Vacuum Quantum Stress Tensor Fluctuations: A Diagonalization Approach

TL;DR

This paper investigates the probability distribution of vacuum stress tensor fluctuations in Minkowski spacetime, showing that large fluctuations are more probable than thermal ones and could have observable consequences.

Contribution

It introduces a diagonalization approach to compute the probability distribution of time-averaged vacuum stress tensor operators, extending previous moment-based analyses.

Findings

Tail of the distribution decreases as exponential of fractional powers.

Large vacuum fluctuations are more probable than thermal fluctuations.

Results suggest potential observable effects of vacuum stress tensor fluctuations.

Abstract

Large vacuum fluctuations of a quantum stress tensor operator can be described by the asymptotic behavior of the probability distribution of the time or spacetime averaged operator. Here we focus on the case of stress tensor operators averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we use the normal ordered square of the time derivative of a massless scalar field in Minkowski spacetime as an example of a stress tensor operator. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lead additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.