Vacuum Energy Density Fluctuations in Minkowski and Casimir States via Smeared Quantum Fields and Point Separation

TL;DR

This paper investigates quantum energy density fluctuations in Minkowski and Casimir states using smeared fields and point separation, challenging prior criteria for semiclassical gravity validity and exploring implications for exotic spacetime phenomena.

Contribution

It introduces a detailed analysis of energy fluctuation ratios with intrinsic scales, providing new insights into regularization and the spatial extent of negative energy regions in quantum fields.

Findings

Variance to mean-squared ratio depends on intrinsic and extrinsic scales.

Identifies spatial regions with negative energy density relevant for wormholes and time machines.

Discusses divergences and regularization issues in quantum energy density calculations.

Abstract

We present calculations of the variance of fluctuations and of the mean of the energy momentum tensor of a massless scalar field for the Minkowski and Casimir vacua as a function of an intrinsic scale defined by a smeared field or by point separation. We point out that contrary to prior claims, the ratio of variance to mean-squared being of the order unity is not necessarily a good criterion for measuring the invalidity of semiclassical gravity. For the Casimir topology we obtain expressions for the variance to mean-squared ratio as a function of the intrinsic scale (defined by a smeared field) compared to the extrinsic scale (defined by the separation of the plates, or the periodicity of space). Our results make it possible to identify the spatial extent where negative energy density prevails which could be useful for studying quantum field effects in worm holes and baby universe, and for examining the design feasibility of real-life `time-machines'. For the Minkowski vacuum we find that the ratio of the variance to the mean-squared, calculated from the coincidence limit, is identical to the value of the Casimir case at the same limit for spatial point separation while identical to the value of a hot flat space result with a temporal point-separation. We analyze the origin of divergences in the fluctuations of the energy density and discuss choices in formulating a procedure for their removal, thus raising new questions into the uniqueness and even the very meaning of regularization of the energy momentum tensor for quantum fields in curved or even flat spacetimes when spacetime is viewed as having an extended structure.