Double slit experiment in 3 dimensions?

[mike1000]

Has anyone performed the double slit experiment in three dimensions? By this I mean, having double slits and a detection screen on three sides? This would imply there are 6 slits and 3 detection screens. What would we observe? Would we see the electron exhibiting wave like behavior (ie interference in 3 directions) and would the particle behavior at the detecting screen show interference patterns on all three detecting screens?

 

[DrClaude]

The way you describe it, this is simply three double-slit experiments running simultaneously in three different directions. I don't see why this would produce any unexpected result.

By the way, there is no such thing as wave-like vs particle-like behavior. the concept of wave-particle duality has been abandoned long ago.

 

[mike1000]

Well, no I do not mean 3 double slit experiments running simultaneously. Only 1 electron is fired, not 3 electrons. There would be 3 double slits and 3 detection screens but only one electron gun. One double slit and detection screen would be in the conventional location. Another double slit and detection screen would be oriented to detect any transverse wave motion (say to the particles right) and another double slit and detection screen will be place to detect any transverse wave motion above or below the particles path.

I think you can think of it as firing an electron into a cube. On 5 sides of the cube there are double slits and detection screens. The electron gun fires an electron in the direction of the 6th side which is open to allow the electron to pass into the cube.

I do not think the concept of wave particle duality has been abandoned. If so can you please tell me what has replaced it? Are you saying that DeBroglie's equation has been discredited?

 

[ZapperZ]

Well, no I do not mean 3 double slit experiments running simultaneously. Only 1 electron is fired, not 3 electrons. There would be 3 double slits and 3 detection screens but only one electron gun. One double slit and detection screen would be in the conventional location. Another double slit and detection screen would be oriented to detect any transverse wave motion (say to the particles right) and another double slit and detection screen will be place to detect any transverse wave motion above or below the particles path.

All this means is that you are using something that had gone through an interference and then having it pass through another slit. The orientation here is irrelevant.

https://www.physicsforums.com/threads/double-slit-experiment-wave-collapse.902726/#post-5683981

I do not think the concept of wave particle duality has been abandoned. If so can you please tell me what has replaced it? Are you saying that DeBroglie's equation has been discredited?

You misunderstood. Read one of your FAQ's here:

https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

Zz.

 

[mike1000]

No, I am not saying to place the double slits AFTER the electron has already passed through a set of slits. Think of firing an electron into box that is open on one side. All the other sides of the box have double slits and beyond each wall of the box is a detection screen. There would be 5 sets of double slits and 5 detection screens.

I read the article you linked to. You are talking about light. I am talking about Debroglies equation, which embodies the concept of wave and particle. His equation implies that a wave has momentum. Has DeBroglies' equation found to be incorrect?

And while I'm on it, what does it mean for a wave to have momentum?

 

[ZapperZ]

No, I am not saying to place the double slits AFTER the electron has already passed through a set of slits. Think of firing an electron into box that is open on one side. All the other sides of the box have double slits and beyond each wall of the box is a detection screen. There would be 5 sets of double slits and 5 detection screens.

But unless you are asserting that the electron goes through ALL of the different double slits ALL AT ONCE, then it will will go through one double slit and then the next, etc... So why is this not the same as what I had described? And why is your setup interesting or tells us anything new?

I've done interference of electrons with not one, but MANY "slits". When I shoot low-energy electrons at a crystal surface, I get a 2D pattern of dots (LEED). I can send these electrons into as many other interference experiments as I want, in whatever direction that they go off. What will that tell me?

Zz.

 

[mike1000]

It is not what you described. You implied that after the electron goes through one set of slits then then that interference wave passes through a successive slit. That is not what I am describing.

Also, I am not asserting that the electron goes through all of the double slits at the same time but I think the Schrodinger Equation may create a wave function that tells us that is what may happen.

Also I read the article you linked to. That is talking about light. I am not talking about light. I am talking about DeBroglies equation. DeBroglies equation assigns momentum to waves. What does it mean when one says that a wave has momentum? Has DeBroglie's equation been discredited?

 

[ZapperZ]

It is not what you described. You implied that after the electron goes through one set of slits then then that interference wave passes through a successive slit. That is not what I am describing.

Also, I am not asserting that the electron goes through all of the double slits at the same time but I think the Schrodinger Equation may create a wave function that tells us that is what may happen.

Then maybe you should draw out your setup, and then explains what you are proposing. Otherwise, after rereading what you wrote earlier, I see no difference with what I described.

