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On the Wikipedia page it says that spin is a form of angular momentum. Wikipedia also say particles are dimensionless. However if particles are actually "dimensionless" there would be no way to deduce angular momentum, since angular momentum requires non-uniform momentum of an entity, which has to mean the entity consists of more than one point in space. Can someone explain to me how these two concepts are compatible?

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marked as duplicate by ACuriousMind, Norbert Schuch, rob, Rob Jeffries, Wolpertinger Oct 5 '16 at 21:41

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/1/2451 , physics.stackexchange.com/q/822/2451 and links therein. $\endgroup$ – Qmechanic Oct 5 '16 at 19:56
  • $\begingroup$ We don't know that they are dimensionless, we only have an upper bound. Spin as up and down is part of an abstract , not real, space. $\endgroup$ – user108787 Oct 5 '16 at 19:56
  • $\begingroup$ Wiki says that they are dimensionless I also don't think those questions address my particular concern of angular momentum of a dimensionless entity. $\endgroup$ – Yogi DMT Oct 5 '16 at 20:17
  • $\begingroup$ spin has units of $h$, which has units of angular momentum $\endgroup$ – user126422 Oct 5 '16 at 20:18
  • $\begingroup$ Comment about terminology: Wikipedia says that they are zero-dimensional. The word dimensionless is instead typically used in the context of dimensional analysis. $\endgroup$ – Qmechanic Oct 5 '16 at 20:49
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well spin it's an intrinsic angular momentum,it's not that the electron is actually spinning ok it's a way to understand the concept since there is not classical analogy for that concept. Also one thing, that not because the particle might be dimensionless, you wont be able to extract information, for example: A ball attach to a string and you make it spin, this has angular momentum but the ball dimension(meaning the volume in space that occupies) never come into play when you calculate the angular momentum it just matter its momentum and the distance($L = \vec{r} \times \vec{p}$).(In quantum mechanics by the way we don't work particles it self, but with state-vectors) Now the wave function that represents the particle in quantum mechanics in Schrodingers theory it's not dimensionless it has dimension of $1/\sqrt{L^{3}}$ . Now the important part of in quantum mechanics is the probability to find a particle somewhere in space and you can do that. If you want to read a bit more of this you can go to a friendly books like concepts and applications in quantum mechanics zettili. Best Regards.

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That is the mystery of "spin". Even point particles can have spin and thus angular momentum as an essential quantum mechanical property even though they have no spatial extension.The spin or angular momentum of e.g. an electron cannot be considered to be the result of a bodily rotation.

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  • $\begingroup$ Tbh my question isn't really QM specific. Angular momentum and an entity with zero dimensional are incompatible concepts abstractually. It's either one or the other, not both. $\endgroup$ – Yogi DMT Oct 5 '16 at 20:31
  • $\begingroup$ No this is not correct. These concepts are only incompatible when you try to explain the intrinsic spin of a particle by classical mechanical models. $\endgroup$ – freecharly Oct 5 '16 at 20:40
  • $\begingroup$ It wouldn't be intrinsic spin then it would be something else $\endgroup$ – Yogi DMT Oct 5 '16 at 20:45

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