The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law

Paul Davies

Arizona State University

Abstract

The finite age of the universe and the existence of cosmological horizons provides a strong argument that the observable universe represents a finite causal region with finite material and informational resources. A similar conclusion follows from the holographic principle. In this paper I address the question of whether the cosmological information bound has implications for fundamental physics. Orthodox physics is based on Platonism: the laws are treated as infinitely precise, perfect, immutable mathematical relationships that transcend the physical universe and remain totally unchanged by physical processes, however extreme. If instead the laws of physics are regarded as akin to computer software, with the physical universe as the corresponding hardware, then the finite computational capacity of the universe imposes a fundamental limit on the precision of the laws and the specifiability of physical states. That limit depends on the age of the universe. I examine how the imprecision of the laws impacts on the evolution of highly entangled states and on the problem of dark energy.

Comments: Chapter for a book celebrating the work of Gregory Chaitin: C.S. Calude, ed. Randomness &
Complexity, from Leibniz to Chaitin, Singapore: World Scientific, 2007 (to appear).