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Time, space, and matter are categories of our reasoning, whose properties appear to be fundamental. However, these require a scrutiny as in the extreme regime of the primordial universe these present quantum properties. What does it mean…
Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on a possibility of the event space modification and on a possibility of stochastic (Brownian)…
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
Quantum non-local correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in…
By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean…
I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among…
In General Relativity without a cosmological constant a non-positive contribution from the space-time geometry to Raychaudhuri equation is found provided that particular energy conditions are assumed and regardless the considered solution…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
An application of the quantum N-portrait to the Universe is discussed, wherein the space-time geometry is understood as a Bose-Einstein condensate of N soft gravitons. If near or at the critical point of a quantum phase transition,…
A novel theory of Quantum Gravity is presented in which the real gravitons manifest themselves as holes in space. In general, these holes propagate at the speed of light through an expanding universe with boundary denoted by U, which is…
This paper argues against the proposal to draw from current research into a physical theory of quantum gravity the ontological conclusion that spacetime or spatiotemporal relations are not fundamental. As things stand, the status of this…
Classical-particle trajectories are calculated for the static Einstein universe without requiring that the 3-space be closed and curved. Freely-moving test particles are found to return to their starting positions because of strong…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a…
By following the general guiding principle that nothing should be prescribed or imposed on the universal entity, spacetime, we establish that it is the homogeneity (by which we mean homogeneity and isotropy of space and homogeneity of time)…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
The ordinary quantum theory points out that general relativity is negligible for spatial distances up to the Planck scale. Consistency in the foundations of the quantum theory requires a``soft'' spacetime structure of the general relativity…
We show that a hypothesis that spacetime is quantum with coordinate algebra $[x^i,t]=\lambda_P x^i$, and spherical symmetry under rotations of the $x^i$, essentially requires in the classical limit that the spacetime metric is the…