Timeline for Is all angular momentum quantized?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2020 at 2:22 | history | edited | benrg | CC BY-SA 4.0 |
clarify
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| Aug 14, 2020 at 1:19 | comment | added | Chris♦ | @benrg And how are you going to implement a counter that counts how many times it has revolved if its Hamiltonian is free? You would need a pawl or something, which clearly alters the Hamiltonian. | |
| Aug 14, 2020 at 1:13 | comment | added | benrg | @Chris The point is that the states after different numbers of revolutions are orthogonal, therefore there's no interference between them, therefore no quantization. The position of the wheel in physical space doesn't matter, what matters is the phase space of the system. | |
| Aug 14, 2020 at 1:10 | comment | added | Chris♦ | @benrg The stored count clearly has nothing to do with the physical motion of the wheel. Keeping a count of that would require an extra term in the Hamiltonian anyway- if it's truly a free particle there's no way to update the count. | |
| Aug 14, 2020 at 1:06 | comment | added | benrg | @Chris Every value of $θ\in\mathbb R$ maps to a distinct state of the system. The system includes the counter and its stored count. | |
| Aug 14, 2020 at 1:05 | comment | added | benrg | @JoshuaTS I am treating these objects as quantum mechanical. | |
| Aug 14, 2020 at 0:04 | comment | added | Chris♦ | The system you've described is not essentially like a free particle in $\mathbb R$, it's essentially like a free particle in a loop (i.e. in $S^1$ rather than $\mathbb R$). The momentum spectrum of a free particle in a loop is not continuous, and neither is the angular momentum spectrum here. | |
| Aug 13, 2020 at 23:58 | comment | added | Technically Natural | Quantization is a quantum effect, so you are completely correct that it doesn't happen if we take the classical limit. However, every object should be treated, technically speaking, with the laws of quantum mechanics, so all angular momentum is quantized, even if those effects are not noticeable. | |
| Aug 13, 2020 at 23:27 | history | answered | benrg | CC BY-SA 4.0 |