Speed of Electrons: A Classic View

[jochem]

Hello,
this is my first forum question, so i hope it's at the right place.
My question is about electrons, i know in a QM view electrons don't have a well defined position or speed.
However i am curious, in a classic view of the electron would electrons closer to the nucleus move faster then electron farther away from the nucleus. I tried to reason it with the centripetal force equal to coulombs law. So i came to the conclusion that electrons closer to the nucleus would move faster then electron further a way. Is this reasoning correct or did i made a mistake?P.S. i am sorry for grammar mistakes

 

[RPinPA]

Yes, in the Bohr model (which is what you're talking about) the dynamics are the same as for planets orbiting a sun. The Coulomb force is an inverse square force as Newtonian gravitation is, so you get all very similar equations (with different constants of course).

So for instance in our solar system, Mercury moves at 47 km/s while Earth, farther out, moves at about 30 km/s.

 

[jochem]

Oke thank you!

 

[BPHH85]

Of course this is just a mind game because in such a classical situation, the electron will lose energy by spinning around the nucleus and will collapse in it.

 

[jochem]

i am not sure, why is that? You could reason that the electron, would haven only one force acting on it. This force would be described by coulombs law. However if the electron has a speed around a stable point, the nucleus. Then it will reach a equilibrium where it will circle the nucleus forever.

 

[Nugatory]

i am not sure, why is that?

An accelerating charged particle (and an orbiting particle is accelerating because its direction of travel is constantly changing) emits electromagnetic radiation as it changes speed and/or direction. This causes it to lose energy and slow down.

Thus, an electron orbiting the nucleus won't be in a stable equilibrium; it will continue to lose energy and move closer to the nucleus until its speed is zero and it collides with the nucleus. Thus, the classical model of the orbiting electron predicts that atoms should decay very quickly - but of course they don't. This was a big problem for 19th-century physicists, not resolved until quanum mechanics was discovered early in the 20th century.

 

[RPinPA]

Yeah, that's the well-known difference between the electromagnetic force and the gravitational force which killed the Bohr model. Accelerating electrons radiate energy. That's predicted by Maxwell's Equations, which date to the 19th century.

 

[jochem]

I am sorry but i don't quite get that.
I can understand why you could say a electron is accelerating in different directions. However why does this need to result in a decrease of its energy?
So i think what i don't understand is why would a charged particle that is just moving a round a point, it is accelerating and thus also decreasing, lose energy in this view? (it is also decreasing right? because it speed in one direction changes to a speed in another direction so it must decrease and increase in another direction)

Sub-question: if an electron would hit a proton it would form a neutron right?

 

[jbriggs444]

I am sorry but i don't quite get that.
I can understand why you could say a electron is accelerating in different directions. However why does this need to result in a decrease of its energy?

It is called synchrotron radiation and is emitted by an electron or any other charged particle accelerating radially in a circular path. If it is emitting radiation, it is emitting energy. If it is emitting energy, it is losing energy.

The classical picture is incomplete, of course. An electron in an atom is not actually accelerating radially and does not emit synchrotron radiation.

Sub-question: if an electron would hit a proton it would form a neutron right?

That is a possibility. See https://physics.stackexchange.com/questions/88059/collision-between-electron-and-proton. In order to conserve lepton number, an electron neutrino is produced as well.

 

[RPinPA]

It is also decreasing right? because it speed in one direction changes to a speed in another direction so it must decrease and increase in another direction

Just want to respond to this comment. The answer is no. An object moving in a circle at constant speed is never increasing or decreasing in speed. Yes, the components change, but the magnitude never does.

 

[jochem]

Just want to respond to this comment. The answer is no. An object moving in a circle at constant speed is never increasing or decreasing in speed. Yes, the components change, but the magnitude never does.

But if the components change, the components undergo a acceleration and or a deceleration right?

 

[jochem]

It is called synchrotron radiation and is emitted by an electron or any other charged particle accelerating radially in a circular path. If it is emitting radiation, it is emitting energy. If it is emitting energy, it is losing energy.

