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Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We…

We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the…

An earlier paper [1] presented a gravity theory based on the optics of de Broglie waves rather than curved space-time. While the universe's geometry is flat, it agrees with the standard tests of general relativity. A second paper [2] showed…

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…

Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…

An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…

A model quantum system is proposed to describe position states of a massive body in flat space on large scales, excluding all standard quantum and gravitational degrees of freedom. The model is based on standard quantum spin commutators,…

Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…

Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…

This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…

Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime…

While it is generally agreed that the nature of spacetime must be drastically different at the Planck scale, it has been a common practice to assume that spacetime is endowed with a full pseudo-Riemannian geometry regardless of the physical…

We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test…

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates…

We discuss the hints for the disappearance of continuum space and time at microscopic scale. These include arguments for a discrete nature of them or for a fundamental non-locality, in a quantum theory of gravity. We discuss how these ideas…

Particle size and shape are the key 3D particle geometry parameters that govern the complex behavior of granular materials. The effect of particle size and shape has often been examined in isolation, typically through separate analyses of…

One of the main goals of contemporary theoretical physics is to find the quantum theory of gravity. There are various working hypotheses, mostly operating in the regime of high-energy physics well above the reach of particle accelerators.…

Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…

`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…

Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a…