Notes on several phenomenological laws of quantum gravity
J. Bruneton. (2013)cite arxiv:1308.4044Comment: 15 pages, 4 figures. Comments welcome.
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'' $l
1/m$ 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 ($mH_0)$ 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.
Description
Notes on several phenomenological laws of quantum gravity
%0 Generic
%1 bruneton2013notes
%A Bruneton, Jean-Philippe
%D 2013
%K gravity notes on quantum
%T Notes on several phenomenological laws of quantum gravity
%U http://arxiv.org/abs/1308.4044
%X 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'' $l
1/m$ 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 ($mH_0)$ 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.
@misc{bruneton2013notes,
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.},
added-at = {2013-08-20T16:31:02.000+0200},
author = {Bruneton, Jean-Philippe},
biburl = {https://www.bibsonomy.org/bibtex/2dd921062ea8ee8606864122c0d863bd5/dkraljic},
description = {Notes on several phenomenological laws of quantum gravity},
interhash = {e4d1915ba63b538f09485089caca8d8d},
intrahash = {dd921062ea8ee8606864122c0d863bd5},
keywords = {gravity notes on quantum},
note = {cite arxiv:1308.4044Comment: 15 pages, 4 figures. Comments welcome},
timestamp = {2013-08-20T16:31:02.000+0200},
title = {Notes on several phenomenological laws of quantum gravity},
url = {http://arxiv.org/abs/1308.4044},
year = 2013
}