Session B16: Quantum Gravity I

Live

We calculate passive gravitational mass of a quantum body with inner degrees of freedom and investigate the possible application of the Equivalence Principle (EP) to it. We show that, in the most practical cases, the EP is applicable, as expected. Nevertheless, in one important case, where we have a coherent macroscopic ensembles of the superpositions of the stationary quantum states (which we call Gravitational demons), the EP is shown by us to be broken [1,2]. We demonstrate that the calculated weight of such ensemble (i.e., its passive gravitational mass) is not related to energy by the Einstein's equation E$=$mc2 anymore and that the corresponding difference can be of order of unity. We also discuss possibilities for experimental observations of this unique phenomena. [1] A.G. Lebed, Int. J. Mod. Phys. D, v. 28, 1930020 (2019). [2] A.G. Lebed, Mod. Phys. Lett. A, v. 35, 2030010 (2020).   

On Demand

This paper reframes Riemannian geometry (RG) as a generalized Lie algebra allowing the equations of both RG and general relativity (GR) to be expressed as commutation relations among fundamental operators along with relativistic quantum theory (RQT) and the standard model (SM). Beginning with an Abelian Lie algebra of n operators X, whose simultaneous eigenvalues, y, define a real n-dimensional space R(n), we then define n additional operators, D whose exponential map is to translate the X operators resulting in a noncommutative algebra of operators (observables) where the ``structure constants'' are shown to be the metric functions of the X operators thus allowing for spatial curvature. The D operators then have a Hilbert space position-diagonal representation as generalized differential operators which with the metric, written as a commutator, can express the Christoffel symbols the Riemann, Ricci, and other tensors as commutators in this representation. Traditional RG and GR are expressed in this generalized Lie algebra providing a more general framework for RG to support an integration among GR, RQT, and the SM by generalizing Lie algebras as described. Non-trivial consequences are discussed.   

Live

In this talk I will discuss a simple symplectic formulation for tetrad gravity that leads to the real Ashtekar variables in a direct and transparent way. It also sheds light on the role of the Immirzi parameter and the time gauge usually consider in the Hamiltonian formulation.   

Live

Isham's group theoretic quantization scheme is designed to naturally extend the notion of canonical quantization to systems whose phase space is topologically nontrivial. Our main interest is in the implications for quantum gravity; but, to develop experience with these ideas, here we apply the scheme to a charged particle moving on a sphere threaded by magnetic flux which is encoded via a modification of the symplectic form. As instructed by Isham, we identify a symplectic symmetry group that acts transitively on the phase space, and we construct the Hilbert space directly from its unitary irreducible representations using ladder operators. In this way, the complete classification of quantizations and the corresponding energy spectra for the particle are recovered algebraically. The famous Dirac quantization condition for the monopole charge follows from the requirement that the classical and quantum Casimir invariants match.   

Live

The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. In this talk I will provide motivation for an energy condition obeyed in semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. I will then then present the proof of a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity and has interesting applications to evaporating black holes. Based on: arXiv:2012.11569   

Live

We study the collapse of a massless scalar field in spherically symmetric loop quantum gravity using the semi-classical effective equations of motion. In spite of the presence of a characteristic length (the Planck length), the phase transition from no black hole to black hole formation remains second order like in classical general relativity. We study several details of the behavior near criticality as a function of the polymerization parameter of loop quantum gravity.   

Live

This review is aimed to shed some light on problems constructing a theory of spacetime and geometry in terms of all degrees of freedom called `Quantum Gravity'. Such a theory, which is effective at all scales of distances and energies, describes the enigma of the beginning of Universe, its possible end and reducing to general relativity at large distances but in a semi-classical approximation. Furthermore, the theory of quantum gravity also describes the Universe as a whole and provides description of most fundamental questions that have puzzled scientists for decades such as: what is space, what is time, and what is the fundamental structure of Universe, is the spacetime discrete, if it is, where does the continuum of spacetime come from at low energies and macroscopic scales and where does it emerge from its fundamentally discrete building blocks? In QFT, atoms are quanta of continuous fields. At smaller scales or higher energies, the continuum description of spacetime fails. Therefore, a new description is required in terms of microscopic constituents (atoms or molecules). The objective of this scientific endeavor is to discuss the above-mentioned problems rigorously and to discuss possible way-out of the problems.   

Live

Primordial inflation produces a vast ensemble of cosmological scale gravitons which can affect both the force of gravity and the propagation of gravitational radiation. I show how these effects can be studied by using the graviton self-energy to quantum correct the linearized Einstein equations. I demonstrate that the graviton self-energy has nine structure functions in a general cosmological background and I show how these structure functions change the linearized Einstein equations. I also present explicit one loop results for the nine structure functions on de Sitter background.