Timeline for Mathematical "proof" of the stability of atoms?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 22, 2013 at 3:08 | comment | added | user21349 | The distance is the same in both scenarios: it's the range of the residual interaction, which is on the order of the Bohr radius. | |
| Jan 22, 2013 at 1:47 | comment | added | Chris Gerig | No, because in one scenario the matter is already close, and the second scenario the matter starts at a distance -- those two pieces of matter don't come close enough for exclusion principle to dominate. | |
| Jan 22, 2013 at 1:45 | comment | added | user21349 | When you talk about the reason we don't fall into the ground, you're referring to the normal force between your foot and the dirt. When you talk about "why matter doesn't collapse in on itself," you're talking about internal normal forces within the matter (plus the fact that the individual atoms don't collapse). In both cases, we're discussing the microscopic explanation for a normal force. The explanation is fundamentally the same in both cases, and in both cases it requires both electrical interactions and the exclusion principle. | |
| Jan 22, 2013 at 1:40 | comment | added | Chris Gerig | I didn't say it was the sole cause, you definitely need both, but electric repulsion is the dominant cause. And stability of matter is different from the separation of two pieces of matter. | |
| Jan 22, 2013 at 0:51 | comment | added | user21349 | "if you want to talk about why we can stand on the ground without falling through it, then the dominate cause is electrostatic repulsion (i.e. the electromagnetic force)." I don't think this is right either. Neither electromagnetic interactions nor the exclusion principle suffice to explain the normal force between your foot and the ground. You need both, and Lieb is forced to invoke both in section II: "The extra factor $N^{2/3}$ is essential for the stability of matter; if electrons were bosons, matter would not be stable." | |
| Jan 22, 2013 at 0:44 | comment | added | user21349 | @Chris Gerig: "the reason for the stability of matter (i.e. why matter doesn't collapse in on itself) is due to the quantum degeneracy pressure (i.e. the Pauli exclusion principle)." I don't think this is accurate. In section I, Lieb proves the stability of an isolated hydrogen atom, where the exclusion principle is irrelevant. If that calculation had come out a different way (say, because we changed the behavior of the electric force), then matter would be unstable for reasons having nothing to do with the exclusion principle. | |
| Jan 21, 2013 at 20:11 | comment | added | Chris Gerig | In particular, the reason for the stability of matter (i.e. why matter doesn't collapse in on itself) is due to the quantum degeneracy pressure (i.e. the Pauli exclusion principle). On the flip-side, if you want to talk about why we can stand on the ground without falling through it, then the dominate cause is electrostatic repulsion (i.e. the electromagnetic force). | |
| Jan 21, 2013 at 18:21 | vote | accept | user30830 | ||
| Jan 21, 2013 at 18:17 | vote | accept | user30830 | ||
| Jan 21, 2013 at 18:17 | |||||
| Jan 21, 2013 at 18:13 | history | answered | Uwe Franz | CC BY-SA 3.0 |