Is the Free Vacuum Energy Infinite?

TL;DR

This paper demonstrates that considering a fundamental cutoff based on uncertainty relations leads to a vacuum energy density that approaches zero in infinite space, offering a natural regularization method for various physical infinities.

Contribution

It introduces a new regularization approach for vacuum energy based on a fundamental cutoff, avoiding traditional mathematical tricks.

Findings

Vacuum energy density is proportional to the inverse fourth power of the space's dimensional distance.

Vacuum energy naturally regularizes to zero in infinite space.

Potential to address the cosmological constant problem and Casimir effect infinities.

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 forth 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 happen in the Casimir effect, the cosmological constant problem and so on without using already known mathematical (not so reasonable) techniques and tricks.