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.
1. Introduction
In the standard quantum field theory, not only does the vacuum (zero-point) energy have an absolute infinite value, but also 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 (). We usually get rid of this irregularity via simple technique of normal ordering by considering the energy difference relative to the vacuum state [1–6]; but, of course, 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].
After a half century of knowing and “living” with the vacuum energy, there are only some mathematical techniques and approaches in regularizing its infinite value without paying enough conceptual attention to the “content” of the quantum vacuum “structure.” In this paper, considering the fundamental assumption that the vacuum energy originates from the “motion” of virtual particles in the quantum vacuum, it is shown that the free vacuum energy can be regularized based on the uncertainty relations’ limit on these particles’ frequency. Indeed, the free vacuum (or any infinitely large vacuum space) energy is automatically regularized to zero value without using any presupposition (e.g., normal ordering) usually used in getting rid of the infinity of the quantum vacuum energy (the vacuum catastrophe). READ MORE...
