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As far as I know, you can't necessarily isolate an electron to observe it, you can only observe its effects on other particles due to fields. Moreover, we can't know an electron's exact location or how much space it occupies, although it has finite mass. It seems that the general model for the electron is either a wave or a rotating spherical particle. Being that we can only observe its mass/energy, how do we know that it is spherical and that some energy comes from a spin?

Edit: We have extensive comments on how the electron may not actually be spherical, and those models are purely for visual purposes. However, I am still wondering how someone determined that an electron spins. The Stern-Gerlach experiment was mentioned, but when I read up on that it seems that it is not a good experiment for charged particles as they will interact with the field.

M Barbosa
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    We don't know that the "electron is spherical". What does that even mean? (Are you referring to some measurement of magnetic moments which are sometimes described as the "shape"?) The evidence for spin, however, is easy to come by: Stern-Gerlach, Einstein-de Haas,... – ACuriousMind Jun 19 '16 at 16:31
  • @ACuriousMind no, I am not speaking of magnetic moments. Something waaaay more simple. Most visual models of the atom (or anything else that includes electrons) has the electron as a spherical body. Spherical means that all the points on its surface are equidistant to a common barycenter. Thanks the name of the experiments help! – M Barbosa Jun 19 '16 at 16:39
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    "Visual models"? Are you talking about the hopelessly outdated Bohr model? Because the proper visualization of atomic orbitals doesn't generally look spherical at all. – ACuriousMind Jun 19 '16 at 16:42
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    It don't spin, in the sense that a football spins. –  Jun 19 '16 at 16:43
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    @ACuriousMind chill man, not everything is a scientific operational definition. By "Visual model" I simply mean something that visually models something else, so if a professor draws a circle and calls that an electron, that is their visual model. That is a minor part of my question anyway, the main part was how did they determine that these particles actually spin, and I have a better idea now. Although Stern-Gerlach can't be used for charged particles because of the effects of the field. But I will figure something out. – M Barbosa Jun 19 '16 at 16:49
  • Possible duplicates: http://physics.stackexchange.com/q/11197/2451 , http://physics.stackexchange.com/q/8188/2451 and links therein. – Qmechanic Jun 19 '16 at 17:50
  • Electrons have intrinsic angular momentum, and this can be determined through observable experiments. http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html –  Jun 19 '16 at 16:27
  • I think it is a classical notion for purely quantum mechanical property of intrinsic angular momentum. – hsinghal Jun 19 '16 at 18:08
  • @Qmechanic that does give some insight, but I want to know specifically about the electron. Most people have been mentioning Stern-Gerlach, but that experiment seems to be invalid for electrons because they have a charge and would have a bent path in the magnetic field any way. – M Barbosa Jun 19 '16 at 18:10
  • @MBarbosa I don't get the question. Visual models are always incomplete, because they're just a cheap approximation to what's actually going on. You're asking us to explain how some aspect of a visual model works and the answer is that it doesn't. It's just a picture, a toy. – knzhou Jun 19 '16 at 18:21
  • @MBarbosa It's like looking at a still life of fruit and asking why the fruit doesn't rot after a few weeks. – knzhou Jun 19 '16 at 18:22
  • @knzhou okay thank you for the clarification on the decoupling of the visual model to the actual physics. But again, my main question is how did we determine that an electron spins. Any ideas on that? Stern-Gerlach does not work on electrons. The best answer so far seems to be that this is "a classical notion." – M Barbosa Jun 19 '16 at 18:26
  • @MBarbosa Have you heard of Einstein-deHaas? If you flip the spins of the electrons in a bar of iron, you can make the iron rotate. This confirms 'spin' is angular momentum. – knzhou Jun 19 '16 at 18:27
  • The reason spin was "invented" was in order to conserve angular momentum at the quantum mechanical level. With no spin on the fermions angular momentum conservation would no longer hold and this would also mean that a lot of fundamental processes that are disallowed by angular momentum conservation , with no spins, should exist. – anna v Jun 19 '16 at 18:27
  • There's an interesting paper of how to visualize electron spin as something 'actually spinning' but I haven't read it in detail. – knzhou Jun 19 '16 at 18:28
  • Thinking of double cover spaces is useful in this regard, but on a lighter note, spin is to electron what mind is to matter, we can only observe it, we need mathematical tools to describe it. – vbj Jun 19 '16 at 18:59

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Electrons And Spin From Scientific American

Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid 'objects' that can 'rotate' in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term 'spin,' however, still remains."

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    Kindly remove the block formatted formatting if this is your writing or give the reference. – hsinghal Jun 19 '16 at 18:04
  • @user108787 what are the quantum mechanics rules that makes the notion that electrons and protons are solid rotating objects in space being difficult? – Ernesto Melo Sep 21 '17 at 17:46
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Spin was assigned to elementary particles so that conservation of angular momentum would hold in the quantum mechanical framework of elementary particles and nuclei.

The Stern–Gerlach experiment involves sending a beam of particles through an inhomogeneous magnetic field and observing their deflection. The results show that particles possess an intrinsic angular momentum that is closely analogous to the angular momentum of a classically spinning object, but that takes only certain quantized values.

We know from this experiment that a spin has to be assigned to the electron.

It is conservation of angular momentum that demands an intrinsic spin.

The study of particles and resonances and their decay and interaction channels definitely showed that there were groupings, certain reactions were found and measured and others were not observed at all . The assignment of spin explained why some reactions were allowed and others not. The very existence of the neutrinos depended for years on conservation laws, including angular momentum conservation.

Spin assignment also revealed the allowed SU(3) representations classified according to spin that led to the symmetries and the quark model.

decuplet

A combination of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. The lower six are hyperons. S = strangeness, Q = electric charge

anna v
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We don't need to separate electrons out in order to observe them. The structure of an atom, as revealed in electron transitions (atomic spectroscopy) is clearly based on orbitals at specific energy levels, with a two-electrons-per-orbital limit. And, the collective behavior of unpaired electrons that gives rise to ferromagnetism, and subtle spectroscopic effects like spin-orbit coupling, are calculable. Those observed effects are verifications of the spin properties of an electron.

An electron need not be considered spherical, however; in an atomic orbital, at any rate, only zero-orbital-angular-momentum electrons are spherical. Those are the so-called S orbital states, but P, D, F orbitals haven't got spherical symmetry.

Whit3rd
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