Double slit experiment in 3 dimensions?

[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?

 

[DrChinese]

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?

Yes. The wall, the screen, whatever you use to record where the particles strike.

 

[mike1000]

Yes. The wall, the screen, whatever you use to record where the particles strike.

Yes, but you are talking the two slit experiment. The electron is forced to go through those two slits. There are only two possible paths. But in 3D experiment the are many more possible paths. There are at least 8 more possible paths the electron could take. And if you take into account possible diffraction patterns there are many many possible new paths the electron could take.

 

[ZapperZ]

Yes, but you are talking the two slit experiment. The electron is forced to go through those two slits. There are only two possible paths. But in 3D experiment the are many more possible paths. There are at least 8 more possible paths the electron could take.

Why not just use a diffraction grating? There can be THOUSANDS of possible paths!

Zz.

 

[DrChinese]

Yes, but you are talking the two slit experiment. The electron is forced to go through those two slits. There are only two possible paths. But in 3D experiment the are many more possible paths. There are at least 8 more possible paths the electron could take.

That completely ignores what I and everyone are telling you. There are a near infinite number of paths an electron can take going from here to there. That includes going to the moon. And yet the one observed is quite nearly a straight line, and is quite nearly the shortest path. If you want to know more about this, you should check out Feynman (he is most closely associated with this) or similar.

Please note that this is why your experiment makes no sense to anyone commenting here. The extra slits make no significant contribution to the outcome.

 

[DrChinese]

PS look up: path integral.

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

 

[mike1000]

That completely ignores what I and everyone are telling you. There are a near infinite number of paths an electron can take going from here to there. That includes going to the moon. And yet the one observed is quite nearly a straight line, and is quite nearly the shortest path. If you want to know more about this, you should check out Feynman (he is most closely associated with this) or similar.

Please note that this is why your experiment makes no sense to anyone commenting here. The extra slits make no significant contribution to the outcome.

There is not an infinite number of paths and most definitely, the moon is not one of them.

If there is 1 slit it can go through 1 slit. If there are two slits it can go through 2 slits. If there are 8 slits can possibly go through 8 slits. If there are 10 slits it can possibly go through 10 slits. The peculiar thing about this experiment is how we arrange the slits. That is the whole point of the experiment is to limit the number of possible paths.

 

[mfb]

The electron gun can be seen as very wide single-slit: The electrons will all be within a narrow beam, with negligible probability to find them elsewhere. If the other slits are outside the beam, they don't matter.

The intensity of the electron beam does not matter, you can have a single electron at a time or many, the interference pattern will look exactly the same.

There is not an infinite number of paths and most definitely, the moon is not one of them.

It is, it is just completely irrelevant.

 

[mike1000]

You do realize that the electron does go through both slits in the double slit experiment?

 

[StevieTNZ]

You do realize that the electron does go through both slits in the double slit experiment?

Read "The Grand Design" by Stephen Hawking and Leonard Mlodinow.

 

[DrChinese]

There is not an infinite number of paths and most definitely, the moon is not one of them.

If there is 1 slit it can go through 1 slit. If there are two slits it can go through 2 slits. If there are 8 slits can possibly go through 8 slits. If there are 10 slits it can possibly go through 10 slits. The peculiar thing about this experiment is how we arrange the slits. That is the whole point of the experiment is to limit the number of possible paths.

It is true that you are limiting the paths, but not in the way you imagine (such as to 2 or 4 or 8). For lack of a better analogy (simplistic as it is), it is as if you have 1/1000 of an infinite number of paths (yes I know that sounds ridiculous - it's my analogy). Still, it is near* infinite, each contributing a small amount to the final result. Which is where the target slit pair comes into play. No one can say through which slit - or both - the particle travels. That is a matter of interpretation.

*Some people say infinite, some say there is a cut-off. That is a subject outside the scope of this thread.

 

[mike1000]

It is true that you are limiting the paths, but not in the way you imagine (such as to 2 or 4 or 8). For lack of a better analogy (simplistic as it is), it is as if you have 1/1000 of an infinite number of paths (yes I know that sounds ridiculous - it's my analogy). Still, it is near* infinite, each contributing a small amount to the final result. Which is where the target slit pair comes into play. No one can say through which slit - or both - the particle travels. That is a matter of interpretation.

