Some remarks on the semi-classical limit of quantum gravity

Abstract

One of the most important issues in quantum gravity is to identify its semi-classical regime. First the issue is to define for we mean by a semi-classical theory of quantum gravity, then we would like to use it to extract physical predictions. Writing an effective theory on a flat background is a way to address this problem and I explain how the non-commutative spacetime of deformed special relativity is the natural arena for such considerations. On the other hand, I discuss how the definition of the semi-classical regime can be formulated in a background independent fashion in terms of quantum information and renormalisation of geometry.Building a theory of Quantum Gravity is one of the biggest problems in theoretical physics. In this context, the concept of semi-classicality is particularly relevant in order to make it a physical theory. Indeed, on a practical level, building an effective theory would allow to extract physics and experimental predictions for quantum gravity. In fact, it would even allow us to say something on quantum gravity without having to build the full consistent theory. This is particularly interesting since experiments like GLAST, AUGER and others, should be able to measure effects due to a quantum gravity regime. Now, in order to define a semi-classical domain, one should first understand the notion of observers in a quantum gravity context. Then one could construct an effective theory for an observer who can define a regime in which geometry doesn't need to be described as quantum anymore. First, I will describe the different limits of quantum gravity and what I call an effective theory. Then I will show that the non-commutative space-time of deformed special relativity provides an effective theory for quantum gravity. And I will define the semi-classical regime of the theory. I will discuss the necessity of introducing coherent states in a noncommutative spacetime in order to describe a semi-classical notion of spacetime points. Section IV will discuss the interplay of quantum information and quantum gravity. Finally, I will discuss the tools necessary in order to understand the semi-classical regime, or more generally a macroscopic regime, in full background independent quantum gravity such as loop quantum gravity. Effective theory and semiclassicalityQuantum Gravity is usually defined as the regime where the Planck quantities become relevant:where G is the Newton coupling constant for gravity, c the speed of light or highest speed of any signal in flat spacetime, the Planck constant of the quantum theory. It is usually believed that gravitational effects (black hole formation) implies that the Planck length l P is a minimal distance and that the geometry is quantized in quanta of size l P . The relevance of the Planck mass m P , or Planck energy E P = m P c 2 , is more subtle. It can not be a maximal mass since macroscopic systems have a rest energy much larger than E P . Obviously, it can not be a minimal mass either. An easy way to characterize it is as the maximal energy or mass...

(2+1) Regge Calculus: Discrete Curvatures, Bianchi Identity, and Gauss-Codazzi Equation

“…The next step, is to write the elements of 3D and 2D curvature in the point of view of O as the origin. For the 3D curvature, it is done by equation (32), while for 2D, it is done by (40). Returning to relation (52), an important remarks we need to emphasize is: the h's are the holonomy circling segments, which is a 3-dimensional properties.…”

“…In between the Plank scale and classical continuous general relativity scale, the mesoscopic scale is defined as the scale where the space behave classically but discrete. This is the scale of the large size and finite numbers of the grains of space, which also known as the semi-classical limit [30][31][32]. The behaviour of spacetime in this scale could be well-approximated by the theory of discrete gravity [32].…”

“…This is the scale of the large size and finite numbers of the grains of space, which also known as the semi-classical limit [30][31][32]. The behaviour of spacetime in this scale could be well-approximated by the theory of discrete gravity [32].…”

Semiclassical corrections to the Einstein equation and Induced Matter Theory

“…It would even allow us to say something on quantum gravity without having to build the full consistent theory. This is particularly interesting since experiments like GLAST, AUGER and others, should be able to measure effects due to a quantum gravity regime [2]. In the semiclassical theory of gravity a classical metric is coupled to the expectation value of the stress tensor…”

“…interesting since experiments like GLAST, AUGER and others, should be able to measure effects due to a quantum gravity regime [2]. In the semiclassical theory of gravity a classical metric is coupled to the expectation value of the stress tensor G µν = −8π G < T µν > .…”