Indistinguishability in Quantum Mechanics

Another unintuitive aspect of quantum mechanics is the indistinguishability of elementary particles. If I have an electron and you have an electron and we put them in a box with other electrons, neither of us can “tag” our electrons in order to pick them out from the crowd later. It is impossible to distinguish between two electrons. This follows from a symmetry of the joint wave function. If you have an electron in one particular spot and make it trade places with an electron in a different spot, nothing will change in terms of the physics, and that is what we mean by exchange symmetry of identical particles. We could go a bit further and say that nature is in some ways democratic. All the electrons in the universe are identical, and all are indistinguishable; there is no preferential treatment of one electron over another!