*Some people say infinite, some say there is a cut-off. That is a subject outside the scope of this thread.

I know there are many more possible paths than just, say 8 if there are 8 slits. I know this because once the wave interferes with itself on the back side of the slits you have the interference pattern and each path that the interference wave can take is also a possible path the electron can take. The number of possible paths is GREATLY increased on the backside of the slits.

I am reading the link on "Path Integral". That theory is designed to replace the wave idea isn't it? With that theory we do not need a wave theory for the electron, it can always be a particle? Is that what you have been trying to tell me all along?

 

[DrChinese]

The idea of multiple paths for particle transport can be easily seen in a reference such as below:

http://lesswrong.com/lw/pk/feynman_paths/

A mirror does NOT reflect solely from a single point in the middle. Many - a near infinite - number of paths contribute to the reflection. That it is as I describe can be easily demonstrated by marking a mirror with etches in precise spots away from that middle. This is often done in such a way is to INCREASE the intensity of the light observed, in contradiction to the more classical expectation (that it would have no effect).

 

[mike1000]

The idea of multiple paths for particle transport can be easily seen in a reference such as below:

http://lesswrong.com/lw/pk/feynman_paths/

A mirror does NOT reflect solely from a single point in the middle. Many - a near infinite - number of paths contribute to the reflection. That it is as I describe can be easily demonstrated by marking a mirror with etches in precise spots away from that middle. This is often done in such a way is to INCREASE the intensity of the light observed, in contradiction to the more classical expectation.

I am reading the link on "Path Integral". That theory is designed to replace the wave idea isn't it? With that theory we do not need a wave theory for the electron, it can always be a particle? Is that what you have been trying to tell me all along?

 

[DrChinese]

I am reading the link on "Path Integral". That theory is designed to replace the wave idea isn't it? With that theory we do not need a wave theory for the electron, it can always be a particle? Is that what you have been trying to tell me all along?

Yes.

Quantum particles have properties that are often called "strange". Most people have dropped the use of the word "wave" but even the word "particle" can be misleading at times.

 

[Strilanc]

If you set up a situation where a sequence of incoming electrons is spread out enough that it could go through five different double-slits that each point in different directions, then what you will find is that:

- Each electron will hit at most one of the screens. (It would be exactly one but some electrons will hit the slits instead of passing through, some will miss, etc.)
- The chance of an electron going to screen A instead of screen B depends on how evenly you spread out the electron's wave function. Presumably you want to arrange things so all the screens are equally likely, but you don't have to.
- Over time, each screen will individually build up an interference pattern in the distribution of electron hits.

I don't think this would be a very interesting experiment to do. From a mathematical perspective, it's a trivial variant of the normal double-slit experiment. Even from a philosophical perspective, it doesn't seem to say anything that other experiments haven't said better. When you branch into multiple experiments, you can model the taking of each branch as a mere probability. You have to merge the branches back together to see any quantum effects.

 

[mike1000]

Yes.

Quantum particles have properties that are often called "strange". Most people have dropped the use of the word "wave" but even the word "particle" can be misleading at times.

Well guess what? It has taken a while but it has been worth it for me. Thanks for hanging in there.

 

[DrChinese]

Well guess what? It has taken a while but it has been worth it for me. Thanks for hanging in there.

As I said earlier:

 

[mike1000]

As I said earlier:

I do appreciate the time you have taken. I am trying to figure out how the "Path Integral" theory handles the diffraction pattern that we see for the electon in the double slit experiment. While googling I came upon this internet article. I think it is a very good article and I wonder if you would read it (at your leisure) and then I can ask you questions about it? I think this article is telling us that the electron does have wave character. Here is the link
https://readingfeynman.org/tag/electron-diffraction/

P.S. Something I did not realize was that the electron size is estimated at 2.8 fentometers (10^-15 meters). The size of the proton is 1.7 fentometers. So the proton is smaller than the electron yet the protons mass is 1800 times greater than that of the electron! And according to the author, because of the protons mass it does not "wiggle" as much as the electron (de Broglie's formula)

 

[DrChinese]

Something I did not realize was that the electron size is estimated at 2.8 fentometers (10^-15 meters). The size of the proton is 1.7 fentometers. So the proton is smaller than the electron yet the protons mass is 1800 times greater than that of the electron! And according to the author, because of the protons mass it does not "wiggle" as much as the electron (de Broglie's formula)

I think they said it in the movie "Men In Black": Size doesn't matter.

