Timeline for In what ways is physical intuition about mathematical objects non-rigorous?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jun 13, 2010 at 2:16 | comment | added | Greg Kuperberg | José: Sure, I'll grant then that by these semantics, it would be difficult to argue for an outright flaw in logic in a theory paper that's supported by experiment. | |
| Jun 13, 2010 at 1:42 | comment | added | José Figueroa-O'Farrill | Greg: A leap of faith in Physics is not the same thing as a flaw in logic, simply because Physics is not a deductive science. Physics is an empirical science and in modelling physical phenomena assumptions are often made which allow one to arrive at predictions (perhaps by simplifying the analysis of the model). In the end, such assumptions either live or die based on their ability to conform to experiment. | |
| Jun 12, 2010 at 23:00 | history | edited | Joseph O'Rourke | CC BY-SA 2.5 |
solve->solved :-)
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| Jun 12, 2010 at 22:19 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
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| Jun 12, 2010 at 22:15 | comment | added | Greg Kuperberg | Well yes, Victor, but such examples fall under case 2. The Copenhagen/von Neumann model of quantum probability is the part that is hard to believe, and it is rigorous. | |
| Jun 12, 2010 at 22:09 | comment | added | Victor Protsak | I am not sure I agree that "quantum mechanics is entirely rigorous". There is an axiomatic conceptual scheme for quantum mechanics, but most interesting physical computations aren't rigorous. For example, look at the derivation of tunneling probabilities using quasiclassical approximation in any QM textbook. It required a major effort on mathematician's part to "rigorize" even some of that theory (Maslov index, Lere's lagrangian analysis, Guillemin-Sternberg's geometric asymptotics). | |
| Jun 12, 2010 at 21:10 | comment | added | Greg Kuperberg | José: It is of course a leap of faith to make approximations without error bounds. For instance, no one can prove that the Navier-Stokes equations even have full solutions, but some of the simplifications of these equations do have solutions. Arguably a more serious case is condensed matter theory (and even molecular physics), where people have a great deal of faith in the Schrodinger equation for N particles, but a great deal less faith in the zillions of approximate models that are inspired by it. | |
| Jun 12, 2010 at 20:35 | comment | added | José Figueroa-O'Farrill | In what sense is the shallow water approximation -- or any approximation, for that matter -- a flaw in logic? And in what sense would it constitute a lack of rigour? | |
| Jun 12, 2010 at 17:38 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |