Chiara Marletto

Abstract:

Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the so-called ‘decision-theoretic approach’, I shall recast that problem in the recently proposed constructor theory of information – where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which constructor theory gives an exact meaning), necessarily arises in superinformation theories. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements can arise under superinformation theories. And I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch–Wallace-type argument – thus defining a class of decision-supporting superinformation theories. This broadens the domain of applicability of that argument to cover constructor-theory compliant theories. In addition, in this version some of the argument’s assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles.

Abstract:

Neo-Darwinian evolutionary theory explains how the appearance of purposive design in the adaptations of living organisms can have come about without their intentionally being designed. The explanation relies crucially on the possibility of certain physical processes: mainly, gene replication and natural selection. In this paper, I show that for those processes to be possible without the design of biological adaptations being encoded in the laws of physics, those laws must have certain other properties. The theory of what these properties are is not part of evolution theory proper, yet without it the neo-Darwinian theory does not fully achieve its purpose of explaining the appearance of design. To this end, I apply constructor theory's new mode of explanation to express exactly within physics the appearance of design, no-design laws, and the logic of self-reproduction and natural selection. I conclude that self-reproduction, replication and natural selection are possible under no-design laws, the only non-trivial condition being that they allow digital information to be physically instantiated. This has an exact characterization in the constructor theory of information. I also show that under no-design laws an accurate replicator requires the existence of a ‘vehicle’ constituting, together with the replicator, a self-reproducer.