Electrons are modeled as point particles (no size) but when bound as part of an atom (or when charge is a factor), their apparent size is much larger.

Protons and neutrons are composed of 3 quarks in very close proximity (so they are not points). But their small size belies the energy/mass within.

 

[Karolus]

I do not think that the wave particle duality is surpassed, in all the books we speak sometimes of the electron as a wave sometimes as a particle. This is a little hard to swallow, but even feynman, who was the inventor of the theory of path integrals, does not deny the dual nature. For example, the electron is seen as a real wave that propagates to 'inside of the crystalline solid with periodicity of the lattice spacing (Bloch theorem) In any case, if indeed it has been established that the electron is behaves as a particle, the interference patterns in the double slit, are identical to those produced by the electromagnetic waves (classically viewed as waves) only for the case? Already but EM waves are also particles, photons, but the same thing happens with the waves of the sea water, for example. So even the waves of the sea water are particles that follow multiple virtual paths?

 

[Karolus]

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

strange, the first chapter of griffiths is titled: the wave function. Griffiths then adopts the principle that electrons are waves? Or this is just an introduction and then prove that they are only particles? Or perhaps use the term wave because so everyone uses?

 

[mfb]

Something I did not realize was that the electron size is estimated at 2.8 fentometers

If they have a size at all, they are certainly much smaller than that (more than a factor 1000 smaller), otherwise high-energy physics would look completely different.

I do not think that the wave particle duality is surpassed, in all the books we speak sometimes of the electron as a wave sometimes as a particle.

Based on quantum mechanics, we know that those models can be reasonably accurate in some cases. That doesn't mean there would be an actual duality. If you install solar panels, you can model the sun as orbiting the Earth. That is perfectly fine for the solar panels - just keep in mind that this model doesn't work elsewhere (e.g. in spaceflight).

 

[Karolus]

Based on quantum mechanics, we know that those models can be reasonably accurate in some cases. That doesn't mean there would be an actual duality. If you install solar panels, you can model the sun as orbiting the Earth. That is perfectly fine for the solar panels - just keep in mind that this model doesn't work elsewhere (e.g. in spaceflight).

I understand what you mean, but not in quantum mechanics. To tell the truth is quite the opposite. Certainly in the solar panels, it is convenient to put in the coordinate system with the Earth fixed. But then there are many other books that explain how things are different. Instead in MQ the wave-particle duality pervades all texts, and no one can evade the issue. This is to account for a wide range of phenomena, and not only limited to a specific case.

 

[bhobba]

How do you calculate the total momentum for a wave?

Just to answer your question, and not entering into the threads main thrust (others I think are doing a good job of that - my view is it will not show any novel features - but I am not an experimental type) you need to investigate Noether's Theorem:
http://www.physics.usu.edu/torre/6010_Fall_2010/Lectures/05.pdf

Noether's theorem says not only must it be conserved for systems with spatial symmetry, but how its actually defined - for anything - waves, classical fields, quantum systems, quantum fields, particles; anything.

If you want to pursue this striking fact further see:
https://www.amazon.com/dp/3319192000/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

Instead in MQ the wave-particle duality pervades all texts, and no one can evade the issue. This is to account for a wide range of phenomena, and not only limited to a specific case.

Untrue, as has been explained in many threads on this forum.

You have been posting for a while, so I would be surprised if you had not seen at least one such thread. But just in case you havent, wave particle duality is left over from the early days of QM. It was done away with when Dirac came up with his transformation theory in 1926 which basically goes by the name QM today.

Here is the history:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

The wave particle duality lead to De-Broglie, then Schrödinger, then a dead end - it was realized it was wrong eg Schrödinger's waves were complex waves of probability in an infinite dimensional Hilbert space - nothing like the usual conception of a wave. Schrödinger was so disgusted when this emerged he regretted having anything to do with it. It' now consigned to the dustbin of history and only talked about in popularization's and beginner texts because of the semi-historical approach they take.

Its a beginner concept used as part of the progress towards more advanced QM - OK in a beginner level thread where it would be merely pointed out as you learn more you will understand its simply a way-station in your QM progress - but not correct for an I level thread.

Thanks
Bill