Related papers: Struggles with the Continuum
Gravity is specifically the attractive force between two masses separated at a distance. Is this force a derived or a fundamental interaction? We believe that all fundamental interactions are quantum in nature but a derived interaction may…
The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems,…
General relativity poses serious problems for counterfactual propositions peculiar to it as a physical theory. Because these problems arise solely from the dynamical nature of spacetime geometry, they are shared by all schools of thought on…
We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a "cosmic censor" which prevents any external observer from perceiving their…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
The idea of gravity as an "emergent" phenomenon has gained popularity in recent years. I discuss some of the obstacles that any such model must overcome in order to agree with the observational underpinnings of general relativity.
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
We recall some of the obstacles which arise when one tries to reconcile the general theory of relativity with quantum theory. We consider the possibility that gravitation theories which include torsion, and not only curvature, provide…
We present here a brief review and discussion on recent developments in the theory of spacetime singularities. After mentioning some key motivations on the main ideas and concepts involved, we take the approach that the singularities will…
Quantum gravity is likely the deepest problem facing current physics. While traditionally associated with short distance nonrenormalizability, it is evident that the long distance problem of unitarity, arising at high energies with black…
The accelerating expansion of the universe presents an exciting, fundamental challenge to the standard models of particle physics and cosmology. I highlight some of the outstanding challenges in both developing theoretical models and…
The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein's general relativity could alleviate the different problems associated with it that result…
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of…