I Double slit experiment in 3 dimensions?

[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 Schrodinger, then a dead end - it was realized it was wrong eg Schrodinger's waves were complex waves of probability in an infinite dimensional Hilbert space - nothing like the usual conception of a wave. Schrodinger 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

 

[bhobba]

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

Dear oh dear.

In Feynman's sum over history approach, which is derivable from ordinary QM, that is exactly what there is.

Thanks
Bill

 

[bhobba]

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.

Really.

Tell me the page its talked about in the following standard text:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

As has been explained its an outdated idea confined to the dustbin of history and not part of more advanced modern treatments.

Here is the double slit without waves particle ideas:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Thanks
Bill

 

[mike1000]

Really.

Tell me the page its talked about in the following standard text:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

As has been explained its an outdated idea confined to the dustbin of history and not part of more advanced modern treatments.

Here is the double slit without waves particle ideas:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Thanks
Bill

Are you saying that the de Broglie equation is wrong?

 

[PeroK]

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?

It is important not to confuse the wave function with the particle itself. The wave function is a complex representation of the particle's state, which itself is an infinite dimensional vector.

 

[DrClaude]

Are you saying that the de Broglie equation is wrong?

Wrong is not the right word. The de Broglie wavelength appears nowhere in modern quantum mechanics. It is not needed, and honestly I don't how you would go about figuring out what it is from the Schrödinger equation.

Thats said, it still can be a useful heuristic to figure out the size of quantum effects. This is done for instance in statistical physics, where Bose-Einstein condensation is seen to appear when the interparticle distance is of the order of the thermal de Broglie wavelength (note that this is the thermal de Broglie wavelength, which differs from the one derived by de Broglie by a factor $\sqrt{\pi}$).

 

[Karolus]

Really.

Tell me the page its talked about in the following standard text:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

As has been explained its an outdated idea confined to the dustbin of history and not part of more advanced modern treatments.

Here is the double slit without waves particle ideas:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Thanks
Bill

I took a look at the Table of Contents of the book

Chapter 1
1.5 Probability Theory (Thing? Probability theory? still talking about probabilities in the "modern" quantum "physics? It is not an outdated concept?

Chapter 2
2.4 Probability Distribution (Again??)

Chapter4

4.2 The Wave equaqion and its interpretations (As? We still speak of the wave equation? But it is not an outdated concept, and now belonging to the physical junk Schrodinger?)

4.5 Conditions on Wave Function (Why? If the concept of wave is rubbish, because devote so much space?)

Chapter 9
9.1 An Example of Spin Measurement
9.2 A general Theorem of Measurement
9.4 Which Wave Function?
We still speak of old obsolete concepts such as "measures" and "wave function" ... BOH?

I have no way to judge the book, that really intrigues me and I tried to take it.
mine was only because it seems too drastic to liquidate the "old quantum theory" (which I have not clear what it refers to) as a physical junk, but without controversy, really, I'm just trying to understand something more,
Nevertheless I plan to read the pdf file.

As for the topic of the thread x Mike1000, you can assume an experiment with all the slices you want, but I do not think, as has already been said, that you get nothing more than the classic experiment double-slice. It is not the matter of having 3d, or other views rotational; Furthermore, the original Young experiment was carried out on crystals, a 3d system far more complex than the one you proposed.
All these variants are conceptually related to the classic double-slit experiment.

 

[DrClaude]

1.5 Probability Theory (Thing? Probability theory? still talking about probabilities in the "modern" quantum "physics? It is not an outdated concept?

[...]

4.2 The Wave equaqion and its interpretations (As? We still speak of the wave equation? But it is not an outdated concept, and now belonging to the physical junk Schrodinger?)

4.5 Conditions on Wave Function (Why? If the concept of wave is rubbish, because devote so much space?)

Chapter 9
9.1 An Example of Spin Measurement
9.2 A general Theorem of Measurement
9.4 Which Wave Function?
We still speak of old obsolete concepts such as "measures" and "wave function" ... BOH?

I'm sorry, but you appear to be approaching this in bad faith. The criticism given here by knowledgeable people is directed towards wave-particle duality. The fact that quantum systems are described by wave functions and that the interpretation of the latter is probabilistic (through the Born rule) is what killed wave-particle duality! The electron is not sometimes a (classical) particle, sometimes a wave, it is a quantum particle whose state evolution is given by the Schrödinger equation, which has a wave character.

