Electron two-slit experiment in classical electromagnetism

[AndreiB]

Was there any study of this experiment in the context of classical electromagnetism? It is often claimed that such an experiment is impossible to explain classically, yet, the only classical model I've seen employed is Newtonian mechanics (bullets).

The EM fields associated with the electrons and nuclei in the barrier could in principle explain the observed pattern but did anybody tried to make some calculations?

 

[PeroK]

The EM fields associated with the electrons and nuclei in the barrier could in principle explain the observed pattern but did anybody tried to make some calculations?

Why don't you give it a try?

 

[AndreiB]

Why don't you give it a try?

I don't have a suitable computer. I tried to find a generic EM simulator online, but failed.

 

[Vanadium 50]

Holy cow did this thread get off to a bad start.

A suitable computer? THE double-slit experiment (as if there was only one)?

This experiment was first done by Thomas Young in 1801. What kind of "suitable computer" do you think he used? What is non-classical about his analysis?

 

[AndreiB]

Holy cow did this thread get off to a bad start.

A suitable computer? THE double-slit experiment (as if there was only one)?

This experiment was first done by Thomas Young in 1801. What kind of "suitable computer" do you think he used? What is non-classical about his analysis?

With EM waves is simple since they are, well, waves. Classically, electrons are not waves but charged particles, so one has to compute their trajectory. This means you have to calculate the electric and magnetic fields generated by the charged particles inside the barrier, calculate the Lorentz force on the electron and determine the trajectory. You need to have quite a few particles to behave like a barrier (hundreds of them). Such calculations can only be done numerically.

 

[Vanadium 50]

Classically, electrons are not waves but charged particles

OK, now we're getting somewhere, although not very far. You mean the electron double-slit experiment. Why didn't you say so?

There are two ways we can proceed.

1. You can write a well-defined question.
2. You can make us slowly tease out the question in your mind by giving us as little information as possible, and only when you are asked.

Since the electron's discovery is historically the demarcation between classical and modern physics there is no classical description of the electron. So you might start by telling us what you mean by this.

 

[AndreiB]

OK, now we're getting somewhere, although not very far. You mean the electron double-slit experiment. Why didn't you say so?

There are two ways we can proceed.

1. You can write a well-defined question.
2. You can make us slowly tease out the question in your mind by giving us as little information as possible, and only when you are asked.

Since the electron's discovery is historically the demarcation between classical and modern physics there is no classical description of the electron. So you might start by telling us what you mean by this.

The title of this thread is "Electron two-slit experiment...". I guess it's the same thing as double-slit.

There is a classical description of the electron, it's a point charge. It can be consistently described in the Born-Infeld model.

My question is what would classical electromagnetism predict for a two-slit experiment with electrons.

 

[Vanadium 50]

Born-Infeld model

OK, that was 1934, so it's hardly "classical".

But you don't get QM effects from Born-Infeld, and indeed the fields involved in bulk materials (and for that matter, atoms) are far below the threshold field.

 

[AndreiB]

But you don't get QM effects from Born-Infeld, and indeed the fields involved in bulk materials (and for that matter, atoms) are far below the threshold field.

What is the threshold field?

 

[PeroK]

With EM waves is simple since they are, well, waves. Classically, electrons are not waves but charged particles, so one has to compute their trajectory. This means you have to calculate the electric and magnetic fields generated by the charged particles inside the barrier, calculate the Lorentz force on the electron and determine the trajectory. You need to have quite a few particles to behave like a barrier (hundreds of them). Such calculations can only be done numerically.

Matter, generally,is electrically neutral, because atoms and molecules are neutral. If you propose this is not the case to explain electron diffraction, then you cannot explain the general lack of evidence for these fields.

The double slit experiment violates classical notions more fundamentally than could be explained by adding a suitable em field.

Classical em cannot explain modern electronics - e.g. quantum tunnelling. We even have quantum computers now.

The world has moved on. QM is established as the bedrock of modern science and it can't be replaced by simply running some classical simulations on a computer.

No matter how badly you wish QM would simply go away, it's here to stay.

 

[Vanadium 50]

What is the threshold field?