I can understand that if, it would emitted radiation it would lose energy. However i can't quite grasp why it would emitted radiation. I read parts of your link and also https://en.wikipedia.org/wiki/Cyclotron_radiation from here. So 2 questions arose, first one: In my mind (i know this is not very scientific) the electron would be in a equilibrium around a nucleus. So why is it unstable.

second question: If its is unstable how exactly would it emitted radiation, i mean not how, but when. We know light is quantised so it must take discreet energy forms, so is the electron emits photons, when its accelerating then it would need to constantly send photons, because in a circle it's constantly accelerating right?

 

[jbriggs444]

I can understand that if, it would emitted radiation it would lose energy. However i can't quite grasp why it would emitted radiation. I read parts of your link and also https://en.wikipedia.org/wiki/Cyclotron_radiation from here. So 2 questions arose, first one: In my mind (i know this is not very scientific) the electron would be in a equilibrium around a nucleus. So why is it unstable.

second question: If its is unstable how exactly would it emitted radiation, i mean not how, but when. We know light is quantised so it must take discreet energy forms, so is the electron emits photons, when its accelerating then it would need to constantly send photons, because in a circle it's constantly accelerating right?

In the Bohr model, electrons do orbit the nucleus and do accelerate. Classical electromagnetism (Maxwell's equations) then predicts that they should radiate. If they radiate, they must lose energy. If they lose energy, they must spiral into the nucleus. That is, classical electromagnetism predicts that electrons orbiting atomic nuclei would be unstable.

That answers your first question.

Your second question contains a contradiction. It is only when using the Bohr model of the atom together with the classical model for electromagnetism that we predict the emission of radiation. We know that prediction is incorrect. There is no radiation. You cannot reasonably ask where or how or when the radiation is emitted as photons because

1. Classical electromagnetism does not predict radiated photons because the model is classical and does not include photons.
2. Reality does not include radiated photons because in reality the Bohr model is wrong and there are no accelerating electrons.
3. Photons are not what you think they are.

 

[BPHH85]

Seems that I kicked something off with my remark...

But if the components change, the components undergo a acceleration and or a deceleration right?

This is according to Newtons first law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

 

[jochem]

oke thanks for your quick answer.

Classical electromagnetism (Maxwell's equations) then predicts that they should radiate.

could you say with equations you main?

Reality does not include radiated photons because in reality the Bohr model is wrong and there are no accelerating electrons.

alritght then, what are the electrons then doing around the nucleus i understand that this is not a well defined question because of QM. But are the electron in QM not acceleration around the nucleus?

 

[jochem]

Seems that I kicked something off with my remark...This is according to Newtons first law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

I am sorry what are you trying to say? there is a force acting on the electron right?

 

[jbriggs444]

could you say with equations you main?

https://en.wikipedia.org/wiki/Maxwell's_equations

alritght then, what are the electrons then doing around the nucleus i understand that this is not a well defined question because of QM. But are the electron in QM not acceleration around the nucleus?

It is not a well defined question. Full stop.

 

[jochem]

Why a full stop, i will ask otherwise. Why does the QM view of a electron and its nucleus not result in the radiation Maxwell predicted.

 

[BPHH85]

I am sorry what are you trying to say? there is a force acting on the electron right?

An electron orbiting a nucleus neither remains in rest nor continuous to move at a constant velocity as the direction of the velocity changes ongoing. So the acceleration isn't zero, according to Newtons first law.

 

[BPHH85]

Why a full stop, i will ask otherwise. Why does the QM view of a electron and its nucleus not result in the radiation Maxwell predicted.

To bring together a QM view on light-matter-interaction, you need a deeper understanding in QED (qauntum-electrodynamics). But this is beyond my knowledge. But to point it out...a point mass like electron with charge -e orbiting around a nucleus is a model from the classical physics point of view. As this model will lead to an electron collapsing in the nucleus leading to unstable matter states leading to a world that isn't the world we all are living in can't discribe the way the microscopic world works. Thats why classical phyics failed discribing microscopic behaviour and QM was needed.

 

[ZapperZ]

Why a full stop, i will ask otherwise. Why does the QM view of a electron and its nucleus not result in the radiation Maxwell predicted.

https://www.physicsforums.com/insights/dont-electrons-crash-nucleus-atoms/

Zz.