No experiment will detect an electron as a wave, it is always a particle, but some results, such as those of the double slit experiment for many electrons will show patterns due to interference and the probabilistic nature of quantum mechanics.

 

[bhobba]

Are you saying that the de Broglie equation is wrong?

Yes.

Go to an inertial frame where the particle is at rest - what happens then?

Thanks
Bill

 

[bhobba]

4.2 The Wave equaqion and its interpretations (As? We still speak of the wave equation? But it is not an outdated concept, and now belonging to the physical junk Schrodinger?)

The wave particle duality lead to De-Broglie, then Schrodinger, then a dead end - it was realized it was wrong eg Schrodinger's waves were complex waves of probability in an infinite dimensional Hilbert space - nothing like the usual conception of a wave. Schrodinger 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.

Precisely what don't you get about the idea solutions to the Schrodinger wave equation are not like ordinary waves as suggested by the so called wave particle duality?

1. They are complex valued - normal waves are not
2. Even though its called the wave equation it often has solutions that look nothing like waves
3. Normal waves are waves of something - not probability
4. They do not promulgate in ordinary space but in an infinite dimensional abstract Hilbert space.
5. For two entangled particles its described by 6 coordinates - not 3 like normal waves.

When all this was realized Schrodinger hated having anything to do with it because it had nothing to do with what he thought it was ie the usual waves of physics like EM waves. Its still called the wave equation - but the name does not reflect what it is. Its simply the equation linking the time derivative of the state to the energy operator ie the Hamiltonian. Why is that? You will find the reason in Chapter 3 of Ballentine, or at a more general and perhaps deeper level in the book on Physics from Symmetry. Specifically it follows from the fact the probabilities predicted by the Born rule is frame independent. Expressed that way it seems utterly obvious and trivial, but strictly speaking you are invoking the principle of relativity which is a symmetry principle.

It's an example of the deep and very mysterious link between physics and symmetry. It was perhaps the greatest and deepest discovery of 20th century physics - why is a mystery no physicist can answer. Philosophers for some reason seem totally unaware of it but I doubt they will be able to resolve it - still one never knows.

Why do beginner texts and popularization's not mention it - it will simply confuse beginners - but this is an I level thread - you have left the basic view (which mostly is at best only partially correct) behind and start facing physics head on. If you don't like it stay with B level threads. You will still be told its wrong but much more gently.

Thanks
Bill

 

[mike1000]

Yes.

Go to an inertial frame where the particle is at rest - what happens then?

Thanks
Bill

When at rest with the particle there is no momentum so the equation states that the wavelength is infinite. It says that when in an inertial reference frame that is at rest with the object it always behaves like a particle. And when in an inertial frame that is not at rest with the particle it behaves like a wave. How does this show that de Broglies equation is wrong? This is a common occurrence in the world of physics. Is the wave nature a relative(not relativistic) effect?

De Broglie's equation says that the product p*λ is quantized. Not p or λ individually, but the product p*λ. Are you saying this is not true either?

 

[weirdoguy]

How does this show that de Broglies equation is wrong?

How did you get that:

It says that when in an inertial reference frame that is at rest with object it always looks like a particle. And when in an inertial frame that is not at rest with the particle it looks like a wave.

in the first place? What does "look like a particle/wave" mean? I look at moving things and thet don't look like waves to me...

 

[bhobba]

When at rest with the particle there is no momentum so the equation states that the wavelength is infinite.

An infinite wavelength extending in all directions forever - the physicality of such is?

Note in QM such can't occur because of the uncertainty principle - but De-Broglie has no such restriction.

De-Broglie is a mishmash of the wave-particle duality and relativity that when pushed too far breaks down. Schrodinger realized this, and was spurred when someone asked him the obvious question - if its a wave it should obey a wave equation. He found one (but made an error although he got the correct answer - by dumb luck):
https://arxiv.org/abs/1204.0653

However analysis of the equation showed it did not do what he wanted it to do. It was shown to be equivalent to Heisenberg's Matrix Mechanics by a number of people, although they had issues of a technical nature. The first actual proof was from Von-Neumann. In the mean time an even more general theory was developed by Dirac at the end of 1926 called the transformation theory that generally goes by the name QM today. It contains nothing about wave-particle duality - but does contain things of dubious mathematical validity ie that damned Dirac Delta function. Von-Neumann in his famous Mathematical Foundations of QM was quite critical - it makes interesting reading. This spurred many of the greatest 20th century mathematicians to fix it up. They succeeded and now via so called Rigged Hilbert spaces is mathematically valid. The spin-off is the so called theory of distributions which has many many applications - not just QM - for example its the best way to do Fourier transforms. It can even handle the weird wave-function of infinite wavelength - but the answer is still the same - its nonphysical.

Thanks
Bill

 

[Karolus]

Why do beginner texts and popularization's not mention it - it will simply confuse beginners -

Even Feynman lectures on physics? So this is a book for beginners, only done to confuse; ... the wave-particle duality is here clearly expressed as one of the founding concepts of MQ. Or maybe it's a dated text that no longer worth reading?
(Too much of other texts, such as the Landau, all based on outdated misconceptions!)

If you don't like it stay with B level threads. You will still be told its wrong but much more gently.

This sounds a bit like a dogmatism, almost a truth of faith. Who does not accept it is a heretic. I do not think it's a truly scientific attitude.
However I accept willingly your objections, I will try to keep myself to the level of the thread to get me more modern and current knowledge of authors who treat the issue. (Though I note that we Off Topic, and turning you turn around you go to always end up on the same question: "what is quantum mechanics?" There who apparently has finally solved the problem and speaks with absolute certainty, but those who evidently still has doubts, or otherwise believes that the issue is controversial and not at all completed)

 

[mike1000]

An infinite wavelength extending in all directions forever - the physicality of such is?

Note in QM such can't occur because of the uncertainty principle - but De-Broglie has no such restriction.

De-Broglie is a mishmash of the wave-particle duality and relativity that when pushed too far breaks down. Schrodinger realized this, and was spurred when someone asked him the obvious question - if its a wave it should obey a wave equation. He found one (but made an error although he got the correct answer - by dumb luck):
https://arxiv.org/abs/1204.0653

However analysis of the equation showed it did not do what he wanted it to do. It was shown to be equivalent to Heisenberg's Matrix Mechanics by a number of people, although they had issues of a technical nature. The first actual proof was from Von-Neumann. In the mean time an even more general theory was developed by Dirac at the end of 1926 called the transformation theory that generally goes by the name QM today. It contains nothing about wave-particle duality - but does contain things of dubious mathematical validity ie that damned Dirac Delta function. Von-Neumann in his famous Mathematical Foundations of QM was quite critical - it makes interesting reading. This spurred many of the greatest 20th century mathematicians to fix it up. They succeeded and now via so called Rigged Hilbert spaces is mathematically valid. The spin-off is the so called theory of distributions which has many many applications - not just QM - for example its the best way to do Fourier transforms. It can even handle the weird wave-function of infinite wavelength - but the answer is still the same - its nonphysical.

Thanks
Bill

I think you avoided most of my question to you by creating a red herring. An infinite wavelength is the same as saying zero frequency. Zero frequency happens all the time, for instance, dc current is zero frequency.

I did not ask you about the Schrodinger equation. I asked you about the deBroglie equation.

 

[bhobba]

De Broglie's equation says that the product p*λ is quantized. Not p or λ individually, but the product p*λ. Are you saying this is not true either?

I think you need to review just what it says. Define quantized? Is the wave function of a free particle either in QM or De-Broglie quantized? Actual quantization is a very difficult issue as to why it occurs, but if you really want to know the following will explain it:


Thanks
Bill

 

[weirdoguy]

So this is a book for beginners

Of course it is. You didn't know that? Read first few pages, you'll find out for whom was the lectures made.

the wave-particle duality is here clearly expressed as one of the founding concepts of MQ

It is - but only in a historical sense. It's not conceptual foundation of 'modern' QM.

Too much of other texts, such as the Landau, all based on outdated misconceptions!

Where in Landau you find wave-particle duality as a foundation of quantum mechanics (Schroedinger equation, etc.)? I have all L&L books on my shelves, I read like 1/3 of QM one and I see no wave-particle duality there. How many QM books (not for the beginners) have you read? It's not about dogmatism, it's about facts. Facts that are quite easy to check.

 

[bhobba]

Even Feynman lectures on physics? So this is a book for beginners, only done to confuse

That is not what I said.

I said it needs to be built up to slowly like it was done historically, and that the way its usually done. I personally don't like it, but I don't teach or write text-books about it. I bow to those that actually do - they obviously do it because other appproaches are problematical.

I prefer:
http://www.scottaaronson.com/democritus/lec9.html

BTW Feynman knew of this issue, lamented it, but saw no other way.

Thanks
Bill

 

[DrClaude]

This thread has run its course. Time to close.