I'm sorry. I thought when you brought up Born-Infeld you alreafy understood what it says.

Born-Infeld has a parameter, sometimes called b, sometimes more confusingly called β, which has dimensions of electric field. As one nears this field, deviations from Maxwellian electrodynamics become noticeable. Its numeric value is around 10²⁰ V/m.

 

[AndreiB]

I'm sorry. I thought when you brought up Born-Infeld you alreafy understood what it says.

Born-Infeld has a parameter, sometimes called b, sometimes more confusingly called β, which has dimensions of electric field. As one nears this field, deviations from Maxwellian electrodynamics become noticeable. Its numeric value is around 10²⁰ V/m.

The reason I mentioned Born-Infeld was your objection:

"there is no classical description of the electron"

I thought you had in mind the difficulty of accommodating point charges in Maxwell's theory, and Born-Infeld was a possible solution to that difficulty.

For the regime where the two-slit experiment unfolds, the original theory is just fine, as you say.

 

[AndreiB]

Matter, generally,is electrically neutral, because atoms and molecules are neutral.

It is neutral in the sense that you have the same number of positive and negative charges. Such systems do generate electric and magnetic fields. True neutral particles such as neutrinos are not suitable for use as a barrier in this experiment. I wonder why.

If you propose this is not the case to explain electron diffraction, then you cannot explain the general lack of evidence for these fields.

Those fields are both theoretically justified and also experimentally proven (Van der Waals forces). For macroscopic objects they cancel out at large distances, but electrons are not macroscopic objects.

The double slit experiment violates classical notions more fundamentally than could be explained by adding a suitable em field.

In what sense? A suitable field can produce any pattern you want, as proven by the existence of CRT TV's.

Classical em cannot explain modern electronics - e.g. quantum tunnelling.

So, I guess you do have a suitable calculation in terms of classical EM for tunneling experiments. Can you point me to a paper where such a calculation is to be found?

We even have quantum computers now.

Yes. So what?

The world has moved on. QM is established as the bedrock of modern science and it can't be replaced by simply running some classical simulations on a computer.

I don't intend to replace anything. I am simply curious about what classical EM predicts for this experiment. All literature uses bullets (Newtonian mechanics) to show how classical physics fails. This is absolutely ridiculous. You cannot explain induction or planetary systems with bullets, yet we have classical explanations for them, provided by field theories like EM or GR.

 

[PeroK]

I don't intend to replace anything. I am simply curious about what classical EM predicts for this experiment. All literature uses bullets (Newtonian mechanics) to show how classical physics fails. This is absolutely ridiculous. You cannot explain induction or planetary systems with bullets, yet we have classical explanations for them, provided by field theories like EM or GR.

If you want to research what was done in the first half of the 20th century, then I suspect a lot of physicists spent a lot of time trying to find alternative explanations for emerging QM phenomena.

There was a recent thread on here about corrections to pure electron diffraction depending on the material from which the slits is made. This may essentially the analysis you are looking for. As you would expect any variations are almost negligible, and in any case don't produce the diffraction pattern in the first place.

You could also search for neutron diffraction to see whether an uncharged particle diffracts?

You could also search for Classical explanations for other QM phenomena.

Unless you postulate some new aspect of Classical EM it's not clear how a computer simulation is going to produce quantum phenomena. For diffraction you would need some sort of oscillating em field for example. If it is not there theoretically, then doing detailed calculations using that theory won't produce such a field out of the blue.

Finally, the onus is on you if you are really interested in why Classical EM cannot replicate QM to do the legwork and research it yourself. Most professional physicists, for the obvious reason, are not going to spend their time trying to resurrect Classical EM.

It's disingenuous to say that this question has nothing to do with QM scepticism. It's clear from your many posts on here that you are seeking evidence to undermine QM.

That's fair enough up to a point, bit there's only so far you can legitimately travel down that road.

 

[PeroK]

PS the other point that undermines your question is that De Broglie predicted electron diffraction (using early QM ideas) before it was experimentally shown.

Then there are two avenues. One is that there must be something in these new ideas and they must be fertile ground for research. The other is that the old ideas must be defended and it must be categorically proven that the old ideas cannot reproduce the new phenomena.