 

[jochem]

To bring together a QM view on light-matter-interaction, you need a deeper understanding in QED (qauntum-electrodynamics). But this is beyond my knowledge. But to point it out...a point mass like electron with charge -e orbiting around a nucleus is a model from the classical physics point of view. As this model will lead to an electron collapsing in the nucleus leading to unstable matter states leading to a world that isn't the world we all are living in can't discribe the way the microscopic world works. Thats why classical phyics failed discribing microscopic behaviour and QM was needed.

oke thnx!

 

[jochem]

https://www.physicsforums.com/insights/dont-electrons-crash-nucleus-atoms/

super thank you! I'm gone read it!

 

[DanMP]

An accelerating charged particle (and an orbiting particle is accelerating because its direction of travel is constantly changing) emits electromagnetic radiation as it changes speed and/or direction. This causes it to lose energy and slow down.

Thus, an electron orbiting the nucleus won't be in a stable equilibrium; it will continue to lose energy and move closer to the nucleus until its speed is zero and it collides with the nucleus. Thus, the classical model of the orbiting electron predicts that atoms should decay very quickly - but of course they don't. This was a big problem for 19th-century physicists, not resolved until quanum mechanics was discovered early in the 20th century.

This is very interesting, but the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

 

[jbriggs444]

This is very interesting, but the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

A particle orbiting in gravitational free fall should not emit. However, if you view it from an accelerating reference frame... https://en.wikipedia.org/wiki/Unruh_effect

In any case, an electron riding on the Earth as the Earth orbits the sun is accelerated much less strongly than a hypothetical classical electron orbiting the nucleus of a hydrogen atom.

 

[ZapperZ]

This is very interesting, but the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

Electrons in the s-orbital of an atom have angular momentum of ZERO. Now explain that with your "orbit" model.

Zz.

 

[DanMP]

A particle orbiting in gravitational free fall should not emit. However, if you view it from an accelerating reference frame... https://en.wikipedia.org/wiki/Unruh_effect

We are not in free fall while rotating around the center of the Earth ... Are we emitting? And if we do, how is this loss of energy affecting the electrons?From your link I got: "It is currently not clear whether the Unruh effect has actually been observed, since the claimed observations are disputed."

 

[jbriggs444]

We are not in free fall while rotating around the center of the Earth ... Are we emitting?

We are neutrally charged.

From your link I got: "It is currently not clear whether the Unruh effect has actually been observed, since the claimed observations are disputed."

Which is a clue that the magnitude of the expected radiation is small.

 

[DanMP]

We are neutrally charged.

Ok, but the electrons in our body are not neutral. Are they emitting? If not, why not? What prevents them to emit?
If yes, they should lose energy ... Is this allowed by the quantum mechanics? And how would this loss of energy affect the electrons? Is it compensated in any way? How?

On the other hand, what keeps the "smeared electron" from falling into the nucleus? Since there is no rotation (on orbits), there is also no centrifugal force ... So what force is preventing the electron to fall on/into the nucleus?

 

[ZapperZ]

Ok, but the electrons in our body are not neutral. Are they emitting? If not, why not? What prevents them to emit?
If yes, they should lose energy ... Is this allowed by the quantum mechanics? And how would this loss of energy affect the electrons? Is it compensated in any way? How?

On the other hand, what keeps the "smeared electron" from falling into the nucleus? Since there is no rotation (on orbits), there is also no centrifugal force ... So what force is preventing the electron to fall on/into the nucleus?

This is another example of trying to go one step forward, but we end up having to take 2 steps back, because we have to explain the explanation.

Try reading this!

https://www.physicsforums.com/insights/dont-electrons-crash-nucleus-atoms/

In other words, you still lack an understanding of the foundation of your question.

BTW, I can see you in the dark with my IR glasses. What do you think that is?

Zz.

 

[DanMP]

This is another example of trying to go one step forward, but we end up having to take 2 steps back, because we have to explain the explanation. ...

As far as I understand, the main goal of this forum is to discuss/explain the current theories, so I'm waiting for some answers, if there are any ...

