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My questions about spin and negative charge of electrons. Stern-Gerlach experiment is very famous in order to find spin of electron. this video created by paris-sud university really well-explained on this experiment except one the video first.

The thing I confuse second step of experiment they use electrons they goes two different ways. Aren't electrons have negative charge only? How they can go two different ways?

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Neat video.

That experimental setup is not measuring the charge of the particles. If it were, you would be correct; you'd get the same result each time for all of the identical particles. Instead, that setup measures some other property of the particles. Physicists gave that property the name spin. Spin is not charge, and charge is not spin.

Spin is a property that is intrinsic to particles. By that, I mean just like all electrons all have some given mass and charge, they all also have a given spin value. What's different about spin (well, one of the differences) is that when you measure which way it's oriented (like in the video), your possible results are always "discreet". That's a fancy way of saying the spin can only be measured to be one of several possible values; a measurements of spin never results an in-between or "continuous" result like the classical magnets showed in your video.

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you are saying experiment is not about charge so in the first part of experiment how magnets decide what way they will go? Wasn't it about charge? – user2783998 Jan 28 '14 at 8:46
Electric charge is not the same as north/south on a magnet. The poles of magnets are not charged in the sense you're thinking of. For example, if you bring a magnet up to your skin, you don't get shocked. – BMS Jan 28 '14 at 14:37
so here is the part 2:… – user2783998 Jan 29 '14 at 15:43

The reason the particles go in two different directions is not because of their charge, but because of their spin. When studying quantum mechanics, you will be introduced to the spin operator $S_i$, as well as others such as for orbital angular momentum $L_i$ and total angular momentum $J_i=L_i+S_i$.

The spin operator is a generator of changes in orientation, and an intrinsic property of fundamental particles. In the Stern-Gerlach experiment, the possible spins were +1/2 and -1/2, hence the particles went in two different directions.

On a more sophisticated level (quantum field theory), spin can be viewed as a relativistic effect. The relation becomes apparent when studying the motivation for the Dirac equation and spinors by investing different representations of the Lorentz group.

Professor Binney (Oxford University) has an excellent introduction to quantum mechanics on YouTube which covers the Stern-Gerlach experiment. His book is also available for free online.

PS: An additional property of spin number is that is quantized, i.e. discrete. That is to say, you can only have very specific spin numbers, and the intervals between those numbers are equal.

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