# item in quantum mechanics **URL:** \ **Category:** Factual Questions\ **Created:** [November 8, 2014, 2:01am UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038 "2014-11-08T02:01:37Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [November 8, 2014, 2:01am UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038/1 "2014-11-08T02:01:37Z")
Spin is a concept in QM which is _kinda sorta_ like the rotation of an object: it has the quality of angular momentum, for instance. > **[Spin (particle physics)](https://en.wikipedia.org/wiki/Spin_%28physics%29)** > > Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin should not be simply understood as in the "rotating internal mass" sense. There is another type of angular momentum that more closely resembles rotation in classical mechanics, called orbital angular momentum. The orbital angular momentum operator appears when there is periodic structure to its wave function as the angle varies. The existen... Is there a analogous QM concept regarding _linear momentum_ which is _not quite_ the same as an object moving through space? OOPS! though this was General Questions. Mods, please relocate. ---
**Author:** ![Itself](https://avatars.discourse-cdn.com/v4/letter/i/d07c76/32.png) [@Itself](https://boards.straightdope.com/u/Itself)\ **Post date:** [November 8, 2014, 2:35am UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038/2 "2014-11-08T02:35:42Z")
I’m not quite sure what sort of thing you’re looking for here. Spin is really just a thing that elementary particles apparently have; the notion of it representing some sort of internal rotation around an axis is an awful analogy. I guess the obvious answer in that momentum is classical mechanics is replaced by 4-momentum, which is just the 4-vector p = (E, p\_1, p\_2, p\_3) (with E = energy). That’s really just a bookkeeping measure, but it’s much better behaved under relativistic transformations than energy and momentum would be separately. As for other interesting conserved quantities, I can’t really think of any nifty ones offhand. Classically, energy, momentum, and (classical) angular momentum arise via Noether’s theorem from symmetries of the universe: time, translation, and rotation. I’m not sure what else would fit into that sequence. There are some more esoteric conservation laws in particle physics, but nothing that would correspond to a special type of momentum. (They’re more along the lines of prohibiting certain categories of processes.) So, going back to the 4-momentum idea, how about this: Classically, photons have zero momentum: They have no mass (and finite velocity), so mv = 0. But photons do have nontrivial kinematics; take Compton scattering, for example. The “extra, hidden” linear momentum is really just a relativistic, rather than quantum-mechanical, thing, but I can’t think of a better example. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [November 8, 2014, 3:53pm UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038/3 "2014-11-08T15:53:32Z")
If you had particles in a box with periodic or anti-periodic boundary conditions, you would have linear momentum behaving analogously to spin. If some particles satisfied periodic boundary conditions, they could have zero linear momentum, or integer multiples of a lowest linear momentum, analogous to bosons. If other particles had anti-periodic boundary conditions, those particles could have 1/2, 3/2, etc. times that lowest linear momentum, analogous to fermions. They couldn’t have zero linear momentum. If the universe is closed, this would be the case, but that discretization would be so small, it would be undetectable. ---
**Author:** ![Idle\_Thoughts](https://avatars.discourse-cdn.com/v4/letter/i/838e76/32.png) [@Idle\_Thoughts](https://boards.straightdope.com/u/Idle_Thoughts)\ **Post date:** [November 8, 2014, 6:52pm UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038/4 "2014-11-08T18:52:09Z")
There you go, in GQ now. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [November 8, 2014, 7:38pm UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038/5 "2014-11-08T19:38:05Z")
I think mass would be the nearest, but not exactly analogous quantity to spin. The non-negative energy irreducible representations of the Poincare group can all be indexed by spin and mass. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [November 9, 2014, 3:36am UTC](https://boards.straightdope.com/t/item-in-quantum-mechanics/704038/6 "2014-11-09T03:36:22Z")
The only answer I could get behind is: no, there is nothing analogous to spin for linear momentum.