I read (and even quote) the link you gave, but didn't find answers to my questions. By the way, my questions above are related to my previous posts:

... the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

We are not in free fall while rotating around the center of the Earth ... Are we emitting?

BTW, I can see you in the dark with my IR glasses. What do you think that is?

As far as I know, IR radiation is emitted by the molecules while changing their rotational-vibrational movements ... How is this related to what I asked?

 

[ZapperZ]

As far as I understand, the main goal of this forum is to discuss/explain the current theories, so I'm waiting for some answers, if there are any ...

I read (and even quote) the link you gave, but didn't find answers to my questions. By the way, my questions above are related to my previous posts:

The answers are in there, but you might have not realized it.

For instance, how are you going to stand on a ladder on a rung that does not exist? It's the same analogy for why there are only discrete states in an atom, and why there are no lower states that are possible. The picture of an electron orbiting a nucleus is the faulty starting point in all of this. But you keep coming back to it and asks us to use that picture to explain why certain things can't happen. That's call handcuffing, and you are asking us to explain why what you understand is wrong based on a wrong starting point that you won't give up on!

That is the whole point of that Insight article, that the starting point of understanding electrons' behavior in an atom needs to be completely revised FIRST and not be tied to the planetary model! It is ONLY THEN can we understand why we have all the properties of the atom that we currently observe.

As far as I know, IR radiation is emitted by the molecules while changing their rotational-vibrational movements ... How is this related to what I asked?

You asked if the neutral human body radiates. Voila, proof! Besides, anyone taking basic physics knows that a neutral object can radiates (current in a wire, electric dipole, radio transmitters, etc.). EM radiation is not give off just due to atomic transitions.

Zz.

 

[DanMP]

The answers are in there, but you might have not realized it. ...

... The picture of an electron orbiting a nucleus is the faulty starting point in all of this. But you keep coming back to it and asks us to use that picture to explain why certain things can't happen. ...

On the contrary, my questions are related to the picture of a "smeared" electron. Please read again. I never wrote (in this thread) about "an electron orbiting a nucleus" ... Did you read this:

On the other hand, what keeps the "smeared electron" from falling into the nucleus? Since there is no rotation (on orbits), there is also no centrifugal force ... So what force is preventing the electron to fall on/into the nucleus?

I was not defending the orbiting electron model. I just tried to better understand the current ("smeared" electron) model.

You asked if the neutral human body radiates. ...

No, I didn't. I was just lazy and asked "are we emitting?" instead of "are the electrons smeared around the nuclei of the atoms in our body emitting?". I thought that it was implied. Please read again.

 

[ZapperZ]

On the contrary, my questions are related to the picture of a "smeared" electron. Please read again. I never wrote (in this thread) about "an electron orbiting a nucleus" ... Did you read this:

I was not defending the orbiting electron model. I just tried to better understand the current ("smeared" electron) model.

But that doesn't make any sense. You keep asking why electrons don't collapse into the nucleus, and why they don't keep on radiating... these are ALL questions that you'd ask if you still were holding on to the orbiting electron picture! Otherwise, why would you ask such a thing?

In any case, if I give you the benefit of the doubt that you are no longer clutching on to this outdated picture, are you still questioning why a ground state atom, or atom in a stable state, does not radiate? Presumably, you've solve the schrodinger equation for the simplest atom, the Hydrogen atom. Do you still doubt this type of formalism as an accurate description of an atom?

Zz.

 

[DanMP]

Do you still doubt this type of formalism as an accurate description of an atom?

I'm not doubting the formalism. I just want to better understand what is going on there. Again: if the electron is "smeared" around the nucleus but not falling into it, a force must keep it from falling. What force is it? And if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked) If yes, how is this loss of energy affecting the electrons?

These are simple, legitimate questions. Why are you so reluctant to directly answer them? This is not a church, to avoid uncomfortable questions.

 

[PeroK]

So what force is preventing the electron to fall on/into the nucleus?

What prevents the electron falling into the nucleus? The Schroedinger equation, of course!

 

[ZapperZ]

I'm not doubting the formalism. I just want to better understand what is going on there. Again: if the electron is "smeared" around the nucleus but not falling into it, a force must keep it from falling. What force is it? And if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked) If yes, how is this loss of energy affecting the electrons?