Also I read the article you linked to. That is talking about light. I am not talking about light. I am talking about DeBroglies equation. DeBroglies equation assigns momentum to waves. What does it mean when one says that a wave has momentum? Has DeBroglie's equation been discredited?

Yeah? deBroglie proposed the existence of "matter waves". Both photons and electrons practically the identical properties. Look at, for example, single-photon interference versus single-electron interference patterns (G. Matteucci et al., Eur. J. Phys. v.34, p.511 (2013)). They are the same! As I've stated in the link to another post, it isn't the object, it is the SITUATION of the superposition of paths that is creating this effect. It is why photons, electrons, neutrons, protons, buckyball, etc... can show the same phenomena!

Zz.

 

[mike1000]

I do not think it is that hard to understand what I am saying. It is actually a quite natural question to ask after one learns about the one dimensional version of the double slit experiment. Don't you want to know that the wave character looks like in 3 dimensions?

You did not answer my question, what does it mean when we say that a wave has momentum?

 

[weirdoguy]

I do not think the concept of wave particle duality has been abandoned. If so can you please tell me what has replaced it?

Quantum mechanics replaced it. There is no wave-particle duality in QM.

 

[ZapperZ]

I do not think it is that hard to understand what I am saying. It is actually a quite natural question to ask after one learns about the one dimensional version of the double slit experiment. Don't you want to know that the wave character looks like in 3 dimensions?

If you have taken basic QM classes, we solve the Schrodinger equation in 3D frequently (look at the hydrogen atom problem). So yes, I am quite aware of MANY situations that are in 3D.

You did not answer my question, what does it mean when we say that a wave has momentum?

It means that it has the ability to "push" on something. What part of p=hk did you not understand?

Zz.

 

[PeroK]

You did not answer my question, what does it mean when we say that a wave has momentum?

If you are paddling in the sea near the shore, and a water wave hits you its momentum could knock you backwards. Why wouldn't a wave have momentum?

 

[DrChinese]

I do not think it is that hard to understand what I am saying. It is actually a quite natural question to ask after one learns about the one dimensional version of the double slit experiment. Don't you want to know that the wave character looks like in 3 dimensions?

You did not answer my question, what does it mean when we say that a wave has momentum?

As you described your 5 sided contraption, there is nothing much of interest to talk about. There would be interference patterns at all slit pairs that are exposed to the source emitter.

As to momentum: when particle momentum is well defined, position is not - and vice versa. Such a particle is not localized in the traditional sense. The trade-off between position and momentum definition is variable - it is not limited to all or nothing. What would you call something in between a wave and a particle? In quantum discussions, the term "particle" is usually used as the generic. Or you could also say electron or photon and be more specific. All particles have momentum, at all times, however it value need not be well defined at all times. Generally it will be conserved.

 

[mike1000]

As you described your 5 sided contraption, there is nothing much of interest to talk about. There would be interference patterns at all slit pairs that are exposed to the source emitter.

And does that mean we will observe electron hits on all 5 detection screens? But we don't know that is what we will see. That is what we think we will observe. That is why we need to run the experiment.

Momentum: when particle momentum is well defined, position is not - and vice versa. Such a particle is not localized in the traditional sense. The trade-off between position and momentum definition is variable - it is not limited to all or nothing. What would you call something in between a wave and a particle? In quantum discussions, the term "particle" is usually used as the generic. Or you could also say electron or photon and be more specific. All particles have momentum, at all times, however it value need not be well defined at all times. Generally it will be conserved.

I know this but that is not a deep enough response for me. What does it mean for a wave to have momentum? Does it have any meaning at all?

 

[ZapperZ]

We don't know that is what we will see. That is what we think we will observe. That is why we need to run the experiment.

Who is this "we" that you think should run your experiment? And do you think this is how one make a proposal to run such an experiment, when many of us here do not see the value of it?

One of the things we all learn when we apply for a research grant is to show not only that something is interesting, but that it is also IMPORTANT. Those two are not always mutually inclusive. Based on your description, I see this satisfying neither criteria.

I know this but that is not a deep enough response for me. What does it mean for a wave to have momentum? Does it have any meaning at all?

But you know the "meaning" of a ball having a momentum?

Zz.

 

[mike1000]

Quite frankly, I find your reaction to this a little harsh. For you to say you find nothing interesting in running an experiment like this I do not find credible. It is obviously of interest.

Yes I do know the meaning of a ball having momentum. Momentum is a vector. How do I apply a vector to a wave?

