Related papers: Small-Scale Structure of Spacetime: Bounds and Con…

Quantum gravity has become a fertile interface between gravitational physics and quantum many-body physics, with its double goal of identifying the microscopic constituents of the universe and their fundamental dynamics, and of…

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…

The physical origin of spacetime discreteness remains a central open problem in quantum gravity, with most existing approaches relying on specific microscopic structures or model-dependent assumptions. In this letter, spacetime discreteness…

In this talk I review a series of recent conceptual developments at the interface of the quantum and gravitational realms. Wherever possible, I comment on the possibility to probe the interface experimentally. It is concluded that the…

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…

The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key…

This paper gives an elementary introduction to some of the conceptual problems of quantum cosmology. Contents: 1. Why quantum cosmology? 2. Time in quantum gravity 3.Decoherence and the recovery of the Schrodinger equation 4. The direction…

The extreme smallness of both the Planck length, on the one side, and the ratio of the gravitational to the electrical forces between, say, two electrons, on the other side has led to a widespread belief that the realm of quantum gravity is…

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum…

Recently, it was shown that the quantum effects of the matter, could be used to determine the conformal degree of freedom of the space-time metric. So both gravity and quantum are geometrical features. Gravity determines the causal…

Asking very elementary relativistic quantum mechanics to meet quantums of area and time, it is possible to observe at a general level: a) the seesaw bound for the mass of neutrinos, and b) the need of a gauge group at energies below Planck…

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a…

The closed-universe recollapse conjecture is studied for the spherically symmetric spacetimes. It is proven that there exists an upper bound to the lengths of timelike curves in any Tolman spacetime that possesses $S^3$ Cauchy surfaces and…

The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…

Cosmological perturbations are generally described by quantum fields on (curved but) classical space-times. While this strategy has a large domain of validity, it can not be justified in the quantum gravity era where curvature and matter…

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…

This article will summarize selected aspects of the semiclassical theory of gravity, which involves a classical gravitational field coupled to quantum matter fields. Among the issues which will be discussed are the role of quantum effects…

A general geometrical scheme is presented for the construction of novel classical gravity theories whose solutions obey two-sided bounds on the sectional curvatures along certain subvarieties of the Grassmannian of two-planes. The…

Our main purpose here is to study some qualitative aspects of space and time. These include the notion of space and time regarded as the containers of respectively bodies and events, the divisibility of space, and the unrepeatability of…

Old and new puzzles of cosmology are reexamined from the point of view of quantum theory of the universe developed here. It is shown that in proposed approach the difficulties of the standard cosmology do not arise. The theory predicts the…