Notes on several phenomenological laws of quantum gravity

TL;DR

This paper reviews phenomenological laws of quantum gravity, proposing covariant bounds, exploring minimal length implications, and discussing holographic principles and maximal quantities, with potential links to dark energy and modified gravity models.

Contribution

It introduces a covariant mass bound conjecture, interprets fundamental constants geometrically, and discusses the implications of these bounds for quantum gravity and cosmology.

Findings

Existence of a minimal area and size constraints.

Mass-dependent maximal acceleration, force, and power.

Holographic principle bounds and their relation to system mass.

Abstract

Phenomenological approaches to quantum gravity try to infer model-independent laws by analyzing thought experiments and combining both quantum, relativistic, and gravitational ingredients. We first review these ingredients -three basic inequalities- and discuss their relationships with the nature of fundamental constants. In particular, we argue for a covariant mass bound conjecture: in a spacetime free of horizon, the mass inside a surface $A$ cannot exceed $16 \pi G^2 m^2< A $, while the reverse holds in a spacetime with horizons. This is given a precise definition using the formalism of light-sheets. We show that $\hbar/c$ may be also given a geometrical interpretation, namely $4 \pi \hbar^2/m^2< A$. We then combine these inequalities and find/review the following: (1) Any system must have a size greater than the Planck length, in the sense that there exists a minimal area (2) We comment on the Minimal Length Scenarios and the fate of Lorentz symmetry near the Planck scale (3) Quanta with transplanckian frequencies are allowed in a large enough boxes (4) There exists a mass-dependent maximal acceleration given by $m c^3/\hbar$ if $m<m_p$ and by $c^4/G m$ if $m>m_p$ (5) There exists a mass dependent maximal force and power (6) There exists a maximal energy density and pressure (7) Physical systems must obey the Holographic Principle (8) Holographic bounds can only be saturated by systems with $m>m_p$; systems lying on the ``Compton line'' $l \sim 1/m$ are fundamental objects without substructures (9) We speculate on a new bound from above for the action. In passing, we note that the maximal acceleration is of the order of Milgrom's acceleration $a_0$ for ultra-light particles ($m\sim H_0)$ that could be associated to the Dark Energy fluid. This suggests designing toy-models in which modified gravity in galaxies is driven by the DE field, via the maximal acceleration principle.