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In this work we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal…
A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained…
A concise review of the derivation of the Born rule and Schr\"odinger equation from first principles is provided. The starting point is a formalization of fundamental notions of measurement and composition, leading to a general framework…
We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schr\"odinger equation and a discussion of semiclassical time as well…
We study static quantum corrections of the Schwarzschild metric in the Boulware vacuum state. Due to the absence of a complete analytic expression for the full semiclassical Einstein equations we approach the problem by considering the…
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…
A special-relativistic scalar-vector theory of gravitation is presented which mimics an important class of solutions of Einstein's gravitational field equations. The theory includes solutions equivalent to Schwarzschild, Kerr,…
Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
In this article we show that the fundamental equations of relativistic Bohmian mechanics for a single particle can be derived from a scalar theory of curved space-time.
The motion of a charged particle is influenced by the self-force arising from the particle's interaction with its own field. In a curved spacetime, this self-force depends on the entire past history of the particle and is difficult to…
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches.…
We argue that the origin of unitarity violation and information loss paradox in our understanding of black holes (BH) lies in the standard way of doing quantum field theory in curved space-time (QFTCS), which is heavily biased on intuition…
Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The…
The braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in…