam inevitably becomes more spread out as it travels. The pattern of a simple electron beam, therefore, will be a circular blob that increases with size the further away you put the detector screen.

It makes no difference whether you draw slits on the screen or not!

Maybe I didn’t explain my scenario too well. Let me try again. Imagine two set up’s. The first set up is just the standard double slit experiment which consists of an electron gun, a filter screen with two slits in it and a detector screen.

The second set up is exactly the same as the first except I remove the filter screen with two slits in it and replace it with a detector screen. Just with the original slits ‘drawn on’ so I can see how many electrons would have gone through the slits if the slits were still there. Obviously this makes the original detector screen behind it redundant.

So I would expect the number of electrons detected in set up one and the number of electrons detected in set up two, where the slits would have been, not to be different. Within any significant statistical difference that is.

I’d also expect the ratio of electrons detected in set up two between the two drawn on slits to be 50/50.

The reason I was thinking about the experiment in this way is we obviously can’t measure directly which slit the electron goes through in set up one. And it doesn’t make sense to do so.

However it made sense to me that although the whole electron wave must go through both slits, otherwise there would not be an interference pattern, the part of the wave where the electron will be detected must go through the two slits equally.

 

[PeroK]

Maybe I didn’t explain my scenario too well. Let me try again. Imagine two set up’s. The first set up is just the standard double slit experiment which consists of an electron gun, a filter screen with two slits in it and a detector screen.

The second set up is exactly the same as the first except I remove the filter screen with two slits in it and replace it with a detector screen. Just with the original slits ‘drawn on’ so I can see how many electrons would have gone through the slits if the slits were still there. Obviously this makes the original detector screen behind it redundant.

So I would expect the number of electrons detected in set up one and the number of electrons detected in set up two, where the slits would have been, not to be different. Within any significant statistical difference that is.

I’d also expect the ratio of electrons detected in set up two between the two drawn on slits to be 50/50.

Yes. Theorectically, that might be a way to ensure you have your experiment set up correctly. Effectively you close both slits and fill them with a thin piece of detecting screen.

Alternatively, you open each slit separately and count how many electrons go through. To put some numbers on this. We might have the case where, for example:

With the left slit open, say 20% of electron gets through. And also 20% with only the right slit open. Then, with both slits open, 40% of electrons would get through. That's all as expected. There's no issue there.

One way to summarise the double slit experiment is as follows:

The double-slit pattern is not the sum of the two single-slit patterns. If the electrons behaved classically, then the double-slit experiment would be an exercise in classical probabilities and we would expect the double slit pattern to be the sum of the two single slit patterns. If we let $x$ be the lateral coordinate of the position on the screen where the electron is detected, then: $$p(x) = p_1(x) + p_2(x)$$
Where $p(x)$ is the probability of an electron hitting the screen at point $x$ with both slits open and $p_1(x), p_2(x)$ are the probabilities of an electron hitting the screen with only the first or second slit open respectively. That's the case according to classical physics. But, of course, that is not what happens!

In QM, the pattern is built up according to probability amplitudes, and we have:$$\psi(x) = \psi_1(x) + \psi_2(x)$$ where $\psi(x)$ etc. are complex probability amplitudes (i.e. complex numbers).

Then, the actual probability of the electron hiting the screen at $x$ is given by:$$p(x) = |\psi(x)|^2 = |\psi_1(x)|^2 + |\psi_2(x)|^2 + 2Re(\psi_1(x)\psi_2(x)^*) = p_1(x) + p_2(x) + 2Re(\psi_1(x)\psi_2(x)^*)$$
And we have an interference term. That's how, via QM probability amplitudes, we get interference in the double-slit experiment.

Note that this analysis avoids all the extraneous nonsense concerning "wave-particle" duality.

However it made sense to me that although the whole electron wave must go through both slits, otherwise there would not be an interference pattern, the part of the wave where the electron will be detected must go through the two slits equally.