But this is exactly the reason why I insisted that you are clinging on to the planetary model, even if you don't realize it!

Let's get this clear first and foremost. If I have a bare nucleus, and then I shoot electrons at the bare nucleus. The electron may hit the nucleus, and a bunch of interesting things may happen. This was a common experiment in the early days of high energy physics. So yes, an electron can definitely reach the nucleus under that situation.

So now, what is the difference with an atom? Why did it take so long, and why did it have to wait until the development of QM to actually be able to account for the most accurate behavior of an atom? Why is the QM description of the atom in terms of the wavefunction so much more accurate than the old Rutherford/Bohr model? What was given up?

Your question has less to do with why an electron doesn't crash into the nucleus, and more to do with why QM is valid and the overall picture of how QM describes our world! This is inescapable once you start with the QM Hamiltonian or the Schrodinger equation. So it isn't the "why", but rather the "how". The issue that you have is bigger than you think.

Until you come to the agreement that that is how we can describe the phenomena at this scale, then the issue here isn't about the electron and the atom, but rather it is about the validity of QM's description.

Period!

Zz.

 

[Nugatory]

Again: if the electron is "smeared" around the nucleus but not falling into it, a force must keep it from falling.

Why must that be so?

This might be a good time to dig into exactly what it means to say "a force must keep it from falling". Force is defined by the equation $F=ma$ and $a$ is defined to be the second derivative of position with respect to time, so any appeal to force as an explanation for electron behavior assumes that the electron has a position. But that assumption is incompatible with the "smeared" model in which the electron has no position. A similar argument applies to the word "falling" which implies that the electron is moving closer to the nucleus - but "closer" only makes sense if the electron has a position so that we can talk about the distance between where it is and the nucleus, and in the "smeared" model there's no position.

Instead, we have to listen to @ZapperZ in post #34 above: Solve Schrodinger's equation for the electron bound to the nucleus. In this solution there are no forces, no positions, no trajectories that seem to fall into the nucleus, no distance from the nucleus... But there is an accurate description of how the electron behaves without any of these misplaced classical notions.

 

[DanMP]

Your question has less to do with why an electron doesn't crash into the nucleus, and more to do with why QM is valid and ...

No, this was your problem all the time: instead of answering my questions, you tried to intimidate me because you thought that I'm against quantum mechanics and "clinging" to Bohr's model. To be clear, I'm not against QM. I'm aware that it is very successful, so I think that its math is OK. Only the interpretation, in my opinion, may be less perfect, so I asked simple, direct, questions, in order to see how this successful theory solved the (apparent?) problems I mentioned.

Nugatory, instead, addressed (one of) my questions and he did it very professionally. Thank you Nugatory!

This might be a good time to dig into exactly what it means to say "a force must keep it from falling". Force is defined by the equation F=maF=maF=ma and aaa is defined to be the second derivative of position with respect to time, so any appeal to force as an explanation for electron behavior assumes that the electron has a position. But that assumption is incompatible with the "smeared" model in which the electron has no position. A similar argument applies to the word "falling" which implies that the electron is moving closer to the nucleus - but "closer" only makes sense if the electron has a position so that we can talk about the distance between where it is and the nucleus, and in the "smeared" model there's no position.

My problem was/is that I thought that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus means that the electron is somehow "smashed" in little pieces and distributed in a particular geometry around the nucleus (if we do something like that with the Moon, after stopping it, the pieces would fall on the Earth). In such a case, electron "pieces" around the nucleus may have a position and should fall ...

How about my other question?

if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked)

 

[Nugatory]

How about my other question?

Same issue - no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

The Bohr model was an effort to reconcile the observed stability of atoms with a classical description of the electrons (small solid object with a definite position) that predicted that atoms would be unstable. The he need for that reconciliation went away when we discovered that the classical description was not right.

 

[DrClaude]

If you accelerate an atom, you are of course accelerating an electron, but you are also accelerating an equal-charge nucleus, and the radiation you would get for each cancel out. You can take the atom as a globally neutral entity, so no emission of radiation due to acceleration.

