Minkowski Vacuum Stress Tensor Fluctuations

TL;DR

This paper investigates the fluctuations of the stress tensor for a massless scalar field in Minkowski spacetime, deriving covariant expressions and analyzing correlations in energy density measurements.

Contribution

It provides covariant formulas for stress tensor correlation functions and explores the nature of energy density measurement correlations in vacuum.

Findings

Stress tensor fluctuations are characterized by covariant derivatives of a scalar function.

Spacetime averages of the correlation function are finite and expressible as integrals.

Energy density measurements can be positively or negatively correlated, indicating possible sign reversals over time.

Abstract

We study the fluctuations of the stress tensor for a massless scalar field in two and four-dimensional Minkowski spacetime in the vacuum state. Covariant expressions for the stress tensor correlation function are obtained as sums of derivatives of a scalar function. These expressions allow one to express spacetime averages of the correlation function as finite integrals. We also study the correlation between measurements of the energy density along a worldline. We find that these measurements may be either positively correlated or anticorrelated. The anticorrelated measurements can be interpreted as telling us that if one measurement yields one sign for the averaged energy density, a successive measurement with a suitable time delay is likely to yield a result with the opposite sign.