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DanMP said: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!
DanMP said:So what force is preventing the electron to fall on/into the nucleus?
DanMP said: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?
Why must that be so?DanMP said:Again: if the electron is "smeared" around the nucleus but not falling into it, a force must keep it from falling.
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.ZapperZ said: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 ...
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 ...Nugatory said: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.
DanMP said: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)
Same issue - no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.DanMP said:How about my other question?
So radiation/photons is/are emitted both by the nuclei and by the "smeared" electrons, but they "cancel out"?DrClaude 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.
In Wikipedia I found (again, the underline is mine):Nugatory said:no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.
... 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, ...
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.DanMP said: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):
Nugatory said:no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.
about accelerating atoms, where the electron is accelerating as part of the atom, but not with respect to the nucleus.DanMP said:How about my other question?
DanMP said: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)
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 said: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 ...
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:DrClaude said: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 said:no position means no meaningful notion of acceleration
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.DrClaude said:I don't know where this Wikipedia quote comes from ...
Again, Nugatory is talking about electrons in an atom, not an accelerating atom.DanMP said: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:
Both of us, because we are not talking about the same thing.DanMP said:Again, who is right? And why?
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.DanMP said: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" ...
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 said: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?
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).DrClaude said:Again, Nugatory is talking about electrons in an atom, not an accelerating atom.
and then, about the "smeared" electron when it accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule):Nugatory 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.
But you said:Nugatory said:Same issue - no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.
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:DrClaude 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
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?DrClaude said: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.
There's an easy way to analyze the radiation produced by accelerating an atom and a hard way.DrClaude said:Again, Nugatory is talking about electrons in an atom, not an accelerating atom.
@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.DanMP said: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?
The energy can come from any source: thermal, collisions, etc.DanMP said: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?
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?DrClaude said:The energy can come from any source: thermal, collisions, etc.
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".Nugatory said: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).
Because this analogy is flawed?DanMP said: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?
Only in bad faith can you infer that this is what I was saying. As light goes through a piece of glass, that piece of glass will heat up and emit photons of lower frequency. Amplification only takes place if you manage to make a laser out of it.DanMP said: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?
You are the one who refuses to understand that @Nugatory was discussing stationary states of the electron in atoms. There is no state of the electron where it can fall into the nucleus.DanMP said: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?