Problems about Causality in Fermi's Two-Atom Model and Possible Resolutions

TL;DR

This paper examines causality issues in Fermi's two-atom model, demonstrating that excitation can occur instantaneously, and discusses potential resolutions and causality notions to address this contradiction.

Contribution

It provides a model-independent proof that excitation probability is nonzero immediately after t=0, challenging finite propagation speed assumptions and exploring causality concepts.

Findings

Excitation probability of B is nonzero immediately after t=0.

Discusses possible resolutions to causality contradictions.

Introduces strong and weak Einstein causality notions.

Abstract

In order to check finite propagation speed Fermi, in 1932, had considered two atoms A and B separated by some distance R. At time t=0, A is in an excited state, B in its ground state, and no photons are present. Fermi's idea was to calculate the excitation probability of B. In a model-independent way and with minimal assumptions - Hilbert space and positive energy only - it is proved, not just for atoms but for any systems A and B, that the excitation probability of B is nonzero immediately after t=0. Possible ways out to avoid a contradiction to finite propagation speed are discussed. The notions of strong and weak Einstein causality are introduced.