## Sunday, October 24, 2010

### Explaining electron spin and Pauli exclusion principle to children

Fundamental particles are the building blocks of nature, of which the photon and the electron have the most visible impact on our everyday life. Photons are all pervasive. If they have the right energy, they can stimulate your eyes' photoreceptor cells. At other energies they will warm you up because they radiate from a warm object. Electrons are more energetic than the photons. They can either be free in space, or bound in atoms. Through their motion, they transmit motion to photons, which in turn can excite other electrons at distant places. This phenomenon, known as electromagnetism, is used in all wireless transmissions. Photons are the electromagnetic force carriers and electrons are the electromagnetic force sources.

In order to understand the behavior of photons and electrons, it is important to have analogies that help us keeping track of them. In previous posts, I mentioned some helpful analogies for photons (for example at this post on polarization). Although electrons also show wave behavior, they act a bit differently from photons. You can not stack electrons near to one another, except if they have compatible spinning motions. For spinning motions to be compatible means that the electrons must:
• either spin at rates whose proportions are expressed with integers: for example one electron spins twice as fast as the other electron,
• or spin in different directions, if they spin with the same velocity.
I sometimes come across situations that remind me of electrons. If you're standing in the bus or in the metro, you grip a pole to keep equilibrium. In the metro-train in my Paris suburb, the poles occur in pairs, like in the picture aside. When my children were younger, one of their favorite games was to spin around those poles. For parents, if you let your kids spin around the poles disorderedly, this game can be quite stressful, ending with fighting or crying. I used to explain to them that they had to spin like electrons in atoms. If one kid spins in one direction, the other kid needs to spin in opposite direction, in order to avoid hard clashes. I recently asked them if they could do it again so that I could put it on movie and post it to illustrate this electron analogy. But they've grown up and are now ashamed to play such games:-) So I decided to create the following simple animations that illustrate the electron spin and the Pauli exclusion principle.

A kid spinning around the pole is alike an electron spinning around a proton in its state of minimum energy, see Figure 1. Physicists designate the spinning direction with the help of the right hand rule. The kid of Figure 1 therefore has its spin down.

If your second kid spins in the same direction around the other pole, you can be sure that this game won't last for long. Their motions are incompatible and it ends up with a clash, see Figure 2.

If you want them to play peacefully, you need to instruct them to follow a natural rule: the Pauli exclusion principle, illustrated in Figure 3. Electrons with same spinning velocity and sharing the same space can only occur if their spins are opposite. Very useful rule to keep harmony in the family!

1. Nice images, but I think that the explanations are incorrect, for the following reasons:
- If the two kids are spinning in phase, they never collide, even if they are spinning in the same direction. There is always between them a distance equal to that between the two poles. They collide only if their phase difference is pi.
- They may collide (although not frontally) even if they are spinning in opposite directions, if their phase difference is appropriately chosen.
- Assuming that your explanation is true despite the observations I've made above, why would it work only for fermions and not for bosons?

2. Hello Christi,

Thanks for these relevant remarks. The illustrations are indeed simplified and my explanation isn't intended to be "true". Just a useful analogy. In an atom, the nucleus can't be modeled by two poles (but by one central point), and the electron spreads at both sides of the nucleus. The important thing to notice is "how does an electron enter the game when it comes from a remote location?". If its spin has same direction as the already bound electron spin, the free electron will always collide harshly when it approaches the atom. For opposite spins the approach occurs more smoothly, both spinning motions facilitating their binding.

Concerning the difference between bosons and fermions, maybe I'll be able to post other illustrations. But the essential difference (in my view) is that the spinning motion of fermions causes them to spread over a sphere, with half integer proportions (see my modeling the electron illustration in the right column), while for bosons, their spinning motions causes them to spread over a disk. You can stack disks much more closely than spheres.

Kind regards,

Arjen

3. Hello Arjen,
the spin is a difficult and abstract subject. Any effort made to explain what it really is, to build the geometrical intuition to others, is a very good thing.
Best regards,
Cristi

4. What if the dimensions of the circle are incorrect? I have a very compelling argument for the circle to be 400 degrees not 360.

5. Hi Kathie,
I don't understand what you mean by circles being 400 degrees (curvature, rotational speed,...). It may depend on how you measure the circle, which unit you use, which reference frame, etc. When electrons spin freely, they in fact rotate 720 deg before returning in the same setting, which may be understood by the fact that there are more than one rotational axis.

6. Hi Arjen,
Could you please give some analogy/diagrammatic illustration/gif explaining the spin of electron being 1/2
You said rotate by 720 degrees/>1 rotational axis...
Regards,
Vimal

1. Hi Vimal,
Please have a look at the diagram "Modeling the electron with a spinning vector" at the right of the page. Or at this image and follow the path of the extremity of the rod. Only after spinning twice around one axis, the rod comes back in the same configuration.

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