This is the wrong way to look at things. The wave is not a physical thing like in classical physics. It's a wave of probability. It's far better to start thinking in terms of probability amplitudes. That's the QM nature of the electron. Seeing it as a classical wave might ultimately give you interference, but then you end up in knots about when and where the electron changes from particle to wave and back again. Although that features in a lot of QM popular science, it's essentially nonsense.

It's worth spending an hour to watch this:

 

[BvU]

Read Feynman for an excellent treatment of the subject

I replace the two slits with just a detector screen with no slits, but where the slit areas and position are drawn onto the detector screen so they are in exactly the same position as the original slits, would the number of electrons detected within the slit areas drawn on to this detector screen be equivalent to the number of electrons detected when the slits were in place in the first set up?

In the first setup he electrons were not detected at the position of the slits but much further downstream !

So in the second setup you get the whole beam blob, as in #1 case b), only closer to the source

However,

So I would expect the number of electrons detected in set up one and the number of electrons detected in set up two, where the slits would have been, not to be different. Within any significant statistical difference that is.

Right, but not very interesting.

I’d also expect the ratio of electrons detected in set up two between the two drawn on slits to be 50/50.

Right, but again not interesting

However it made sense to me that although the whole electron wave must go through both slits, otherwise there would not be an interference pattern, the part of the wave where the electron will be detected must go through the two slits equally.

You are mixing up $\lambda$ scale interference with marble bridge games like

Again, just as @PeroK advises:

Read Feynman for an excellent treatment of the subject

 

[rede96]

The double-slit pattern is not the sum of the two single-slit patterns.

Yes I got that, but I wasn't referring to the pattern directly. For now I was interested in just the number of electrons detected in the two set ups and if they would be the same.

And we have an interference term. That's how, via QM probability amplitudes, we get interference in the double-slit experiment.

I need to get my head around the Math more, but I can get the concept. However what I was saying is that the only reason there is an interference pattern is because there are two (or more) open slits. This never happens with just one slit. So however we may describe an electron, it has to go through both slits to create an interference pattern. That's all I was saying. A lot of pop science states that it doesn't go through both, it doesn't go through the left or the right slit... etc. Which just seems nonsense.

This is the wrong way to look at things. The wave is not a physical thing like in classical physics. It's a wave of probability. It's far better to start thinking in terms of probability amplitudes. That's the QM nature of the electron.

I am not sure what you mean here? Obviously the electrons that are detected in the standard double slit experiment go through the slits. And as we have an interference pattern that only occurs when two or more slits are open it is logical to deduce the electrons go through both slits. When the wave collapses as the electron hits the screen we see the electron in a specific location on the screen, which is governed by probability. So it is logical to assume that this probability is a function, or property of the electron itself.

It's worth spending an hour to watch this:

Thanks for that :) I watch a lot of Leonard Susskind lectures too which I find really useful.

 

[PeroK]

So however we may describe an electron, it has to go through both slits to create an interference pattern. That's all I was saying. A lot of pop science states that it doesn't go through both, it doesn't go through the left or the right slit... etc. Which just seems nonsense.

You can only say where an electron is as the result of a measurement. The electron does not, according to QM, do anything specific like go through both slits. Its wave-function evolves. That's what QM says.

The whole double-slit experiment can be described by evolution of the wave-function. Statements like: the electron went here or the electron went here and there and meaningless.

And as we have an interference pattern that only occurs when two or more slits are open it is logical to deduce the electrons go through both slits.

It's not logical at all. It's common-sensical. And common-sense does not necessarily apply to QM.

The Feynman lecture above emphasises this point.

The problem also is that "going through both slits" does not explain interference. And specifically, not quantitatively. Common sense would say that if the electron does through both slits then two separate dots of low intensity impact the screen: two half-electrons impact the screen.

Saying the electron goes through both slits explains nothing - and is not QM. Whereas, evolution of the wave-function explains everything. And that is Quantum Mechanics.

