Probability Distributions for Space and Time Averaged Quantum Stress Tensors

TL;DR

This paper extends quantum stress tensor operator analysis to include spatial averaging, revealing that vacuum fluctuations can dominate thermal ones and may have observable consequences.

Contribution

It introduces a combined space-time averaging framework for quantum stress tensors, highlighting the impact on fluctuation probabilities and potential observability.

Findings

Spatial averaging reduces large fluctuation probabilities compared to time averaging.

Probability distribution decreases slower than exponential for large energy densities.

Vacuum fluctuations can surpass thermal fluctuations and be observable.

Abstract

We extend previous work on quantum stress tensor operators which have been averaged over finite time intervals to include averaging over finite regions of space as well. The space and time averaging can be viewed as describing a measurement process for a stress tensor component, such as the energy density of a quantized field in its vacuum state. Although spatial averaging reduces the probability of large vacuum fluctuations compared to time averaging alone, we find that the probability distribution decreases more slowly than exponentially as the magnitude of the measured energy density increases. This implies that vacuum fluctuations can sometimes dominate over thermal fluctuations and potentially have observable effects.