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If electrons have no substructure and are considered point particles (according to the Standard Model), then how can they also have intrinsic spin? It would seem that the fact that they exhibit spin would indicate some further complexity to their structure, even if it may not be readily determined.

Jiminion
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    What do you think spin is? – Kyle Kanos Feb 09 '15 at 17:02
  • I think spin is something which has a physical property. Proton spin is alignment can be discerned by its quarks, but with no substructure, electrons can't do this. – Jiminion Feb 09 '15 at 17:14
  • @Jim: You may want to read this answer. – Kyle Kanos Feb 09 '15 at 17:25
  • By the way, the accepted answer in this related question and similar posts talk about spin arising naturally from the extension of the space in which the angular-momentum commutation relations act. They are correct in the sense they show that 1) spin must exist and 2) it is an intrinsic quantity. Read the O'Hanian paper linked in my answer to get a feeling of what is spin. – Hector Feb 09 '15 at 17:31
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    Various comments relating to a ... ehm ... "off-the-beaten-track" ... yeah, that ... theory deleted. – dmckee --- ex-moderator kitten Feb 09 '15 at 17:37
  • I'm willing to delete this question if you want, but at least the related one is only 6 months or so old. (I changed the title to something more specific.) – Jiminion Feb 09 '15 at 18:01
  • You can take a look at this quesion – Self-Made Man Feb 09 '15 at 18:11
  • @KyleKanos, thank you for the referred question, but the answer (to it) asserts that electrons are point particles to "prove" that spin has no classical connection. I feel that it is assumed electrons are point particles, but this is not proven. I also believe quantum spin has some footing or presence in the classical world. These seems to be the case with other quantum properties. – Jiminion Feb 09 '15 at 18:31
  • Interesting. The answer provided contradicts the accepted answer from the related question added to the original post... – Jiminion Feb 09 '15 at 20:08
  • Pardon my French, but that marking is crap! The question that "has been asked before" has a completely different answer! – Jiminion Feb 10 '15 at 05:41

1 Answers1

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First, the electron is not a point particle. The abstraction you are thinking of is what we would call a naked electron. In an experiment, you do not see the naked particle ever. It is always surrounded by virtual pairs. Hence, what you measure as the electron is really a many-body system.

Second, you might want to read this. The take-home message is "the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron". Another useful quote: "The spin is intrinsic, or inherent, i.e., it is a fixed feature of the wave field that does not depend on environmental circumstances. But it is not internal, i.e., it is not within the internal structure of the electron or photon".

Hector
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  • First, the electron is not a point particle. but why not? – Paul Feb 09 '15 at 17:21
  • @Paul: Naked electrons might be point particles, but we cannot see them. Just like elves might have pointy ears. Asking 'why not' about properties of things we do not see is like asking why shouldn't elves have pointy ears. Even when you have electrons in a vacuum, you have that the vacuum is polarized and what you really measure is the overall effect of the naked particle plus the cloud around it. – Hector Feb 09 '15 at 17:27
  • I like the second part of the answer (last sentence) but not so much the first part. If spin is intrinsic to a many-bodied system around an electron, then it's not intrinsic to the electron. – Jiminion Feb 09 '15 at 18:00
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    @Jim: A naked electron is no different than dry water, inextensible strings, single photons, and other mathematical abstractions that ease our calculations but do not exist in nature. – Hector Feb 09 '15 at 18:11
  • Then wouldn't the spin be shared amongst the interacting bodies? Is this an accepted assertion? – Jiminion Feb 09 '15 at 18:31
  • @Jim: Sort of. You cannot separate the naked particle from the polarized vacuum around it. You measure the spin of the whole system. Your sentence 'wouldn't the spin be shared amongst the interacting bodies' might also be interpreted as: every little constituent has spin 0.0001 that adds up to 0.5. This last interpretation would be incorrect. – Hector Feb 09 '15 at 18:50
  • OK, I'm grooving on this explanation a bit more; that spin has a classical analogue in the movement of the electron as-wave. But wouldn't this mean that spin would disappear with electrons as-particles? Maybe that doesn't matter or is a nonsensical statement. – Jiminion Feb 09 '15 at 19:50
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    @Jim: Even if electrons were billiard balls of infinitesimal radius, they would produce an electromagnetic field in its surroundings. The energy of that field would still be circulating to produce the spin. I added a quote from Ohanian's paper to the answer. It deals with 'intrinsic' but not 'internal'. Read the paper, it is full of nice quotes such as "spin is essentially a wave property, but whether the wave is classical or quantum mechanical is of secondary importance". After reading that paper, you will agree that "We no longer need to regard the spin as a mysterious entity." – Hector Feb 09 '15 at 20:00
  • I like what the paper says, but is that widely accepted? I hear lots of other Physicists (even on this site) saying a very different thing; that electron spin is basically an intrinsic magic we need to simply accept. (I.e., this answer basically completely contradicts the accepted answer from the related question added to my original post!) – Jiminion Feb 09 '15 at 20:05
  • Well, then do some research and 1) try to find published rebuttals to that paper, 2) reproduce the calculations yourself trying to find flaws in the reasoning, and 3) share with your peers your ongoing results. Just do not accept magic (unless you are an engineer, in which case a black box is fine). Cheers. – Hector Feb 09 '15 at 20:23
  • @Jim as with everything else, the black box approach (it is a magic number) has its uses. The same way most of the time you "accept" $E=mc^2$, without going through the whole derivation. Most QM situations in this case don't require knowing where the spin comes from, and explaining it would derail far away from the question. – Davidmh Feb 09 '15 at 22:08
  • I have to correct a comment of mine. What produces the spin of the electron is not the electromagnetic field but the electron field. So, my comment should have been "Even if electrons were billiard balls of infinitesimal radius, they are excitations of the electron field in its surroundings…" – Hector Feb 10 '15 at 03:35
  • I'm accepting this answer because 1) It is thoughtful, 2) It is the only answer! and 3) It contradicts the answer from the so-called "same question". So perhaps it's good this question is here; people it seems, can just pick and choose the Physics they want to see...... :) – Jiminion Feb 10 '15 at 05:43