Affiliation:
1. The Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
Abstract
In quantum theory, physical systems are usually assumed to evolve relative to a c-number time. This c-number time is unphysical and has turned out to be unnecessary for explaining dynamics: in the timeless approach to quantum theory developed by Page & Wootters 1983
Phys. Rev. D
27
, 2885. (
doi:10.1103/PhysRevD.27.2885
), subsystems of a stationary universe can instead evolve relative to a ‘clock', which is a quantum system with a q-number time observable. Page & Wootters formulated their construction in the Schrödinger picture, which left open the possibility that the c-number time still plays an explanatory role in the Heisenberg picture. I formulate their construction in the Heisenberg picture and demonstrate how to eliminate c-number time from that picture, too. When the Page–Wootters construction is formulated in the Heisenberg picture, the descriptors of physical systems are functions of the clock's q-number time, and derivatives with respect to this q-number time can be defined in terms of the clock's algebra of observables, which results in a calculus for q-numbers.
Funder
Prins Bernhard Cultuurfonds
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Reference23 articles.
1. Newton I. 1696 The mathematical principles of natural philosophy (translated into English by Andrew motte in 1729). London, UK: Royal Society.
2. Time Without Change
3. Barbour J. 2009 The nature of time. arXiv preprint gr-qc/0903.3489.
4. Evolution without evolution: Dynamics described by stationary observables
5. Information flow in entangled quantum systems
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献