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Asked by rajathjackson to Chris, Dave, David, Fiona, Jack on 20 Jun 2013.
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Jack Miller answered on 20 Jun 2013:
Like the wildcard on QI, I feel like holding up a sign saying ‘Nobody knows’! This is a very deep and fundamental question, and if I knew the answer I’d probably be busy going to Stockholm to pick up a nobel prize.
Sometimes we just have to accept that things just _are_ a certain way in our universe. It turns out that things have this property we call spin, and electrons have half a lot of it. We can do experiments to measure this (the most famous of which is called the Stern-Gerlach experiment — there’s a good video at http://en.wikipedia.org/wiki/Stern-Gerlach). We can deduce a lot of things from spin (and a related theorem, called the spin-statistics theorem, which describes what impact spin has on a particle), and it explains an awful lot, from chemistry to iron bar magnets (along with NMR and MRI…).
Yet why do things have spin? Nobody knows, and if they did, my bet is that the answer would be similar to ‘because something else has another property, let’s call it spaghettification, and it equals one’. It’s just a fundamental fact of our universe.
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David Freeborn answered on 20 Jun 2013:
Hi rajathjackson,
As with a lot of physics, the best answer we can give to this is an appeal to the concept of symmetry. In physics, we use an area of mathematics called group theory to try to describe the difference symmetries in our theories. Generally, we try to make ou theories as symmetric as possible unless there is some reason to break the symmetry (the different masses of particles is one example of a symmetry being broken). Symmetric theories correspond to theories that are elegant and simple, which is intuitively how we would like nature to behave.
Symmetry really means that you can change something and it will still appear the same way. So reflection symmetry means we can reflect an object and it looks the same way. Rotational symmetry means we can rotate an object and it looks the same way. In physics we also have some other very important symmetries: space and time symmetry, and a concept called “gauge symmetry”, which means we can add a constant term to our field equations and they still behave the same way.
The spin of a particle actually corresponds to its rotational symmetry in space-time. An electron with spin-1/2 means it is in a highly symmetric state.
We try to make our theories as symmetric as possible, and the theory of electromagnetism, Quantum Electrodynamics is a particularly simple and symmetric theory. To keep the theory as symmetric as possible, we need photons to have spin-1 and electrons to have spin-1/2. So electrons with spin-1/2 turns out to be a particularly mathematically elegant solution.
String theory might offer a deeper explanation. In string theory, the particle behaviours correspond to different ways to twist a string, and the particle spins correspond to different ways to rotate a spin. So that might be the fundamental reason.
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