David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with what we know about (...) classical particles. In this article we analyze the origin of this paradox. We shall argue that in the classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided. (shrink)

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature β become small. Thus, microscopic particles like electrons must (...) remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2πħ)3 are reduced to points in the phase space, the partition functionTr{exp(−βĤ) for N identical bosons (fermions) approaches (2πħ)−3N(N!) ∫ ... ∫ d3r1 d3p1 ... d3rN d3pN exp(−βH). The two factors, (2πħ)−3N and (N!)−1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles. (shrink)

I attempt to get as clear as possible on the chain of reasoning by which irreversible macrodynamics is derivable from time-reversible microphysics, and in particular to clarify just what kinds of assumptions about the initial state of the universe, and about the nature of the microdynamics, are needed in these derivations. I conclude that while a “Past Hypothesis” about the early Universe does seem necessary to carry out such derivations, that Hypothesis is not correctly understood as a constraint on the (...) early Universe’s entropy. (shrink)

It is only when mixing two or more pure substances along a reversible path that the entropy of the mixing can be made physically manifest. It is not, in this case, a mere mathematical artifact. This mixing requires a process of successive stages. In any finite number of stages, the external manifestation of the entropy change, as a definite and measurable quantity of heat, isa fully continuous function of the relevant variables. It is only at an infinite and unattainable limit (...) thata non-uniform convergence occurs. And this occurs when considered in terms of the number of stages together with a distinguishability parameter appropriate to the particular device which is used to achieve reversibility. These considerations, which are of technological interest to chemical engineers, resolve a paradox derived in chemical theory called Gibbs'' Paradox. (shrink)

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The (...) relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed. (shrink)

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. In particular, the Gibbs paradox has sometimes been interpreted as a sign of the untenability of the classical concept of a particle and as a premonition that quantum theory is needed. This idea of a ‘quantum connection’ stubbornly persists in the literature, (...) even though it has also been criticized frequently. Here we shall argue that although this criticism is justified, the proposed alternative solutions have often been wrong and have not put the paradox in its right perspective. In fact, the Gibbs paradox is unrelated to fundamental issues of particle identity; only distinguishability in a pragmatic sense plays a role , and in principle the paradox always is there as long as the concept of a particle applies at all. In line with this we show that the paradox survives even in quantum mechanics, in spite of the quantum mechanical symmetrization postulates. (shrink)