It seems obvious to me where the talented research physicists would focus their efforts.

 

[vanhees71]

With EM waves is simple since they are, well, waves. Classically, electrons are not waves but charged particles, so one has to compute their trajectory. This means you have to calculate the electric and magnetic fields generated by the charged particles inside the barrier, calculate the Lorentz force on the electron and determine the trajectory. You need to have quite a few particles to behave like a barrier (hundreds of them). Such calculations can only be done numerically.

Well, it's not that simple! That historically the electron was discovered as being a "particle" is just by chance, i.e., because in cathod ray tubes (and indeed the rays were electrons) the electrons behave pretty particle-like and that's why finally J. J. Thomson demonstrated indeed that the rays could be described as the motion of charged particles. Even before H. A. Lorentz started to develop his classical theory of electrons including the idea of electromagnetic mass generation. That's why traditionally the electron was established as a particle and the wave aspects were only discovered later after quantum mechanics (particularly wave mechanics a la de Broglie and Schrödinger) was developed in an attempt to demonstrate this wave features of electrons, also leading to the development of the electron microscope.

In this respect the discovery of X rays is also interesting. First it was just a side effect of experimenting with cathode ray tubes with a better vacuum, when Röntgen discovered another kind of rays penetrating matter easily, and for quite a while it was not clear what these Röntgen rays were. It took about 8 years until von Laue demonstrated the electromagnetic nature of the X rays in his famous diffraction experiments on crystals, which was not only the demonstration that X rays are electromagnetic waves but another hint at the atomic structure of matter and particularly crystals as a regular lattice of atoms, which was not yet established knowledge among physicists at this time.

 

[AndreiB]

If you want to research what was done in the first half of the 20th century, then I suspect a lot of physicists spent a lot of time trying to find alternative explanations for emerging QM phenomena.

Maybe.

There was a recent thread on here about corrections to pure electron diffraction depending on the material from which the slits is made. This may essentially the analysis you are looking for.

It's not. Any material is nothing but a bunch of positive and negative charges, fundamentally they are all the same.

As you would expect any variations are almost negligible, and in any case don't produce the diffraction pattern in the first place.

So these calculations were made, right? Please give me the reference!

You could also search for neutron diffraction to see whether an uncharged particle diffracts?

The neutron is neutral in the same sense the barrier is neutral. It contains an equal number of positive and negative charges. It has a magnetic moment, too.

You could also search for Classical explanations for other QM phenomena.

The thread is about this phenomenon. If you think some other experiment is more relevant, just open a thread and I'll do my best to provide an answer.

Unless you postulate some new aspect of Classical EM it's not clear how a computer simulation is going to produce quantum phenomena.

I don't postulate anything new. I am interested to see what the theory, as it is, predicts. After that, we may try to add some modifications, if necessary, but at this point it's pure speculation.

For diffraction you would need some sort of oscillating em field for example.

Why? And why this oscillating field should not be there? I expect the charges to move in some way.

If it is not there theoretically, then doing detailed calculations using that theory won't produce such a field out of the blue.

IF.

Finally, the onus is on you if you are really interested in why Classical EM cannot replicate QM to do the legwork and research it yourself.

I did. I came out empty-handed, just like you.

Most professional physicists, for the obvious reason, are not going to spend their time trying to resurrect Classical EM.

There are physicists doing that. Quite a few are working on stochastic electrodynamics (at least 3 different teams in US, Mexico and Netherlands). I don't know if this counts as "many" or not.

It's disingenuous to say that this question has nothing to do with QM scepticism.

I didn't say anything about QM scepticism, this is not a QM forum.

It's clear from your many posts on here that you are seeking evidence to undermine QM.

I do not want to "undermine QM", I think it is correct. And what is wrong with looking for evidence, anyway?

 

[AndreiB]

PS the other point that undermines your question is that De Broglie predicted electron diffraction (using early QM ideas) before it was experimentally shown.

My question is:

"What classical EM predicts for the two-slit experiment?"

I don't understand how this question could be "undermined". It could be answered by presenting some calculation.