 

[DanMP]

If you accelerate an atom, you are of course accelerating an electron, but you are also accelerating an equal-charge nucleus, and the radiation you would get for each cancel out.

So radiation/photons is/are emitted both by the nuclei and by the "smeared" electrons, but they "cancel out"?

Nugatory wrote (the underline is mine):

no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

In Wikipedia I found (again, the underline is mine):

... As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.[1]:67 The charges thus radiate their own electromagnetic wave that is at the same frequency, ...

Who is right then?

And if the electrons in a material can be "shaken" by the EM fields, then they also would be attracted by the nuclei and fall into it ...

 

[DrClaude]

So radiation/photons is/are emitted both by the nuclei and by the "smeared" electrons, but they "cancel out"?

Nugatory wrote (the underline is mine):

no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

You have to decide what you want to discuss. What Nugatory wrote is correct: no acceleration means no radiation. And by "no acceleration," he is discussing. electrons in atoms.

I was answering you question

How about my other question?

if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked)

about accelerating atoms, where the electron is accelerating as part of the atom, but not with respect to the nucleus.

And if the electrons in a material can be "shaken" by the EM fields, then they also would be attracted by the nuclei and fall into it ...

I don't know where this Wikipedia quote comes from, but this is pop-sci language. If no lower energy states are accessible to the electron in the atom, it will stay in the same state. If an lower energy state is available, it will eventually decay to it, releasing a photon. This emission as nothing to do with the emission of radiation due to accelerating charges.

 

[DanMP]

I was answering you question
about accelerating atoms, where the electron is accelerating as part of the atom, but not with respect to the nucleus.

Nugatory answered the exact same question, about accelerating atoms ... and his answer was "no radiation" from the electrons, because the "smeared" electron has no position, so it doesn't accelerate when the atom accelerates:

no position means no meaningful notion of acceleration

Again, who is right? And why?

I don't know where this Wikipedia quote comes from ...

Just follow the link ... It's an explanation of how/why light is slowed down in transparent materials and, according to it, the "smeared" electrons can be "shaken" ... so they not only emit EM radiation, but also can be attracted by the nucleus (contrary to what Nugatory said) and fall into it, if no other force prevents it.
Is the Wikipedia explanation wrong? Why? And how is correct?

 

[DrClaude]

Nugatory answered the exact same question, about accelerating atoms ... and his answer was "no radiation" from the electrons, because the "smeared" electron has no position, so it doesn't accelerate when the atom accelerates:

Again, Nugatory is talking about electrons in an atom, not an accelerating atom.

Again, who is right? And why?

Both of us, because we are not talking about the same thing.

Just follow the link ... It's an explanation of how/why light is slowed down in transparent materials and, according to it, the "smeared" electrons can be "shaken" ...

Even in the Wikipedia link, "shaken" is in quotes, because this is simply colloquial language to explain something more complicated. Yes, the electromagnetic radiation will change the wave function of the electrons, and this change will oscillate with the field. This results in an oscillating dipole, and it is this oscillating dipole that will radiate back. Electrons are not really shaken in the classical sense.

so they not only emit EM radiation, but also can be attracted by the nucleus (contrary to what Nugatory said) and fall into it, if no other force prevents it.
Is the Wikipedia explanation wrong? Why? And how is correct?

Nobody said that electrons are not attracted by the nucleus, to the contrary. Thinking of the situation in terms of forces is not the proper approach in quantum mechanics. Have a look at the resource indicated in post #21.

 

[DanMP]

Again, Nugatory is talking about electrons in an atom, not an accelerating atom.

He was talking about electrons in an atom, yes, but the atom was accelerating (due to rotation around the center of the Earth, or due to vibration - if the atom was part of a molecule).

