Timeline for Why are discreteness and smoothness in physics inversed with respect to geometry?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2022 at 10:25 | vote | accept | Roland Bacher | ||
| Jun 17, 2022 at 7:25 | comment | added | Konrad Waldorf | Quantization is not a matter of zooming in or zooming out, it is a matter of high energy vs. low energy. | |
| Jun 14, 2022 at 19:45 | history | became hot network question | |||
| Jun 14, 2022 at 15:10 | comment | added | Moishe Kohan | Well, your question was about examples of mathematical objects with certain behavior. What the actual physical world is like we do not really know and such questions would be off-topic at MO. Maybe you want to add more restrictions. | |
| Jun 14, 2022 at 13:43 | answer | added | Carlo Beenakker | timeline score: 6 | |
| Jun 14, 2022 at 13:34 | comment | added | Roland Bacher | @MoisheKohan Kantor sets are obtained by removing pieces recursively and this has the same feeling as the 'It's turtles all-the-way-down'-thing. But perhaps I am wrong and the Universe is indeed 'turtling down'. | |
| Jun 14, 2022 at 13:24 | comment | added | მამუკა ჯიბლაძე | Very interesting question! I know next to nothing about it, but in physics there is a host of different kinds of dualities, including ones interchanging small and large scales. On the other hand there are some dualities in mathematics that might be similar in spirit to that. Back in 2017 I asked a question about possible relevance of the Spanier-Whitehead duality for physics but it did not produce much feedback, except for Aaron Bergman mentioning that possibly Alexander duality is more or less physicist's duality between charges and fields... | |
| Jun 14, 2022 at 13:19 | comment | added | Moishe Kohan | Ok, then tell me what do you mean by "natural": I find my example natural. | |
| Jun 14, 2022 at 13:16 | history | edited | Roland Bacher | CC BY-SA 4.0 |
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| Jun 14, 2022 at 12:57 | comment | added | Roland Bacher | @MoisheKohan Not a bad example (by the way, many similar examples arise from geometric group theory, e.g. fundamental groups of hyperbolic manifolds), but I feel somehow cheated: Things are not as 'natural' as in the manifold-case and our Universe seems quite natural to me. | |
| Jun 14, 2022 at 12:41 | comment | added | Moishe Kohan | Sure: Consider $M$ equal to all integer translates of a Cantor subset of $[0,1]$ and equip $M$ with the distance $d(x,y)=|x-y|$. As you zoom in, everything is totally disconnected ("discrete" in your terminology, I assume), when, as you zoom out, in the (Gromov-Hausdorff) limit you recover geometry of the straight line. | |
| Jun 14, 2022 at 11:55 | history | edited | Roland Bacher | CC BY-SA 4.0 |
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| Jun 14, 2022 at 11:44 | history | asked | Roland Bacher | CC BY-SA 4.0 |