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I was recently reading about Higgs boson and particle spin and I stumbled upon a question that explains what is spin.

It explains that electrons have no size yet they have angular momentum. I don't understand what exactly is meant by that. Does it refer to the angular momentum of the magnetic field? I just don't see how something with no size can have any sort of angular momentum.

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Xitcod13
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  • You've check marked wrong answer. Spin is an attribute of individual electron.. not of a collection of electrons. – Earth is a Spoon Jul 07 '12 at 10:10
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    Please do not accept wrong/vacuous answers, it dilutes the value of the site. Sachin Shekar's answer is not good. The spin angular momentum is a real honest to goodness angular momentum, not a mathematical analogy. It can be seen in the Einstein deHaas effect. – Ron Maimon Jul 08 '12 at 07:33
  • Thank you for your comment I will look into it. I do not know enough about it to decide which answer is the best yet but i will read the Einstein deHaas effect and then try to judge. I dont know what to do in a situation like this If there is a way to start a discussion about which answer is better or have community resolve this problem in another way. Otherwise I will do my best. – Xitcod13 Jul 08 '12 at 20:58

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It means exactly what it says--- the point particle has an angular momentum. In quantum mechanics, angular momentum is dimensionless (since hbar has units of angular momentum), and saying the spinning electron has angular momentum means that if you have a large number of electrons with spin up sitting on a disk (like a disk magnetized with a B field going in one direction perpendicular to the disk), and you suddenly reverse the B, so that all the electrons flip their spin to the other direction, then the disk starts spinning to conserve the angular momentum of the flip. This is the famous Einstein deHaas experiment that established that magnetization is carried by electron spin.

