Note on a new fundamental length scale $l$ instead of the Newtonian constant $G$

TL;DR

This paper proposes replacing the Newtonian gravitational constant G with a new fundamental length scale l, derived from quantum space-time structure, to better understand gravity and Lorentz violation.

Contribution

It introduces a new fundamental length scale l as a replacement for G, linking gravity to quantum space-time and Lorentz-violating observations.

Findings

G can be derived from the length scale l.

l is measurable from Lorentz-violating experiments.

The approach impacts fundamental physics and natural units.

Abstract

The newly proposed entropic gravity suggests gravity as an emergent force rather than a fundamental one. In this approach, the Newtonian constant $G$ does not play a fundamental role any more, and a new fundamental constant is required to replace its position. This request also arises from some philosophical considerations to contemplate the physical foundations for the unification of theories. We here consider the suggestion to derive $G$ from more fundamental quantities in the presence of a new fundamental length scale $l$, which is suspected to originate from the structure of quantum space-time, and can be measured directly from Lorentz-violating observations. Our results are relevant to the fundamental understanding of physics, and more practically, of natural units, as well as explanations of experimental constraints in searching for Lorentz violation.