Timeline for Poincaré recurrence and its implications for statistical physics and the arrow of time
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2022 at 3:11 | comment | added | Aaron Bergman | Somewhere between physics and philosophy lies Boltzmann Brains. | |
| Aug 30, 2022 at 18:59 | comment | added | display llvll | maybe people downvoting could explain what’s so upsetting about this question… | |
| Aug 29, 2022 at 19:02 | answer | added | Buzz | timeline score: 7 | |
| Aug 29, 2022 at 8:54 | vote | accept | display llvll | ||
| Aug 29, 2022 at 1:15 | history | became hot network question | |||
| Aug 28, 2022 at 20:07 | comment | added | Robert Furber | The accelerating expansion of the universe spoils attempts to prove that the whole configuration of the entire universe will recur (even up to $\epsilon$). | |
| Aug 28, 2022 at 19:45 | answer | added | Carlo Beenakker | timeline score: 12 | |
| Aug 28, 2022 at 19:31 | comment | added | user164898 | It does not really answer the question, but here is what Arnold had to say, in "Mathematical methods of classical mechanics": "The following prediction is a paradoxical conclusion from the theorems of Poincare and Liouville: if you open a partition separating a chamber containing gas and a chamber with a vacuum, then after a while the gas molecules will again collect in the first chamber[...] The resolution of the paradox lies in the fact that 'a while' may be longer than the duration of the solar system's existence." | |
| Aug 28, 2022 at 19:16 | history | edited | display llvll | CC BY-SA 4.0 |
added 209 characters in body
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| Aug 28, 2022 at 19:11 | comment | added | display llvll | @QiaochuYuan I don’t think it’s the same as for the central limit theorem. To me what you say is just that we cannot ever experience nor observe the example of the gas, which of course I agree with. But the rest of what you say is quite speculative: I may be wrong but i don’t think in physics there is a clear consensus about the “expected lifetime” of the universe, let alone what would it mean for it to “end”, and it does not exclude a recurrence phenomen. | |
| Aug 28, 2022 at 18:31 | comment | added | Qiaochu Yuan | The Poincare recurrence time for a macroscopic gas is on the order of something like $2^{10^{23}}$, a completely unphysical number that physicists don't care about, and much larger than the expected lifetime of the universe. It's like arguing that the central limit theorem can technically fail with some tiny probability for a large but finite number of independent samples; that's true but with sufficiently many observations it's vanishingly unlikely. | |
| Aug 28, 2022 at 17:59 | comment | added | display llvll | thanks for the comment. I see your point, but i believe interpretations of mathematical physics theorems should be seen as part of mathematical physics, hence of mathematics. Hence an answer to this question would be of interest for a mathematical audience. But someone already downvoted this question, so maybe people share your view. | |
| Aug 28, 2022 at 17:25 | comment | added | Sam Hopkins | To me this question - asking for the physical interpretation of a mathematical result - is more physics than math; but anyways I have routinely seen ergodicity (including Poincaré’s work) contrasted with KAM theory (which would say something "opposite": that the system retains some knowledge of its initial conditions). For example I believe Cédric Villani has given many talks with this theme. But probably others who are experts in mathematical physics can say more. | |
| Aug 28, 2022 at 17:22 | history | edited | display llvll | CC BY-SA 4.0 |
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| Aug 28, 2022 at 17:14 | history | asked | display llvll | CC BY-SA 4.0 |