There is no reason to believe that only one theory could give correct predictions. Both Newton's and Einstein's gravity give the same predictions for a wide range of phenomena. So de Broglie's succes does not prove that classical EM must fail.

Then there are two avenues. One is that there must be something in these new ideas and they must be fertile ground for research.

Sure.

The other is that the old ideas must be defended and it must be categorically proven that the old ideas cannot reproduce the new phenomena.

Again, this is not a QM forum, but my motivation to look for alternative explanations is based on the EPR argument. Your point of view (that QM is fundamental) is, in my opinion, falsified. The evidence for locality is rock solid. I do not reject the possibility that physics is non-local, but I see no reason to accept it without looking at the evidence very seriously.

It seems obvious to me where the talented research physicists would focus their efforts.

Indeed, on string theory. Their success is astonishing.

 

[vanhees71]

I don't know what you mean by "classical EM"? Is it classical electron theory a la Lorentz? This would of course predict no interference in the double-slit experiment with electrons, because electrons are treated as classical (relativistic) point particles. Lorentz wouldn't even have come to the idea that there could be interference effects or other wave-like properties of electrons before the early 1920ies when de Broglie (with Einstein's help in convincing Langevin) got his PhD for the hypothesis of wave-like properties for particles in analogy to Einstein's wave-particle duality for light.

It's of course clear that the idea to go back to classical electron theory is a step backwards and doesn't lead to anything useful. The only consistent theory about the behavior of matter we have, including (sub)atomic particles, is quantum (field) theory. There's no more wave-particle duality and other inconsistencies of the old quantum theory of before 1925 left.

 

[AndreiB]

Well, it's not that simple! That historically the electron was discovered as being a "particle" is just by chance, i.e., because in cathod ray tubes (and indeed the rays were electrons) the electrons behave pretty particle-like and that's why finally J. J. Thomson demonstrated indeed that the rays could be described as the motion of charged particles.

True, but the problem is that a continuous charge description does not seem to fit the data we have. So, I guess, the best classical model is still a particle model.

I also have a problem with waves being considered a kind of object in the same way as particles are. I think this is wrong. A wave is a kind of motion. You can have water staying still, you can have laminar flow, you can have a vortex and you can have a wave. All those are different states a large number of water molecules could be in. To say that something is a wave is meaningless. A wave of what? EM waves are the same, but you have E and M fields in the place of water molecules. You can have an electric field without an EM wave, but you can't have a EM wave without an electric field.

 

[vanhees71]

According to our contemporary theories fields are the fundamental building blocks and what "moves" are indeed the fields as dynamical descriptions of Nature, and these "motions" are indeed wavelike, because the equations of the fields often take the form of wave equations. There are of course also other solutions like static electric or magnetic fields etc. Of course you need quantum (field) theory to understand how particle-like phenomena occur and why macroscopic matter consisting of very many interacting particles can be well described by classical physics.

 

[AndreiB]

I don't know what you mean by "classical EM"? Is it classical electron theory a la Lorentz?

Yes.

This would of course predict no interference in the double-slit experiment with electrons, because electrons are treated as classical (relativistic) point particles.

If you define "interference" as something that requires a wave, then, yes, a point particle should not behave like that. But if you take this "interference" pattern to be just the consequence of how the electrons are guided by the EM fields associated with the atoms in the barrier, I see no theoretical problem.

Lorentz wouldn't even have come to the idea that there could be interference effects or other wave-like properties of electrons before the early 1920ies when de Broglie (with Einstein's help in convincing Langevin) got his PhD for the hypothesis of wave-like properties for particles in analogy to Einstein's wave-particle duality for light.

See above!

It's of course clear that the idea to go back to classical electron theory is a step backwards and doesn't lead to anything useful.

I understand you believe that, but the necessary evidence is lacking.

The only consistent theory about the behavior of matter we have, including (sub)atomic particles, is quantum (field) theory.

Yes, it's the only one we have, maybe we will have another one.

There's no more wave-particle duality and other inconsistencies of the old quantum theory of before 1925 left.

There is the problem of non-locality (I know, QFT has microcausality, but it does not forbid non-local effects, EPR argument still applies).

