Collective micro-causality in homogeneous quantum ensembles

TL;DR

This paper demonstrates that micro-causality can be compatible with quantum theory in homogeneous ensembles, leading to deterministic evolution of state amplitudes, especially in complex systems with small amplitudes.

Contribution

It introduces the concept of collective micro-causality in quantum ensembles and shows its consistency with quantum theory, extending to dissimilar particles and complex systems.

Findings

Micro-causality does not contradict quantum theory in homogeneous ensembles.

Amplitudes can be divided into small portions with deterministic evolution.

Micro-causality applies to complex systems with small individual state amplitudes.

Abstract

It is shown that for quantum ensembles consisting of equal particles, the collective micro-causality does not contradict the quantum theory. The amplitudes of the states of such an ensemble can be divided into small portions, for each of which evolution in time will be accurately determined, without any randomness. For ensembles of dissimilar particles, whose Hamiltonian is represented as a sum of operators belonging to homogeneous systems, micro-causality will take place on separate small segments, on which only the selected component will act. In this case, the duration of the terms for different ensembles will be different. Micro causality is a consequence of the quantization of amplitudes, which plays a peculiar role for complex systems in which the amplitudes of individual states are very small. For such systems, the stochastic description, typical in the standard quantum theory should be replaced by a causal, i.e. deterministic one. In the article micro-causality is illustrated by the example of ensembles of two-level atoms in an optical cavity, considered under the Tavis-Cummings model in the rotating wave approximation; however, the conclusions are general.