 

[PeroK]

I know this but that is not a deep enough response for me. What does it mean for a wave to have momentum? Does it have any meaning at all?

One answer to your question lies in Special Relativity, and specifically the energy-momentum four-vector. In SR, the energy of a particle is the component of its momentum in the time dimension. This ties together energy and momentum, where classical physics does not. An electromagnetic wave also has both energy and momentum, as they are in fact different components of the same vector.

A wave is clearly a vector as it has direction of motion, if nothing else.

 

[weirdoguy]

It is obviously of interest.

Whose interest, and whose opinion you find credible?

 

[DrChinese]

1. And does that mean we will observe electron hits on all 5 detection screens? But we don't know that is what we will see. That is what we think we will observe. That is why we need to run the experiment.

2. I know this but that is not a deep enough response for me. What does it mean for a wave to have momentum? Does it have any meaning at all?

1. It would be unreasonable for others to run experiments that have no theoretical point in question - just to satisfy your curiosity. You are of course welcome to run any experiment you like. You won't find much interest, however, for experiments that are completely in accord with theory and have little or no unique twist. Generally, scientists don't run experiments "just to see what happens". They have something specific in mind.2. Waves have momentum, which is defined as mass x velocity.

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

To get a "deeper" response, you will need to do more self-study.

NOTE: Rather than worry whether anyone is being harsh, you might pause to note that a number of experienced folks (including 2 mentors!) have taken time to help you.

 

[mike1000]

One answer to your question lies in Special Relativity, and specifically the energy-momentum four-vector. In SR, the energy of a particle is the component of its momentum in the time dimension. This ties together energy and momentum, where classical physics does not. An electromagnetic wave also has both energy and momentum, as they are in fact different components of the same vector.

A wave is clearly a vector as it has direction of motion, if nothing else.

How do you calculate the total momentum for a wave? And if I did calculate the total momentum for the wave would I find that it was equal to the total momentum of the electron when it strikes the screen and all the mass is localized instead of spread out in a wave?

And where is the center of mass for the wave?

 

[mike1000]

1.
NOTE: Rather than worry whether anyone is being harsh, you might pause to note that a number of experienced folks (including 2 mentors!) have taken time to help you.

I don't think they took the time to help me, it felt more like an attack.

I am going to stick to my opinion that I find it hard to believe that no one thinks that would be an important experiment to perform.

 

[mfb]

If you fire an electron into the cube, it will either hit the back wall (most likely) or go through the double-slit at that wall, and produce an interference pattern behind that.
The other walls don't matter because we don't shoot the electron at them.

To have those walls matter, you cannot shoot an electron in one direction. You could try to carefully place an electron in the center of the cube at nearly zero expected momentum. In that case you would detect it at one of the screens at random. With many of those electrons, you get 5 (or 6 if you close the cube) interference patterns.

I'm quite sure exactly this experiment has not been performed yet, but it is not necessary. To know that objects fall down (in vacuum), you don't have to literally take every object on Earth and test it. Your experiment would be as interesting as "we should go to this specific location in this town, pick up the third rock from the left, drop it and see if it will fall down". There is no need to do it. Similar experiments have been performed. As an example, you can take a double slit and then put a barrier behind it, leading to two single-slit experiments in one. You'll see two single-slit interference patterns. This is an experiment so easy you can do it at home.

 

[DrChinese]

I don't think they took the time to help me, it felt more like an attack.

I am going to stick to my opinion ...

Sorry you feel like you are being attacked. On the other hand, I can't say I'm entirely surprised by the second point.

 

[mike1000]

If you fire an electron into the cube, it will either hit the back wall (most likely) or go through the double-slit at that wall, and produce an interference pattern behind that.
The other walls don't matter because we don't shoot the electron at them.
.

Your response makes it clear to me that I am not being clear enough on how to conduct this experiment.

The double slits are on the walls. Five of the walls have double slits. Beyond each wall there is a detection screen to capture an electron hit. The question becomes will we see electron hits on all 5 of the detection screens even though the electron was fired exclusively at only one of the walls? When the electron spreads out does it spread out in all directions or does it spread out only in the direction of its motion?

 

[mfb]

Your response makes it clear to me that I am not being clear enough on how to conduct this experiment.

No, I think you don't understand how an electron gun works. It produces a beam with a tiny spread. You'll find a few stray electrons here and there once in a while, but those don't really matter. If you make an electron gun that, for some weird reason, has a beam so large that it will cover all 5 slits (which is essentially the suggestion I made afterwards: carefully place an electron in the cube), you'll get interference pattern behind all 5 slits. Note that the incidence angle for 4 of the slit pairs is completely different, which will change the interference pattern.

