Is the Free Vacuum Energy Infinite?

H Razmi,S M Shirazi

doi:10.1155/2015/278502

Abstract

Considering the fundamental cutoff applied by the uncertainty relations’ limit on virtual particles’ frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the fourth power of the dimensional distance of the space under consideration and thus the corresponding vacuum energy automatically regularized to zero value for an infinitely large free space. This can be used in regularizing a number of unwanted infinities that happen in the Casimir effect, the cosmological constant problem, and so on without using already known mathematical (not so reasonable) techniques and tricks.

Highlights

IntroductionIn quantum (field) theory, it is well known that the reason for naming the quantum vacuum particles as virtual particles is that they are in “existence” and can have observable effects (e.g., the Casimir effect, spontaneous emission, and Lamb shift), they cannot be directly detected (i.e., they are unobservable)
In the standard quantum field theory, does the vacuum energy have an absolute infinite value, and all the real excited states have such an irregular value; this is because these energies correspond to the zero-point energy of an infinite number of harmonic oscillators (W = (1/2) ∑k,σ ħωk → ∞)
We usually get rid of this irregularity via simple technique of normal ordering by considering the energy difference relative to the vacuum state [1,2,3,4,5,6]; but, there are some important situations where one deals directly with the absolute vacuum energy as in the cosmological constant problem [7] or in the regularization of the vacuum energy in the Casimir effect [8]

Summary

Introduction

In quantum (field) theory, it is well known that the reason for naming the quantum vacuum particles as virtual particles is that they are in “existence” and can have observable effects (e.g., the Casimir effect, spontaneous emission, and Lamb shift), they cannot be directly detected (i.e., they are unobservable). For these unobservable (virtual) particles, the energy and lifetime values are constrained due to the uncertainty relation and can take, at most, the minimum values of uncertainties for real particles. The uncertainties in energy and lifetime of real (detectable) particles satisfy the relation

The Vacuum Energy Density of Infinitely Large Free Spaces

Discussion