Ron Maimon
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  • Electron disc spinning has to do with "Orbital Angular Momentum". The experiment you mentioned is related with this.. – Earth is a Spoon Jul 07 '12 at 08:55
  • Spin quantum number is unitless.. it doesn't mean, Spin is dimensionless. Spin does have dimension of angular momentum.. – Earth is a Spoon Jul 07 '12 at 09:00
  • @SachinShekhar: The experiment I mentioned is (mostly) to do with spin angular momentum, or at the very least gets a large spin component. About the units, once you do quantum mechanics, you should change your units to make $\hbar=1$, and then angular momentum becomes dimensionless. If you keep ordinary units, then of course you are right. – Ron Maimon Jul 07 '12 at 19:17
  • The experiment you mentioned shows classical relationship between magnetism, orbital angular momentum and spin. So, it doesn't involve spin by large credit. The disc is actually for orbital angular momentum. – Earth is a Spoon Jul 07 '12 at 19:48
  • Another thing: The experiment assumed electrons have radius. It wasn't quantum world. So, you shouldn't use it. – Earth is a Spoon Jul 07 '12 at 19:49
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    @SachinShekhar: This is incorrect--- the transfer is not due to field angular momentum, it isn't a macroscopic spinning up of the magnet because of field action. It's to do with the spin angular momentum of the electrons. When you flip the spin of all the electrons in a magnet, you start the magnet spinning macroscopically due to the angular momentum of the spinning electrons. The experimental paper might have assumed an electron radius (I didn't read it), but it doesn't need to, all it is using is that electrons have angular momentum. It's a reproduced classic experiment, why not use it? – Ron Maimon Jul 07 '12 at 19:56
  • What!!! You are changing Spin of electrons by changing direction of $\vec B$? And, you have all electrons having same Spin? Go read Pauli Exclusion Principle, first. – Earth is a Spoon Jul 07 '12 at 20:15
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    @SachinShekhar: yes, you are changing the spin of a sizable fraction of the electrons in the magnet by changing the direction of B. This is how it is done in a lab. "All" the electrons can have the same spin, they have different positions. By "all" I don't literally mean every single one, just the ones involved in making the magnet magnetized. When you flip B, you flip the magnetization, 2% of the electrons flip their spin, and the bar starts to rotate with the exact amount of angular momentum lost by the electrons. I prefer thinking to reading. – Ron Maimon Jul 07 '12 at 20:40
  • Electrons sharing same quantum state can't have same Spin. Position has nothing to do with this. In any atom, many electron pairs share same quantum states. And, you're talking about millions of atoms. Your basic concepts are not clear (no offense). – Earth is a Spoon Jul 07 '12 at 20:50
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    @SachinShekhar: They are clear, you just didn't understand them. Two electrons in the "same quantum state" have the same position distribution as well as spin. Electrons on different atoms can have the same spin. The electrons on different atoms in a magnet are spinning in the same direction, this is why you have magnetization. When you flip the magnetization, you can detect the change in angular momentum of the electrons--- the magnet rotates. – Ron Maimon Jul 07 '12 at 21:09
  • Look.. in any atom, if two electrons share same quantum state, it means they have different Spins. How are you really making them same? – Earth is a Spoon Jul 07 '12 at 21:39
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    @SachinShekhar: The electrons with the same spin in a ferromagnetic are on different atoms. – Ron Maimon Jul 08 '12 at 06:42
  • Fine.. you've accepted that all have not same spins. Now, see this: Paired ones cancel each other. So, what matters in ferromagnetic is the non-paired ones in Orbital. Also, remember, both spins and orbital angular momentum contribute to magnetism. So, you can't just reverse back just to Spin. – Earth is a Spoon Jul 08 '12 at 07:04
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    @SachinShekhar: I have not "accepted" anything! You have just misinterpreted my comments in absurd ways. Of course not all the electrons have the same spins, all the unpaired electrons have the same spins, the unpaired electrons in interior orbitals are responsible for magnetism. Orbital angular momentum of these electrons does not contribute to magnetism angular momentum change, because when you change the magnetism, the orbital is exactly the same, only the spin of the electron changes. This is the reason the Einstein deHaas experiment works to measure electron spin angular momentum. – Ron Maimon Jul 08 '12 at 07:11
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    To make it completely clear: you have a block consisting of 50 iron atoms, with 50 unpaired d-electrons, one per atom. You apply a magnetic field to make all 50 unpaired electrons spin one direction, while holding the clump in place to keep it from rotating. Then you release the block and reverse the direction of the field. The 50 unpaired d-electrons reverse their spin. At the same time, the clump begins to rotate in the plane perpendicular to the B-field at a certain rate. The new angular momentum of the block is equal to twice the angular momentum the spinning d-electrons had originally. – Ron Maimon Jul 08 '12 at 07:14
  • Finally, you've accepted that you can't change spin of all electrons. – Earth is a Spoon Jul 08 '12 at 07:19
  • Your last part isn't complete. Orbital Angular Momentum also contribute in it by large amount. – Earth is a Spoon Jul 08 '12 at 07:20
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    @SachinShekhar: I never said you can change the spin of all the electrons! It never crossed my mind that someone could interpret that "all the electrons" means electrons not involved in magnetism, like inner shell S-wave electrons. That's like saying "Aha, but the electrons in the Andromeda galaxy didn't flip!" (I didn't explicitly say these are not involved either). The orbital angular momentum contributes exactly zero amount! This is why Einstein and deHaas did the experiment, it's a clear measurement of the spin angular momentum of the electron. – Ron Maimon Jul 08 '12 at 07:21
  • You did say ALL. That's why you were saying about position. Now, discussion is moot.. – Earth is a Spoon Jul 08 '12 at 07:30
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As a answer, first I'd like to ask why you're asking a quantum mechanics problem with classical mechanics mental model.

There are two types of angular momentum in quantum mechanics:

  1. Orbital angular momentum, which is a generalization of angular momentum in classical mechanics (L=r×p). I think, you shouldn't have problem with this because Orbital has size.

  2. Spin, which has no analogue in classical mechanics. You can understand it as a number appeared in quantum equation. It can be understood like charge(with physical dimension), which is a number to denote one of basic attributes of particles. Yes, Spin does have physical dimension of angular momentum. But, its because it is a type of angular momentum, mathematically.

Xitcod13
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Earth is a Spoon
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    to answer your first question is because i would understand quantum mechanics i would not ask questions about it. Q.M. has a lot of confusing vocabulary which means something else in "regular" english. Also what exactly do you mean by "which is a number (with physical dimensions)" numbers cant have physical dimensions. You mean the charge with physical dimensions? – Xitcod13 Jul 06 '12 at 13:08
  • @Xitcod13 I meant charge is ((just a number)) with physical dimension.. Ofcourse, numbers don't have physical dimensions. :) – Earth is a Spoon Jul 06 '12 at 13:17
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    Spin is not a type of angular momentum, it is angular momentum, period. This is demonstrated by the Einstein deHaas experiment detailed in my answer. – Ron Maimon Jul 08 '12 at 06:45
  • @Ron That experiment is out-dated. At that time, there wasn't any concept of Orbital. – Earth is a Spoon Jul 08 '12 at 07:21