 

[DrChinese]

...So however we may describe an electron, it has to go through both slits to create an interference pattern.

As PeroK has already mentioned, "going through both slits" is not in and of itself QM's description. I think of it "as if" something goes through both slits. Or the probability goes through both slits. But we don't have an exact description of its behavior when it is not being otherwise observed. So we might say:

Chance of detection in a specific region = X% chance it went though L slit + Y% chance it went though R slit (but you cannot specify which)

So that formula does not imply it went through both slits. It implies that the outcome probability is due to a superposition of the L slit and the R slit probabilities.

 

[rede96]

You can only say where an electron is as the result of a measurement.

Yes, I agree you can only say where the point like element of an electron is once measured, I wasn't trying to say otherwise. But I was wondering if the electron, or any particle is more than just what we measure. What I mean by that is that I don't imagine a particle to be a point like object that moves around in space with a certain probability of where it might be. I imagine it to be system. And it's only when we measure that system in some way that it manifests itself into a point like particle with a specific location.

The whole double-slit experiment can be described by evolution of the wave-function. Statements like: the electron went here or the electron went here and there and meaningless.

It's not logical at all. It's common-sensical. And common-sense does not necessarily apply to QM.

Again, I would agree if the electron is thought of as a point like particle with a certain random trajectory. But that's not how I imagine an electron. I imagine the electron to be the whole system. What I imagined is that when an electron is detected (measured) then that system collapses into a point like particle with a definite position. But up until that point I think of the electron as a 'wave' loosely speaking, with certain properties.

I can't do the Math but obviously there is a certain range outside of which we will not detect an electron hitting the screen. So anything within that range I was thinking of as the electron. It's just a way of visualizing it for me personally.

The problem also is that "going through both slits" does not explain interference. And specifically, not quantitatively.

Again not sure I understand. Interference only happens when there are two or more open slits. So although the interference pattern can not be described by the two slits, it only happens because there are two open slits. That's all I was saying.

Common sense would say that if the electron does through both slits then two separate dots of low intensity impact the screen: two half-electrons impact the screen.

That wasn't how I was imagining it. When I say the electron passes through both slits, I don't mean a point like particle passes through both slits, so I would not expect to see two points detected. I mean the electron as a system passes through both slits. Because there isn't an 'electron', as in a point like particle, until we measure it.

 

[rede96]

As PeroK has already mentioned, "going through both slits" is not in and of itself QM's description. I think of it "as if" something goes through both slits. Or the probability goes through both slits. But we don't have an exact description of its behavior when it is not being otherwise observed.

Thanks for that, yes that is how I was thinking of it too. (see last reply to PeroK) Not sure what goes through both slits, but I certainly wasn't thinking if it as a point like particle, more some sort of 'wave' with certain properties.

 

[PeroK]

I imagine it to be system. And it's only when we measure that system in some way that it manifests itself into a point like particle with a specific location.

It's not important how you or I like to imagine the electron, it's about what QM says. QM says the wave-function evolves according to the SDE (Schroedinger equation).

I imagine the electron to be the whole system. What I imagined is that when an electron is detected (measured) then that system collapses into a point like particle with a definite position. But up until that point I think of the electron as a 'wave' loosely speaking, with certain properties.

QM doesn't describe the electron as a wave. The electron is a particle whose dynamic properties are governed by its wave-function. There's a big difference between being a wave and having a wave-function.

Again not sure I understand. Interference only happens when there are two or more open slits. So although the interference pattern can not be described by the two slits, it only happens because there are two open slits. That's all I was saying.

We all know that. But, we need a theory to explain why that is.

That wasn't how I was imagining it. When I say the electron passes through both slits, I don't mean a point like particle passes through both slits, so I would not expect to see two points detected. I mean the electron as a system passes through both slits.

Yes, but we need a mathematical description of what "an electron as a system passes through both slits" actually means. Here is the critical point:

Have the electron "as a system" pass though both slits and apply classical probability theory and you get one thing. And not what happens.

Have an electron "as a system" pass through both slits using wave-function evolution and QM probability amplitudes and you have quantitatively what happens.

Unless and until you apply the wave-function evolution and probability amplitudes you do not have QM; and you do not have a quantitative description of nature.

 

[Nugatory]

Obviously the electrons that are detected in the standard double slit experiment go through the slits.

Actually, that is not obvious at all.

The facts that we have are that an electron was emitted at the source and an electron was detected at the screen; the only obvious conclusion is that it was not absorbed by the barrier. We might also make an assumption about the behavior of unobserved ("non-interacting" might be a better term) electrons in the vicinity of the barrier, and on that basis conclude that the electron went through the slits - but we need that assumption to draw the "obvious" conclusion.

 

[Nugatory]

Interference only happens when there are two or more open slits.

That's actually not quite right - with just a single slit open we still get a diffraction pattern. We never see, except as an approximation, the pattern that would be produced if we were shooting little bullets through the single slit - the probability wave effect is always present.

The same probability amplitude concept is used to calculate that diffraction pattern as in the two-slit interference case; we don't often see this in intro textbooks because the calculation is more complicated and the effect is harder to observe with realistic lab equipment.

 

[rede96]

The facts that we have are that an electron was emitted at the source and an electron was detected at the screen; the only obvious conclusion is that it was not absorbed by the barrier.

I would have thought when we shoot an electron at the screen, there are only two possibilities? It either gets absorbed by the barrier or it is detected. So be default if the only obvious conclusion is that it was not absorbed by the barrier doesn't that imply it went through the slits?

That's actually not quite right - with just a single slit open we still get a diffraction pattern

Isn't that diffraction pattern caused by the 'wave' bending around a slit or opening and not the same as the interference pattern which is caused by two or more waves interacting?

 

[rede96]

Unless and until you apply the wave-function evolution and probability amplitudes you do not have QM; and you do not have a quantitative description of nature.

At the risk of being pedantic, as I understand it the wave function only describes the probability of finding the electron at a certain place and time in space when measured. It doesn't really describe the true nature of the electron. Would you say that is true?

We all know that. But, we need a theory to explain why that is.

Have there been any theories put forward?

 

[PeroK]

At the risk of being pedantic, as I understand it the wave function only describes the probability of finding the electron at a certain place and time in space when measured. It doesn't really describe the true nature of the electron. Would you say that is true?

No. In physics there is no "true nature". That is a metaphysical question. The charge, mass and spin of the electron are fixed (by the standard model of particle physics); its dynamic properties are defined by its wavefunction. In physics that is all you get. The electron has no immortal soul or true nature.

Have there been any theories put forward?

Quantum Mechanics! And very successful it's been.

 

[Nugatory]

I would have thought when we shoot an electron at the screen, there are only two possibilities? It either gets absorbed by the barrier or it is detected. So be default if the only obvious conclusion is that it was not absorbed by the barrier doesn't that imply it went through the slits?

Those are the only two possibilities, yes. But that’s not enough to support the implication that it went through the slits; we need an additional assumption, namely that an electron emitted at point A and detected at point B must have gone through every point on a path between A and B. That assumption is so fundamental to our common sense notion of how physical things get from one place to another that we seldom notice it - but it’s still an assumption, and applying it to quantum particles is never necessary, seldom helpful, and often misleading.

Isn't that diffraction pattern caused by the 'wave' bending around a slit or opening and not the same as the interference pattern which is caused by two or more waves interacting?

Google for “single slit diffraction pattern” to find images of the pattern formed on the screen. This pattern is caused by interference between the waves originating at one part of a single slit and another instead of between the waves originating at different slits, but it’s the same basic phenomenon: we add the amplitudes of the waves arriving from all open points in the barrier, and they interfere constructively in some areas and destructively in others.

