Timeline for Why is there no need in extra knowledge to go from the classical to the quantum desctiption of a system?
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| Sep 7, 2016 at 13:58 | comment | added | Weather Report | @ACuriousMind Well, that's might be it, the textbooks fool us! I've always been suspecting that. Unfortunately, this would be hard to back up in detail. Let it stay a working assumption unless something better will show up. | |
| Sep 7, 2016 at 13:28 | comment | added | ACuriousMind♦ | @WeatherReport: The naive approach is not as naive as it seems: Try it with polar coordinates, or action-angle variables (this was Bohr's and Sommerfeld's original attempt) and it goes wrong rather quickly. The canonical quantization we teach today is finely crafted to be as naive-looking as possible while getting as much right as possible. | |
| Sep 7, 2016 at 13:24 | comment | added | Weather Report | I agree with your technical points but not with the general attitude. To quote your last sentence "it is remarkable how well quantization works as a general guiding principle". But that's what my question is about! Given a proper (quantum) theory aren't we able to explain this surprising universality of the classical limits which allow to reconstruct a lot of quantum behaviour without additional input, $f(\hbar)$ from $f(0)$? There are exceptions, of course, but they should not be surprising. It is the success of the naive approach which in my view deserves an explanation. | |
| Sep 7, 2016 at 12:58 | comment | added | image357 | I can't agree with your first sentence: "The "reason" why the procedure of quantization works cannot be known. Asking why that which describes nature describes nature is not a question physics can answer." There could simply be an underlying principle that in turn leads to the need of applying quantization rules to Lagrangian-theories. That principle could in fact just be as reasonable as the principle of relativity or some experimental confirmable statement (e.g. constancy of light for relativistic mechanics). | |
| Sep 7, 2016 at 12:20 | history | answered | ACuriousMind♦ | CC BY-SA 3.0 |