Operational definition of (brane induced) space-time and constraints on the fundamental parameters

TL;DR

This paper explores how the operational definition of space-time aligns with quantum mechanics and general relativity, especially in braneworld models with low gravity scales, highlighting the impact of extra dimensions on quantum fluctuations.

Contribution

It extends the operational definition of space-time to braneworld scenarios and analyzes the effects of extra dimensions on quantum gravitational fluctuations.

Findings

Quantum fluctuations are suppressed by the Planck scale in four dimensions.

In braneworld models, fluctuations can become large due to higher-dimensional effects.

Shape moduli of extra dimensions can stabilize against large fluctuations.

Abstract

First we contemplate the operational definition of space-time in four dimensions in light of basic principles of quantum mechanics and general relativity and consider some of its phenomenological consequences. The quantum gravitational fluctuations of the background metric that comes through the operational definition of space-time are controlled by the Planck scale and are therefore strongly suppressed. Then we extend our analysis to the braneworld setup with low fundamental scale of gravity. It is observed that in this case the quantum gravitational fluctuations on the brane may become unacceptably large. The magnification of fluctuations is not linked directly to the low quantum gravity scale but rather to the higher-dimensional modification of Newton's inverse square law at relatively large distances. For models with compact extra dimensions the shape modulus of extra space can be used as a most natural and safe stabilization mechanism against these fluctuations.