 

[vanhees71]

I have even no idea, how you can come to the conclusion the phenomena of electron diffraction could be described by classical electron theory. Also what you call "non-local" is in fact long-ranged correlations, which have nothing to do with any violation of microcausality. I also do not know, what you mean by "EPR argument", which is for me not even clearly stated. The connected idea of a local deterministic hidden-variable theory, which is clearly defined by Bell and seems indeed to be a valid interpretation of what's called "realistic" in the EPR paper, is clearly empirically refuted.

 

[PeroK]

If you define "interference" as something that requires a wave, then, yes, a point particle should not behave like that. But if you take this "interference" pattern to be just the consequence of how the electrons are guided by the EM fields associated with the atoms in the barrier, I see no theoretical problem.

There is a theoretical problem, whether you can see it or not. There is no way to reconstruct quantum behaviour using EM fields.

The aberration is yours, not that of the mainstream theoretical physics.

This is why the quantum computer is relevant. Because ultimately you'd have to explain all QM phenomena using classical EM.

Imagine going to a lab that has built a quantum computer and trying to persuade them that you see no theoretical problem with building such a computer using classical EM theory.

They are either going to say that you are mad or suggest you go and build one yourself. What they are not going to do is waste their time trying to build one and failing, just to prove you wrong.

 

[AndreiB]

I have even no idea, how you can come to the conclusion the phenomena of electron diffraction could be described by classical electron theory.

I didn't come to any conclusion, I'm looking to see if there is some evidence pointing one way or another. As far as I can see there is not.

Also what you call "non-local" is in fact long-ranged correlations, which have nothing to do with any violation of microcausality.

I didn't say they violate microcausality. I said that microcausality is too week a condition to guarantee that one event cannot produce effects as space-like separation, like in the case of A and B measurements.

I also do not know, what you mean by "EPR argument", which is for me not even clearly stated. The connected idea of a local deterministic hidden-variable theory, which is clearly defined by Bell and seems indeed to be a valid interpretation of what's called "realistic" in the EPR paper, is clearly empirically refuted.

My solution to this is superdeterminism. It has not been refuted.

 

[AndreiB]

There is a theoretical problem, whether you can see it or not. There is no way to reconstruct quantum behaviour using EM fields.

An assertion without evidence. Empty words.

The aberration is yours, not that of the mainstream theoretical physics.

Well, then show me that mainstream paper where classical EM has been found incompatible with the two-slit experiment. Please, don't show me bulets and billiard balls!

This is why the quantum computer is relevant. Because ultimately you'd have to explain all QM phenomena using classical EM.

Let's take one example at a time!

Imagine going to a lab that has built a quantum computer and trying to persuade them that you see no theoretical problem with building such a computer using classical EM theory.

I see no theoretical problem. It's just a bunch of charges going around. What problem is there?

They are either going to say that you are mad or suggest you go and build one yourself. What they are not going to do is waste their time trying to build one and failing, just to prove you wrong.

They build it from atoms. The building process has nothing to do with the nature of the electrons. They are what they are. Are you saying that if you believe the electrons are classical you would fail to build a quantum computer?

 

[PeroK]

I see no theoretical problem. It's just a bunch of charges going around. What problem is there?

That probably sums up your view of theoretical physics!

 

[AndreiB]

Imagine going to a lab that has built a quantum computer and trying to persuade them that you see no theoretical problem with building such a computer using classical EM theory.

Let me clarify this a little bit. My hypothesis here (a hypothesis I would like to see tested by direct calculations or a rigurous argument) is that QM might be for classical EM (with or without some modifications) what QM is for Newtonian mechanics. If you want to build a bridge you aren't going to use quantum mechanics, you would use an approximate theory that makes calculations easy and gets the job done. QM's description of the two-slit experiment is simple, the equivalent description in terms of all those interacting charges is unbelievable complex. Such a calculation would still be interesting for theoretical reasons. Practically, nobody would do it that way. So, if you want to build a quantum computer you would use QM, not classical EM, even if classical EM would work in principle.

In my first reply I intended to convey that I see no theoretical contradiction between classical EM being right and the existence of quantum computers, not that it would be practical to use classical EM in this case.

