Timeline for What is the uncertainty principle?
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| May 2, 2015 at 8:18 | comment | added | Stan Liou | @Muphrid the differences are that (1) wavenumbers would have no role in that description at all, (2) even Hilbert space, the uncertainty principle is more general than square-integrable functions. So I was recommending that context of your answer to be be explicitly specified. If you don't agree, ok. It's not so important as to fight over. | |
| May 2, 2015 at 8:00 | comment | added | Muphrid | @StanLiou Sorry, I don't really see the difference. I described (on a very broad and hopefully accessible level) the notion of standard deviation of some function or distribution. I used the word "wave" to emphasize the connection with wavefunctions in Hilbert space, yes, but this is applicable to any square integrable function. Even in phase space formalism, one ultimately arrives at a statement of uncertainty that involves a product of standard deviations, does one not? So I'm not appreciating any fundamental difference here. | |
| May 2, 2015 at 7:03 | comment | added | Stan Liou | @Muphrid just that. For example, if do QM in phase space, what you would use is a real-valued quasiprobability distribution $P(x,p)$ that's possibly negative but whose absolute value is bounded by something $\propto 1/h^3$, so you can't localize it arbitrarily, but not for reasons of waves. ... Physically, QM doesn't happen "in Hilbert space"; the Hilbert space is just one description. ... But even in Hilbert space, one should be mindful that all kinds of observables can have uncertainty between them, and the wave/Fourier analogy only works for those with commutator $i\hbar$ or similar. | |
| May 2, 2015 at 6:55 | comment | added | Muphrid | Sorry, what do you mean by, "this is only a peculiarity of the Hilbert space formulation"? | |
| May 2, 2015 at 6:53 | comment | added | Stan Liou | I think you should specify that you're only concerned with one particular description of one particular pair of observables. Otherwise, this answer does neither the physics nor mathematics all that well... Even for $x,p$, this is only a peculiarity of the Hilbert space formulation; it's not physically fundamental. But there is intrinsic uncertainty between any non-commuting of observables, so even mathematically, the uncertainty principle is not really about waves. (The accepted answer has a similar lack, but it's much more obvious how to generalize an instrumentalist description.) | |
| S May 2, 2015 at 3:58 | history | mod moved comments to chat | |||
| S May 2, 2015 at 3:58 | comment | added | David Z | Comments are not for extended discussion; this conversation has been moved to chat. | |
| May 1, 2015 at 20:47 | history | answered | Muphrid | CC BY-SA 3.0 |