MadSci Network: Physics |
I am not sure what you mean when you ask "WHY does an electron have spin 1/2" (in angular momentum quantum units)? It is an experimental fact that the behavior of electrons is correctly predicted by a model in which the electron has spin 1/2. Therefore the model of spin 1/2 electrons is a useful model for understanding our universe. But I can't tell you WHY the universe is made this way. Spin 1/2 means much more than the fact that you have to rotate an electron around twice to have it look the same. Because an electron has spin 1/2, if you put it in a magnetic field it can have two different "eigenstates". Its spin can point either parallel (up) or antiparallel (down) relative to the magnetic field. All spin 1/2 particles are "fermions". Fermions have the symmetry property that if you have several of them, then the quantum mechanical wave-function which describes these particles acquires a minus sign under interchange of any two of them. Because of this, if you try to put two electrons into the same quantum state, the wave-function must be zero. This is the "Pauli Principle", and it means that such a state is not allowed. This property of electron wave-functions is the basis for understanding the properties of atoms and molecules. The reason why spin 1/2 particles must be fermions is explained by the "Spin-Statistics Theorem", which is usually considered to be a fundamental result of relativistic quantum theory. The same theorem also explains why spinless particles must be "bosons", which have the property that the quantum mechanical wave-function is unchanged under the interchange of two of them. The reasons why the Spin-Statistics Theorem is true are a subject of continuing interest. See, for example, the recent article by I. Duck and E. C. G. Sudarshan, American Journal of Physics 66: 284-303 (1998). There are many books which discuss this subject at an introductory level. My favorite is Volume 3 of "The Feynman Lectures on Physics".
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