 

[Lord Jestocost]

QM's description of the two-slit experiment is simple, the equivalent description in terms of all those interacting charges is unbelievable complex.

In case I correctly follow your line of thinking: One could try to simulate electron and neutron diffraction at simple periodic lattice structures. This should be more easily manageable.

 

[vanhees71]

It is a well-established fact that classical electromagnetism is an approximation to the more comprehensive quantum electrodynamics. You have to quantize both "particles" as well as "radiation"/"fields" to get a consistent picture in accordance with the observations. There is no classical way to describe diffraction of electrons a la Davisson and Germer or their use in electron microscopes, which are direct applications of the wave properties of electrons as described by QED.

Also the electromagnetic field has to be quantized. The most simple evidence for this is spontaneous emission and the Bose-Einstein statistics as demonstrated by black-body radiation, the very phenomenon where the discovery of quantum theory started on Dec/14/1900. Today there are many more amazing experiments with single photons demonstrating the necessity for field quantization.

So neither phenomena concerning electromagnetic fields nor those concerning matter and their mutual interaction are completely describable within classical electrodynamics.

 

[vanhees71]

In case I correctly follow your line of thinking: One could try to simulate electron and neutron diffraction at simple periodic lattice structures. This should be more easily manageable.

But it's impossible to describe these phenomena in terms of classical particle mechanics!

 

[PeroK]

Let me clarify this a little bit. My hypothesis here (a hypothesis I would like to see tested by direct calculations or a rigurous argument) is that QM might be for classical EM (with or without some modifications) what QM is for Newtonian mechanics.

In my first reply I intended to convey that I see no theoretical contradiction between classical EM being right and the existence of quantum computers, not that it would be practical to use classical EM in this case.

This personal theory depends on ignoring all the experimental evidence to the contrary. As in your other posts, we are debating under the bizarre assumption that no experiments have been carried out that contradict classical EM.

Even something as simple as the magentic moment of the electron is different under QM than classical EM: it's approximately twice what it should be under classical EM:

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

Modern QM is so far beyond classical EM that it's absurd that we even debating this. Trying to pretend that classical EM could produce an alternative to QCD and the quark-model, the weak force and nuclear decay is blind personal theorising. You yourself even noted that the neutron has a magnetic moment:

The neutron is neutral in the same sense the barrier is neutral. It contains an equal number of positive and negative charges. It has a magnetic moment, too.

Where does that come from in classical EM? Where are the quarks, where is the strong force? Where is colour confinement? Those are all quantum mechanical models.

Finally, particle scattering experiments, when modeled using QT, produce different results from classical EM. The experiments have been carried out and shown that the classical Coulomb's law breaks down at high energies. Reduce the energy and the classical formulas are seen as an approximation to the quantum formulas.

These are not isolated experiments. All of high-energy physics for the last 100 years has been non-classical - all of it! The fact that you are aware of none of it is irrelevant. I'll pick one example from yesterday:

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.110.213001

This is where modern QM physics has reached. It's 150 years beyond Maxwell. His theory was groundbreaking in 1865. But, that is the physics of 1865, not of 2021.

And don't ask: where's the evidence for this? The evidence is the entire body of 20th and 21st century experimental high-energy physics, from the photoelecetric effect, to electron diffraction, Compton scattering, particle scattering, experimental confirmation of the standard model of particle physics, the Higgs boson, and everything else.

 

[berkeman]

Thread closed for Moderation.

 

[bhobba]

Was there any study of this experiment in the context of classical electromagnetism?

No - because classical electromagnetism does not describe the election. Attempts were made early on to do it, but they all ran into difficulties. For example, if it was a classical particle, it should spiral into the nucleus. Only by assuming it is a quantum particle can the double-slit using electrons be explained, as well as the spiralling issue:
https://arxiv.org/pdf/quant-ph/0703126.pdf

A big issue in physics is that models must explain the phenomena being looked at and others. If not, it is not worth pursuing.

With my moderator's hat on, it is important discussions like this proceed on that basis. It will not get anywhere otherwise, and like this may be shut down.

Thanks
Bill

 

[berkeman]

After a Mentor discussion (and some other actions), thread will remain closed.