ABSTRACT
This chapter purports to show that, according to standard quantum mechanical theory, the probability is zero for the existence of self-reproducing states. The derivation is not a rigorous one: it is based on an assumption which is analogous to one's belief that in no system of any complexity is there any accidental degeneracy. It is even more closely similar to the assumption on the basis of which the second law of thermodynamics was derived. The assumption is that the Hamiltonian which governs the behaviour of a complicated system is a random symmetric matrix, with no particular properties except for its symmetric nature. It is by assuming this property for the Hamiltonian, when written in the co-ordinate system in which the observables are diagonal, that Neumann proved the second law of thermodynamics to be a consequence of quantum mechanical theory.
