Timeline for Can we alter the axioms of Euclidean space to have $\mathbb{Q}^3$ as a unique model?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Dec 12, 2010 at 15:13 | comment | added | Hans-Peter Stricker | What are the real rational integers? Googling (google.com/search?q="real+rational+integers") didn't reveal a lot. | |
| Dec 10, 2010 at 19:04 | comment | added | Nick S | For me a more natural candidate would be the $A^3$, where $A$ is the set of real rational integers. Otherwise, you would end up with certain standard curves (which physisist are interested) only having finitely many points. The question is then: what is arclenght or area and how do you calculate it? | |
| Dec 10, 2010 at 13:15 | answer | added | sleepless in beantown | timeline score: 1 | |
| Dec 10, 2010 at 7:53 | comment | added | Hans-Peter Stricker | That's a good point, thank you! (Nevertheless, in principle it might be the case, that physical space is locally isomorphic to $\mathbb{Q}^3$, isn't it? But we just could not - by finitary means - distinguish it from $\mathbb{R}^3$?) | |
| Dec 10, 2010 at 7:10 | comment | added | S. Carnahan♦ | The reasons that physicists tend to give for considering discrete models of spacetime also eliminate metric spaces like $\mathbb{Q}^3$ from consideration. In particular, path integration seems to be significantly harder to axiomatize in your model than in the traditional picture. | |
| Dec 9, 2010 at 12:33 | answer | added | user2529 | timeline score: 6 | |
| Dec 9, 2010 at 11:57 | history | edited | Hans-Peter Stricker | CC BY-SA 2.5 |
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| Dec 9, 2010 at 9:13 | history | asked | Hans-Peter Stricker | CC BY-SA 2.5 |