Relativistic time-of-arrival measurements: predictions, post-selection and causality problem

TL;DR

This paper investigates relativistic time-of-arrival measurements within quantum field theory, highlighting unique predictions, the role of apparatus post-selection, and the challenges of causality due to non-causal transient effects.

Contribution

It provides a detailed analysis of time-of-arrival probabilities in relativistic quantum measurements, emphasizing the impact of post-selection and the inherent causality issues from Feynman propagators.

Findings

QFT predicts a unique time-of-arrival distribution with apparatus-dependent post-selection.

Detection probabilities show small transient non-causal terms outside the light-cone.

Restoring causality may be fundamentally limited in certain measurement models.

Abstract

We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus into the initial state. We also show that an experimental distinction of different probability assigments is possible especially in near-field measurements. We also analyze causality in relativistic measurements. We consider a quantum state obtained by a spacetime-localized operation on the vacuum, and we show that detection probabilities are typically characterized by small transient non-causal terms. We explain that these terms originate from Feynman-propagation of the initial operation, because the Feynman propagator does not vanish outside the light-cone. We discuss possible ways to restore causality, and we argue that this may not be possible in measurement models that involve switching the field-apparatus coupling on and off.