Notes on several phenomenological laws of quantum gravity

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 $\hslash /c$ may be also given a geometrical interpretation, namely $4\pi {\hslash }^2/m^2<A$. 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 $m{c}^3/\hslash$ if $m<m_p$ and by $c^4/Gm$ 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.

15 pages, 4 figures. Comments welcome

References in corpus (4)

• A Reformulation of the Hoop Conjecture
• Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum
• Comment on "Can we measure structures to a precision better than the Planck length?"[arXiv:1205.3636], by Sabine Hossenfelder
• The Penrose Inequality

Cited by in corpus (3)

• Quantum theory of the Generalised Uncertainty Principle
• Maximum force and cosmic censorship
• Reconsidering maximum luminosity