lew@ihuxr.UUCP (Lew Mammel, Jr.) (11/28/84)
As an undergraduate, the question of the meaning of indistinguishability troubled me quite a bit. I couldn't accept that there was any difference between a box of marbles which were IN PRACTICE indistinguishable and a box of electrons which were IN PRINCIPLE indistinguishable. Actually, the phrase, "inditinguishable particles", is already misleading. The word, "particles", implies that these have a seperate identity, even if we can't tell them apart. This conflict was resolved for me by realizing that when two electrons are localized together (as in the Helium atom) we obtain a NEW PARTICLE. Namely, a two electron state. This way of thinking is a commonplace in solid state physics, and particularly in superconductor theory. The point is that this two electron particle, although it can be split into two electrons, has properties that are not attributable to two single electrons. Spin and charge distribution, for example. The rules for calculating the properties of this two electron particle can be expressed loosely as a set of principles, including indistinguishability, but these principles are really only heuristic devices. Historically, the specific heat of solids gave convincing evidence of the reality of these rules. It was realized that the electrons in a solid, which can be thought of as a gas, gave a very small contribution to its heat capacity. Classically, you'd expect 3/2kT per electron. However, the many electron state formed by quantum rules has many fewer degrees of freedom than its classical counterpart, and hence fewer ways to store energy. Subsequently, the macroscopic implications of Quantum Statistics were exploited in a number of ways, many of them with profound economic and sociological impact. Lew Mammel, Jr. ihnp4!ihuxr!lew