Good question- this was a clear and troubling problem in the classical atomic models before quantum mechanics. Thinking of electrons as little balls whizzing around, being attracted and repelled by various field forces does seem to lend itself to this question.
The current understanding is that since electrons are quantum particles, they can only gain or lose energy through quantized packets, and can only occupy certain energy states. In fact, it's much more accurate to describe electrons by their probability fields, and not as those little balls. Quantum mechanics then describes probability shells called Sommerfeld orbits, where the chance of finding an electron at any given point peaks. Unless energy is added or removed from the system by those aformentioned quantized packets, electrons tend to remain at their respective energy levels and shells.
Just to clarify. An electron moving freely through a vacuum can move at any speed; it is not restricted to certain energy levels. (Speed and therefore kinetic energy is relative to the reference frame anyway.)
The quantization of energy comes into play when the electron is spatially confined in some system. This is related to the wave behavior of the particle, and because energy is related to wavelength. Much like how a standing wave on a string can only have wavelengths such that an integer multiple of them fit on the string.
I'd guess having an intuition about why only the first orbital is spherical is probably part of understanding this all properly too, will keep-on reading!
https://en.wikipedia.org/wiki/Earnshaw%27s_theorem
> Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic fields, but was first applied to electrostatic fields.
My (student of physics) answer to that would be that they are pretty much collapsed as much as they can. It’s just that under quantum mechanics that least energetic state is not the one in which the electron is perfectly co-localized with the positive charge. (As that perfect co-localization is not even physically attainable.)
It seems to me this is simply a statement that an electron is a fermion not a boson, right?
But if a layperson wants an intuitive sense of the situation, then that doesn't really illuminate. It's a fermion, but why should it be?
I like to read Wikipedia and popularized stuff. The problem is I come away unsatisfied, because even the best writing directed at people who aren't good at math, is more about giving the feeling of understanding than actual understanding.
My point about bosons and fermions, is I read the summary on Wikipedia, but they are just labels to me. I don't have the intuition or math except that it says the one kind of thing can "overlap" in ways the other can't.
Richard Feynman's "QED: The Strange Theory of Light and Matter" has been much praised though. What did I get out of it? I guess that quantum mechanics has something to do with multiplying complex numbers.
I'm not sure exactly what I'm missing, but I get the impression that if I could understand Hamiltonians, Lagrangians, or variational calculus, then I would have some insight into modern physics.
Some of it sounds tantalizingly straightforward, but at the same time beyond my mental capacity - imagine a space, a field, etc. - but it's infinite-dimensional or something. Or it's a space of functions.
Still, on Wikipedia you can keep clicking on things - what's a "fiber bundle", etc.
I completely know what you mean about the complex numbers and Hamiltonians etc. A lot of the time I think I could even have a reasonable chance of understanding the concepts given a few graphs/diagrams and some kind of translation to prose/pseudocode (or even just code) but there is so much symbolic syntax in both maths and physics (too much for me!) - I think it's probably hard to become fluent unless you use it every day I reckon.
I can also imagine something like a 'reasonably realistic' subatomic particle simulation framework in a 3D engine where one could fully control time space, energies, polarisation, quantum stuff etc and really examine the events in detail. I think one could perhaps start to get a feel for how it all fits together just by playing with the various interactions and watching/virtually-measuring carefully?
Not really, that's a property of any quantum particle, bosons also. They don't occupy a single point in space like you would imagine classical particles do. They also cannot occupy a single point in space relative to another particle.
> It's a fermion, but why should it be?
Well there's the spin-statistics theorem in quantum field theory which starts from some likely assumptions and then shows that particles with non-integral spin must be fermions while particles with integral spin must be bosons. Other than that I take it simply as an experimental fact. I don't think there's a nice reason for it one could give (today, that is).
But then, you have (or would have.. I think it's not experimentally verified) degenerate states of matter, like in a neutron star, where pressure is so big that the electrons collapse into protons to form neutrons.