on distinguishability versus indistinguishability

The following comments are from the book Quantum Mechanics by Claude CohenTannoudji, Bernard Diu, and Franck Laloë. Identical particles: definition Two particles are said to be identical if all their intrinsic properties (mass, spin, charge, etc.) are exactly the same: no experiment can distinguish one from the other. Thus, all electrons in the universe are identical, as are all the protons and all the hydrogen atoms. Note that this definition is independent of the experimental conditions. Even if, in a given experiment, the charges of the particles are not measured, an electron and a positron can never be treated as identical particles. An important consequence can be deduced from this definition: when a physical system contains two identical particles, there is no change in its properties or its evolution if the roles of these two particles are exchanged. In classical mechanics, the presence of identical particles in a system poses no particular problems. Each particle moves along a well-defined trajectory, which enables us to distinguish it from the others and follow it throughout the evolution of the system. It is immediately apparent that the situation is radically different in quantum mechanics, since the particles no longer have definite trajectories, but rather are treated in a probabilistic manner. For example, in figure 2 two identical particles approach one another. When the two particles are still far away from each other, they are distinguishable due to their spatial separation: we can label them “1” and “2”. But when they interact with each other (when they collide), we lose track of which is which, so, looking at figure 3, we are not sure which particle hits the detector (labeled “D”). Nothing in the theory of quantum mechanics enables us to determine which particle hits the detector. The Symmetrization Postulate We add a new postulate to the theory of quantum mechanics to deal with this. Statement of the Postulate When a system includes several identical particles, only certain wavefunctions can describe its physical states. Physical wavefunctions are, depending of the nature of the indentical particles, either completely symmetric or completely antisymmetric with respect to permutation of these particles. Those particles for which the physical wavefunctions are