Related papers: Quantum effects from a purely geometrical relativi…
In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We…
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…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
Classical general relativity predicts that a contracting, spherically symmetric matter system with a large-enough mass will result in the formation of a trapped region whose outer boundary is an apparent horizon where the gravitational…
After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational…
We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum…
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups,…
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…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…
We review quantum causal histories starting with their interpretations as a quantum field theory on a causal set and a quantum geometry. We discuss the difficulties that background independent theories based on quantum geometry encounter in…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
The postulate of universal Weyl conformal symmetry for all elementary physical fields introduces nonclassical gravitational effects in both conformal gravitation(CG) and the conformal Higgs model (CHM). The resulting theory is found to…