 

[mike1000]

No, I think you don't understand how an electron gun works. It produces a beam with a tiny spread. You'll find a few stray electrons here and there once in a while, but those don't really matter. If you make an electron gun that, for some weird reason, has a beam so large that it will cover all 5 slits (which is essentially the suggestion I made afterwards: carefully place an electron in the cube), you'll get interference pattern behind all 5 slits. Note that the incidence angle for 4 of the slit pairs is completely different, which will change the interference pattern.

In the double slit experiment they fired one electron at a time. One electron at a time so the electrons cannot interfere with each other. Not an electron beam.

 

[DrChinese]

In the double slit experiment they fired one electron at a time. One electron at a time so the electrons cannot interfere with each other. Not an electron beam.

The electron beam is a collection of individual electrons that have no discernible relationship to one another... they don't interfere one with the other.

Technically, you could say an electron's possible paths involves a spread. Although as a practical matter, most paths cancel out and there is no electron ever found in a region where it isn't expected.

 

[PeroK]

How do you calculate the total momentum for a wave? And if I did calculate the total momentum for the wave would I find that it was equal to the total momentum of the electron when it strikes the screen and all the mass is localized instead of spread out in a wave?

And where is the center of mass for the wave?

As has been mentioned, modern QM tends to avoid the wave-particle duality, which is generally at the centre of popular science books and videos.

One of the most popular QM undergraduate textbooks (by Griffiths) only mentions the wave-particle duality in passing, as a historical footnote.

My answer to your question is, therefore, that an electron is not a wave.

 

[mike1000]

As I think about this ...

I bet the electron acts like

The electron beam is a collection of individual electrons that have no discernible relationship to one another... they don't interfere one with the other.

Technically, you could say an electron's possible paths involves a spread. Although as a practical matter, most paths cancel out and there is no electron ever found in a region where it isn't expected.

Can you fire an electron one at a time so that at any time only one electron could ever be in the box? Isn't that what they did in the double slit experiment, except they only had one set of slits?

 

[DrChinese]

Can you fire an electron one at a time so that at any time only one electron could ever be in the box? Isn't that what they did in the double slit experiment, except they only had one set of slits?

Sure. And as mentioned, that electron will move in a fairly straight line. So that only 1 of the slit pairs is the target and the others are essentially ignored. Or, you could excite an electron starting in the box so that all 5 slit pairs have an equal, but low, chance of being the target.

And in none of those situations would we expect any behavior worth studying further. So perhaps I should ask: what exactly would you expect differently than a typical interference pattern?

 

[mike1000]

Ok, let's fire the electron and aim it exclusively at one set of slits. You make the statement that the other sets of slits are ignored. I don't think you can make that statement because you do not know what the unlocalized electron looks like. That is what we want to find out, will those other slits be ignored or not. Why do you think that the electron will will not pass through all of the slits?

 

[ZapperZ]

Ok, let's fire the electron and aim it exclusively at one set of slits. You make the statement that the other set of slits are ignored. I don't think you can make that statement because you do not know what the unlocalized electron looks like. That is what we want to find out, will those other slits be ignored or not. Why do you think that the electron will will not pass through all of the slits?

This is rather odd. We CAN and DO control the trajectory of particle beams such as electrons. We do this all the time in particle accelerators. Otherwise, your old CRT tube won't work!

So yes, we can aim the electrons to be at a particular spot.

Zz.

 

[DrChinese]

Ok, let's fire the electron and aim it exclusively at one set of slits. You make the statement that the other sets of slits are ignored. I don't think you can make that statement because you do not know what the unlocalized electron looks like. That is what we want to find out, will those other slits be ignored or not. Why do you think that the electron will will not pass through all of the slits?

Well, the obvious explanation is that the pattern on the wall does not change (in any observable fashion) according to things away from the general path. On the other hand, you could also say it goes everywhere but those "weird" paths make no net contribution to the observed result.

 

[DrChinese]

And my point about the "weird" paths (i.e. not the straight-most line) is this: Yes, they can be (and have been) proven to exist. And yes, they can be proven to contribute nothing to the final results in the normal case.

 

[mike1000]

Well, the obvious explanation is that the pattern on the wall does not change (in any observable fashion) according to things away from the general path.

I do not understand what you are trying to say here. What wall? and what pattern? Do you mean the diffraction pattern observed on the detection screen behind the slits?