Related papers: Massless spacetime: On spacetime geometry above th…
This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy…
This is the first part in a series of two papers, where we consider a specific microscopic model of spacetime. In our model Planck size quantum black holes are taken to be the fundamental building blocks of space and time. Spacetime is…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view…
We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and…
Space-Time in general relativity is a dynamical entity because it is subject to the Einstein field equations. The space-time metric provides different geometrical structures: conformal, volume, projective and linear connection. A deep…
The newest model for space-time is based on sub-Riemannian geometry. In this paper, we use a combination of Lorentzian and sub-Riemannian geometry, the suggest a new model which likes to its ancestors, but with the most efficient in…
This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's…
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…
A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty…
Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl…
We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to…
Classical macroscopic space-time is pictured in terms of Rydberg states of an underlying discritzed `atomic' quantum geometry at Planck scales. While quantum geometry on such scales involves several very short lived transitions changing…
A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…