Micro-Anthropic Principle for Quantum theory

Abstract

Probabilistic models (developped by workers such as Boltzmann, on foundations due to pioneers such as Bayes) were commonly regarded merely as approximations to a deterministic reality before the roles were reversed by the quantum revolution (under the leadership of Heisenberg and Dirac) whereby it was the deterministic description that was reduced to the status of an approximation, while the role of the observer became particularly prominent. The concomitant problem of lack of objectivity in the original Copenhagen interpretation has not been satisfactorily resolved in newer approaches of the kind pioneered by Everett. The deficiency of such interpretations is attributable to failure to allow for the anthropic aspect of the problem, meaning {\it a priori} uncertainty about the identity of the observer. The required reconciliation of subjectivity with objectivity is achieved here by distinguishing the concept of an observer from that of a perceptor, whose chances of identification with a particular observer need to be prescribed by a suitable anthropic principle. It is proposed that this should be done by an entropy ansatz according to which the relevant micro-anthropic weighting is taken to be proportional to the logarithm of the relevant number of Everett type branch-channels.Comment: 29 pages Latex, 1 figure. Contribution to `Universe or Multiverse?' ed. B.J. Carr, for Cambridge U.