I.e., classical approximations are wrong. Does that make them useless? It seems to me that's in the eye of the beholder. One could ask the same question about planets: why don't they fall onto the sun the same way everything that goes up comes down? One could give the same answer: they have angular momentum so the planet would have to speed up to a ridiculous extent. One could raise the same objection to the answer: the angular momentum is carried away as gravity waves. It seems to me that doesn't make the Newtonian picture of celestial mechanics useless; YMMV.
Sure; but how much angular momentum would leak away in the emitted light and how much would remain in the electron, hence, how fast would the electron be going? Back of the envelope, I make it about three times the speed of light...
Oh, okay, my bad. Can you explain the distinction?
And in quantum mechanics, everything is more complicated than any simple summary. Once in a while, if the various energy levels are just right, the electrons and the protons in atoms really do click together like all things with opposite charges do. Radioactive rubidium-83 decays by electron capture. An electron and a proton turn into a neutron and emit a neutrino to carry away the extra angular momentum, just as if it were in a neutron star.
That makes them less than useless.
Your theory is not even wrong. Electron rotating around nucleus DOES lose angular momentum and DOES fall, in both in QM and in classical mechanics. It's just in QM it stops falling down when it reaches lowest possible orbit, which has zero angular momentum,
1/137 of speed C.
One is about black body radiation, another about electron falling on a nucleus due to radiation.
Curious, why call out photons and electrons? The effects we see in atoms can be similar as well. The double slit experiment can be done with buckyballs which are enormously massive compared to electrons.
Honestly, analogies are overleveraged for value. I hate analogies because they rarely ever describe what needs to be described.
If you say so. Forty-odd years ago I attended a lecture by Dr. Chandrasekhar. He opened with a demonstration of the power of dimensional analysis, using a classical model of the atom to derive a formula in a couple of minutes with which he calculated that the total number of chemical elements was about a hundred. Uselessness appears to be a matter of opinion.
Only in the s orbitals. Most of the electrons in most of the elements still have orbital angular momentum.
That's the speed in an orbit at the scale of an atom; we were talking what the speed would be if an electron were able to spiral down to the nucleus, about a hundred thousand times closer.
Because electrons are the things being discussed? I wasn't 'calling them out', I was just using them as examples. The photon I picked because it's a convenient zero rest-mass entity with strong relevance to electron behaviour, and exemplifies the fact that I am not just discussing massive particles.
Sure.
I rather like analogies, and I think they can be very helpful. But not in this case, because there really isn't a commonly experienced entity that is analogous to the things being discussed.
It really seems to be neither. It lacks features of both that are widely expected to be defining. For example, a particle has a defined location, and a wave occurs in a medium. Electrons (and photons, and other quantum scale objects) don't fit either criterion.
I think it gets lost that electrons aren't remotely special in this behavior. You are correct though that the subject was electrons, not just 'crap that does "odd" stuff in the quantum world'.
The problem is, people are crap with analogies.
This applies to larger things as well. If buckyballs act as a wave and we "know" that they are particles, it suggests particles themselves aren't exactly just particles.
My question is, if we do a double slit experiment with billiard balls, what is the result? I mean other than using up impossible resources to scale the experiment.