At the risk of being pedantic, as I understand it the wave function only describes the probability of finding the electron at a certain place and time in space when measured. It doesn't really describe the true nature of the electron.

As far as the theory of quantum mechanics is concerned, that wave function is the true nature of the electron. The theory has nothing more to say about electrons, and we have observed nothing about electrons that the theory hasn’t said. There might be some deeper theory that tells us something about electron behavior that quantum mechanics hasn’t, but so far no one has come up with such a theory. Unless and until someone does, there’s no reason to think that there’s any “true nature of the electron” beyond what quantum mechanics offers.

 

[rede96]

Those are the only two possibilities, yes. But that’s not enough to support the implication that it went through the slits; we need an additional assumption, namely that an electron emitted at point A and detected at point B must have gone through every point on a path between A and B. That assumption is so fundamental to our common sense notion of how physical things get from one place to another that we seldom notice it - but it’s still an assumption, and applying it to quantum particles is never necessary, seldom helpful, and often misleading.

Yes but that’s simply because of the random nature of a particle that we can’t calculate every point between A and B. And as far as I am aware it doesn’t rule out that it went through other various points between A and B does it?

Google for “single slit diffraction pattern” to find images of the pattern formed on the screen. This pattern is caused by interference between the waves originating at one part of a single slit and another instead of between the waves originating at different slits, but it’s the same basic phenomenon: we add the amplitudes of the waves arriving from all open points in the barrier, and they interfere constructively in some areas and destructively in others.

Ah ok, interesting. Didn’t know that, thanks. However my point was more that the pattern is unique to having two slits open. (assuming other elements of the set up of the experiment are not changed.)

So what ever the electron ‘does’ if I make a change to the slits the pattern changes. So the slits effect the outcome. So it seems to make sense that the slits interact with the electrons in some way that we don’t fully understand. It can’t be otherwise can it?

As far as the theory of quantum mechanics is concerned, that wave function is the true nature of the electron. The theory has nothing more to say about electrons, and we have observed nothing about electrons that the theory hasn’t said. There might be some deeper theory that tells us something about electron behavior that quantum mechanics hasn’t, but so far no one has come up with such a theory. Unless and until someone does, there’s no reason to think that there’s any “true nature of the electron” beyond what quantum mechanics offers.

Well I can’t argue with that. But as you’ve said there are things we don’t fully understand and that there aren’t theories for. So guess I was just touching on some of those I guess.

 

[BvU]

Yes but that’s simply because of the random nature of a particle that we can’t calculate every point between A and B. And as far as I am aware it doesn’t rule out that it went through other various points between A and B does it?

You are missing the essence completely. Feynman can not explain it to you, we apparently can't either. Read @Nugatory 's posts with a more open mind instead of insisting on marble bridge behaviour.

So what ever the electron ‘does’ if I make a change to the slits the pattern changes. So the slits effect the outcome. So it seems to make sense that the slits interact with the electrons in some way that we don’t fully understand. It can’t be otherwise can it?

We fully understand the slits to block 100% outside the openings and to pass 100% within. Nothing more, nothing less. Repeat: Nothing more, nothing less.

Well I can’t argue with that. But as you’ve said there are things we don’t fully understand and that there aren’t theories for. So guess I was just touching on some of those I guess.

You spy a microscopic opening and want to press a train through. No, this setup / experiment is fully, completely and utterly understood and can be calculated to any desirable precision. Yes, there are things we don't understand, but this doesn't even come near.

$\$

 

[PeroK]

But as you’ve said there are things we don’t fully understand and that there aren’t theories for. So guess I was just touching on some of those I guess.

Sorry, this is nonsense. You've asked basic questions that have been answered. I'm not sure why you think you're pushing the boundaries of human knowldege here.

 

[rede96]

You are missing the essence completely. Feynman can not explain it to you, we apparently can't either. Read @Nugatory 's posts with a more open mind instead of insisting on marble bridge behaviour.

