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by posterboy
3152 days ago
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As would be the case for particles in intergalactic space. Recent news relayed studies confirming cold gas ligaments between galaxy clusters, in which particles are very far apart, moving really slow and radiation is emitted which is interpreted as a gauge for the temperature (which is so weak, ie. cold, it wasn't detected in previous surveys). edit:
The point is, the far distance leaves the particles "alone" pretty much. If it doesn't make sense for a single paryicle to be seen as a closed system, of course it can't be assigned a temperature. But with regards to cooling and a strict loss of energy, the system is semipermeable, isolated in one direction. Then from our point of view, there's heat. So for example, couldn't the temperature "be in" the electrons movement around the core (for lack of a better expression)? I mean, for a true resting state I would expect the electrons to fall into the core, not just ground state (annihilating the charges, so an atom really couldn't exist at absolut zero. But if you are looking at a point source as the center of your frame of reference, it couldn't exhibit brownian motion. Then maybe curves described by spacetime has potential wells and exited states above that and maybe particles jitter between closely parallel worldlines, if they are entangled with anything besides. |
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Note that neutrons are heavier than protons, and when alone undergo beta decay with a lifetime of about 15 minutes, turning into a proton, emitting an electron and an antineutrino. So a hydrogen atom, left alone, cannot undergo the process you suggest---there simply isn't enough energy for it. It's only at very high density that the coulomb interaction provides enough energy to perform this conversion. There may be new physics, such as proton decay, that changes this story, but as far as anybody knows, there is not.
Perhaps more precisely, at absolute zero temperature atoms with orbitals are mathematically what quantum mechanics predicts. I of course don't know how to produce an atom that cold in the lab :) Except... of course... I do know how to produce an atom where the electron is in its ground state. If I've just got one atom, that's easy-peasy. Then, what is its temperature? Because it's just one atom, it's not well defined.
There's a more interesting question you ask, though: can the electron have a tempature? The different energy eigenstates are populated with different amplitudes. The way those states are populated can have a well-defined distribution in terms of a superposition. But if we restrict ourselves to a classical case, as OP was thinking about, superpositions are not allowed. Then, again, you at least have a definite energy.
Moreover, just a single electron in a superposition of energy eigenstates... it's not clear to me that that thing has a well-defined temperature either, because 'average' energy means something other than an ensemble average.