Related papers: Time evolution as refining, coarse graining and en…
Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…
In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…
We discuss the emergence of time in quantum gravity, and ask whether time is always "something that flows"'. We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time…
We establish the general conditions under which evolution in the laws of physics and matter creation or destruction are closely intertwined. They make use of global time variables canonically dual to the constants of Nature. Such times flow…
The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast into an iterative differential system of basis functions. These functions can be encoded within…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: i) the physical inner product in the timeless framework equals the…
A new definition of coarse-grained quantities describing the dust flow in General Relativity is proposed. It assigns the coarse--grained expansion, shear and vorticity to finite-size comoving domains of fluid in a covariant,…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
Given the lack of an absolute time parameter in general relativistic systems, quantum cosmology often describes the expansion of the universe in terms of relational changes between two degrees of freedom, such as matter and geometry.…
In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a…
In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.…
The interface between quantum theory and gravity represents still uncharted territory. Recently, some works suggested promising alternative approaches aimed at witnessing quantum features to test the fundamental nature of gravity in…
We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively…