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. Generalizing 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.
Highlights
Quantum theory without the Born Rule is deterministic [1]
Principle I requires subsidiary theories to have two crucial properties: (i) they must support a topology on the set of physical processes they apply to, which gives a meaning to a sequence of approximate constructions, converging to an exact performance of T; (ii) they must be non-probabilistic—as they must be expressed exclusively as statements about possible/impossible tasks
I have reformulated the problem of reconciling unitary quantum theory, unpredictability and the appearance of stochasticity in quantum systems, within the constructor theory of information, where unitary quantum theory is a particular superinformation theory—a non-probabilistic theory obeying constructor-theoretic principles
Summary
Quantum theory without the Born Rule (hereinafter: unitary quantum theory) is deterministic [1]. This distinguishes it from (apparent) randomness, which, as I shall explain, requires a quantitative explanation Another key finding of this paper is a sufficient set of conditions for superinformation theories to support a generalization of the decision-theory approach to probability, thereby explaining the appearance of stochasticity, namely that repeated identical measurements have different unpredictable outcomes but are to all appearances, random. My version of the decision-theory argument explains how the numbers fx can inform decisions of a player satisfying non-probabilistic rationality axioms under certain superinformation theories (§7) Those theories would account for the appearance of stochasticity at least as adequately as unitary quantum theory.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Proceedings. Mathematical, physical, and engineering sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.