The flow of time in a quantum world

Abstract

The matter-antimatter arrow of time associated with the weak force in neutral Kaon decay has been an enigma for 40 years. While other arrows (cosmological, electromagnetic, thermodynamic and psychological) have been linked together the matter-antimatter arrow stands alone. It is often regarded as having negligible effect on time in our daily lives. The main reason for this view appears to be the relatively small violation of the Charge-Parity conjugation (CP) invariance involved. However a small difference in a quantum state fidelity for a single particle can lead to a large difference that grows exponentially with number for a collection of particles. In principle the smallness of the violation is not an obstacle in terms of macroscopic effects, provided sufficient numbers of particles are involved. In this talk we will examine the effect of the violation of CP invariance (or equivalently time reversal invariance) on the dynamics of a large system such as the universe. The analysis will be in the context of Pegg's quantum time formalism where time is defined within the system and not imposed as an external parameter. The state of the universe is the ground state of the Hamiltonian in accord with the Wheeler-deWitt equation, and is expressed as a superposition of "time"-ordered states. Care is taken to avoid inserting a bias in time direction when dealing with a CP non-invariant Hamiltonian. Everett's Many Worlds interpretation is used to follow the trajectories of the state of the system. An arbitrary initial state involving neutral kaons is seen to perform a random walk with a drift towards one direction, the "future". Within this formalism, the seemingly insignificant kaons appear to be responsible for our apparent motion through time.