Well if all one had to do to understand QM was watch a Feynman lecture and make a few posts on PF we’d all be experts in no time. So rather than be critical of my lack of understanding maybe you could try and help by detailing specifically just what about my reply (I’ve reposted below)I’m missing.

Yes but that’s simply because of the random nature of a particle that we can’t calculate every point between A and B. And as far as I am aware it doesn’t rule out that it went through other various points between A and B does it?

We fully understand the slits to block 100% outside the openings and to pass 100% within. Nothing more, nothing less. Repeat: Nothing more, nothing less.

Not sure what you mean by that?

You spy a microscopic opening and want to press a train through.

Again not sure what you mean by that? Can you clarify by detailing what assumptions I seem to have made in my posts that are incorrect please. It’ll help me understand where I’m going wrong.

 

[Nugatory]

Yes but that’s simply because of the random nature of a particle that we can’t calculate every point between A and B. And as far as I am aware it doesn’t rule out that it went through other various points between A and B does it?

What "other points"? I said "a path", not some particular path. As far as the theory of quantum mechanics is concerned, the particle was never at any point anywhere in the region of space between A and B.

You are right that we haven't ruled out the possibility that it was somewhere in that region at some time between the emission and the detection events. But no one is trying to rule that possibility out, we're saying that the two facts we have (emitted at A, detected at B) do not show the particle was anywhere in the space in between. To conclude that we need an additional assumption, namely that a particle can't get from A to B without having sometime been somewhere in between. And - to repeat myself - that assumption is never necessary, seldom helpful, and often misleading. You are making it and it is misleading you.

However my point was more that the pattern is unique to having two slits open. (assuming other elements of the set up of the experiment are not changed.)

It's unique only in the trivial sense that if we know the configuration of the openings in the barrier we can calculate the probability of an electron being detected at any point on the screen - so different numbers of openings of different shapes produce different patterns.

So what ever the electron ‘does’ if I make a change to the slits the pattern changes. So the slits effect the outcome. So it seems to make sense that the slits interact with the electrons in some way that we don’t fully understand. It can’t be otherwise can it?

Yes, the configuration of the slits affect the outcome. But we can't get from there to "the slits interact with the electrons in some way" without some theory of what that interaction might be. Unless and until we have such a candidate theory, we're left with: the conjecture that such a theory might exist; and the fact that given the configuration of the barrier we can calculate the probability of an electron being detected at any given point on the screen.

 

[rede96]

As far as the theory of quantum mechanics is concerned, the particle was never at any point anywhere in the region of space between A and B.

Ah ok, I see what you were getting at. Is that what is meant when we say the electron is in a superposition?

It's unique only in the trivial sense that if we know the configuration of the openings in the barrier we can calculate the probability of an electron being detected at any point on the screen

May I ask when calculating the probability of a single electron being detected are both slits included in the calculation?

Yes, the configuration of the slits affect the outcome. But we can't get from there to "the slits interact with the electrons in some way" without some theory of what that interaction might be. Unless and until we have such a candidate theory, we're left with: the conjecture that such a theory might exist; and the fact that given the configuration of the barrier we can calculate the probability of an electron being detected at any given point on the screen.

Not sure I fully understand this part, maybe it’s just my use of words or classical thinking. Can’t help but think if the slits effect the outcome then there is something going on with the electron and the slits, even if we don’t need to know what that is to calculate the probability of an electron being detected at a certain point on the screen. Not important for QM of course but can’t help but wonder what it could be. :)

 

[PeterDonis]

if the slits effect the outcome then there is something going on with the electron and the slits

If you want to look at models that investigate that, you will need, as has already been suggested, to look at models of single-slit electron diffraction. (IIRC, the original electron diffraction experiment was actually done with a circular pinhole, not a slit, but the basic idea is the same.) I believe there are treatments of that that actually try to model interactions between the electron and the atoms at the edge of the slit, in order to derive predictions for what the resulting diffraction pattern should look like.