He first said:

... any appeal to force as an explanation for electron behavior assumes that the electron has a position. But that assumption is incompatible with the "smeared" model in which the electron has no position. A similar argument applies to the word "falling" which implies that the electron is moving closer to the nucleus - but "closer" only makes sense if the electron has a position so that we can talk about the distance between where it is and the nucleus, and in the "smeared" model there's no position.

and then, about the "smeared" electron when it accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule):

Same issue - no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

But you said:

If you accelerate an atom, you are of course accelerating an electron, but you are also accelerating an equal-charge nucleus, and the radiation you would get for each cancel out

So you contradicted Nugatory about the "ability" of a "smeared" electron to accelerate (and consequently emit EM radiation). You like it or not, one of you is wrong. Who is wrong? And, more important, how is right/correct?Regarding the microscopic explanation (of how light is slowed down in materials) you wrote:

Even in the Wikipedia link, "shaken" is in quotes, because this is simply colloquial language to explain something more complicated. Yes, the electromagnetic radiation will change the wave function of the electrons, and this change will oscillate with the field. This results in an oscillating dipole, and it is this oscillating dipole that will radiate back.

By "radiate back" you imply that photons are emitted, right? So photons are produced apparently without incident photons being absorbed. This sounds like producing photons/energy without consuming energy. How is this possible? What am I missing?

 

[Nugatory]

Again, Nugatory is talking about electrons in an atom, not an accelerating atom.

There's an easy way to analyze the radiation produced by accelerating an atom and a hard way.

The easy way: The atom as a whole is neutral. Accelerating a neutral object produces no radiation. Done.

The hard way: Treat the atom as a complicated distribution of positive and negative electrical charges (the mathematical representation of the "smeared" mental model that you're using - did I not say something about solving Schrödinger's equation somewhere above?), shift to a classical model to calculate what happens when we accelerate it, note that all the effects cancel so that no radiation is emitted. (Or if you can't make them cancel go back through calculations to find your error).

 

[DrClaude]

So you contradicted Nugatory about the "ability" of a "smeared" electron to accelerate (and consequently emit EM radiation). You like it or not, one of you is wrong. Who is wrong? And, more important, how is right/correct?

@Nugatory and I are not contradicting each other. There are two situations: the electron with respect to the nucleus, and the electron as part of the atom as a whole. The electron does not orbit around the nucleus, but is in a "smeared" stationary state (wave function), and therefore does not accelerate, so no emission of radiation and no loss of energy. If the atom as a whole is accelerated, then the electron, as part of that atom, is also accelerated, but the change in the electric field created by that is exactly canceled by the acceleration of the nucleus, so again no emission. The fact that the electron is "smeared" plays no role in this latter case.

By "radiate back" you imply that photons are emitted, right? So photons are produced apparently without incident photons being absorbed. This sounds like producing photons/energy without consuming energy. How is this possible? What am I missing?

The energy can come from any source: thermal, collisions, etc.

 

[DanMP]

The energy can come from any source: thermal, collisions, etc.

Really? So, if we "send" a single photon through an ordinary glass window, we will observe/measure at the other end countless similar photons? And the "amplification" would increase with the width of the glass, because there are more atoms ready to "produce" new photons? In what world/reality is this true?

The hard way: Treat the atom as a complicated distribution of positive and negative electrical charges (the mathematical representation of the "smeared" mental model that you're using - did I not say something about solving Schrödinger's equation somewhere above?), shift to a classical model to calculate what happens when we accelerate it, note that all the effects cancel so that no radiation is emitted. (Or if you can't make them cancel go back through calculations to find your error).

So, you (kind off) admit that DrClaude was right: radiation is (or may be) emitted by the "positive and negative electrical charges", but "all the effects cancel".

For me, the apparent absence of radiation is not the main issue. The idea that the "smeared" electron can/may emit is the problem. You previously said that "no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating", and now you seem to forget/dismiss it ... This raises again the issue about falling towards the nucleus, as long as there is no force in this "smeared" electron interpretation to prevent it. Again, a "complicated distribution" of a static Moon around the Earth, would result in pieces of the Moon falling to the ground. Why is this not happening with the "smeared" electron? Maybe because the electron still rotates, but it's much more convenient to work with wave functions instead of particles?

And if the "smeared" electron does emit when the atom accelerates (rotates or vibrates), how is the electron energy "replenished"? This was a big issue for the orbiting electron ...

 

[A.T.]

Again, a "complicated distribution" of a static Moon around the Earth, would result in pieces of the Moon falling to the ground. Why is this not happening with the "smeared" electron?

Because this analogy is flawed?