 

[Nugatory]

Is that what is meant when we say the electron is in a superposition?

No. Superposition refers to a mathematical property of the wave function, namely that any wave function can be written as the sum of other wave functions.

May I ask when calculating the probability of a single electron being detected are both slits included in the calculation?

From #23 of this thread: “we add the amplitudes of the waves arriving from all open points in the barrier”. That means “all open points” whether these points are all in one slit or in multiple slits.

You may have been confused by the way that elementary and non-serious explanations treat the double-slit case as something somehow fundamentally different from the single slit case. It’s not, it’s just the easiest example of interference. What’s going on here is that if two openings are small compared with the wavelength of the incident beam, and if they are separated by a distance that is large compared with that wavelength but are still close enough together to both be illuminated by the beam... then to very good approximation we can say that there are just two points and two amplitudes, one from each point, to add - @PeroK showed you that calculation in post #10.
But if these conditions do not hold, then the calculation requires adding the amplitudes from each point; there are an infinite number of points in any non-zero area no matter how small so we end up having to do a seriously non-trivial integration across the area of all the openings (one slit, two slits, twenty-three slits, the holes left by a volley of machine-gun fire, ...) in the barrier.
No pop-sci treatment is going to inflict this integral on the audience when a “just add two things” example is an option, so we miss out on the general principle. The introductory QM course for an undergraduate physics major is a different matter; we don’t start that until after we’ve spent an entire semester with something like this so we that we can do the general calculation for any configuration of the barrier.

maybe it’s just my use of words or classical thinking. Can’t help but think if the slits effect the outcome then there is something going on with the electron and the slits, even if we don’t need to know what that is to calculate the probability of an electron being detected at a certain point on the screen. Not important for QM of course but can’t help but wonder what it could be. :)

That’s classical thinking. We’re using the classical idea that a particle can’t be at A and later at B without having been somewhere in between; without that assumption there’s no reason to think that the particle was ever anywhere near the barrier and slits.

 

[DennisN]

Isn't that diffraction pattern caused by the 'wave' bending around a slit or opening and not the same as the interference pattern which is caused by two or more waves interacting?

Google for “single slit diffraction pattern” to find images of the pattern formed on the screen.

Hi, @rede96 , I posted such an image in this post.

 

[BvU]

Well if all one had to do to understand QM was watch a Feynman lecture and make a few posts on PF we’d all be experts in no time. So rather than be critical of my lack of understanding maybe you could try and help by detailing specifically just what about my reply (I’ve reposted below)I’m missing.
...
Not sure what you mean by that?
...
Again not sure what you mean by that? Can you clarify by detailing what assumptions I seem to have made in my posts that are incorrect please. It’ll help me understand where I’m going wrong.

My apologies - the post isn't really helpful and inspired more by exasperation and despondency than by ideas on how to get you on the right path.

The difficulty here is that you want to know answers to questions that shouldn't be asked (such as through which slit what fraction passed, the 'role' of the slit(s) and similar issues). Easy to say, even for non-experts like me. But there is admittedly a very difficult transition from the marble bridge to $\lambda$ scale phenomena, and human curiosity is naturally reluctant wrt the required changes in perception.

The frequent reference to Feynman is because he's so good at helping to bridge the gap. He gives a layman lecture on photon behaviour and then says "they're particles". Another often quoted phrase is "shut up and calculate".

You've been given quite a bit of very good help in this thread, especially from @Nugatory , whose patience I really admire, and I suggest you re-read the stuff and the links and references to get the right taste for further questions !

Perhaps we can find some relief in the parallel between QM and thermodynamics: If you think you understand it, you don't By the way: single slit, double slit -- it's all one and the same thing: wave behaviour

$\$

 

[PeroK]

By the way: single slit, double slit -- it's all one and the same thing: wave behaviour

You mean "particle behaviour"?