Related papers: Splitting the source term for the Einstein equatio…
Based on a Planck scale underpinning for the universe, we deduce an expression for the gravitational constant which exhibits it as a distributional effect over all the particles of the universe. This solves a long standing puzzle, the so…
It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…
The anomaly-induced effective action is a useful tool for deriving the contributions coming from quantum effects of massless conformal fields. It is well-known that such corrections in the higher derivative vacuum sector of the…
The time-dependent cosmological term arises from the energy-momentum tensor calculated in a state different from the ground state. We discuss the expectation value of the energy-momentum tensor on the rhs of Einstein equations in various…
The Einstein equation in a semi-classical approximation is applied to a spherical region of the universe, with the stress-energy tensor consisting of the mass density and pressure of the LambdaCDM cosmological model plus an additional…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large…
Quantum mechanical interference of wave functions leads to some difficulties if a probability density is considered as a source of gravity. We show that an introduction of a quantum energy-momentum tensor as a source term in Einstein…
Quantum gravity effects of zeroth order in the Planck constant are investigated in the framework of the low-energy effective theory. A special emphasis is placed on establishing the correspondence between classical and quantum theories, for…
The cosmological constant problem is one of the greatest challenges in contemporary physics, since it is deeply rooted in the problematic interplay between quantum fields and gravity. The aim of this work is to review the key conceptual…
Giving up Einstein's assumption, implicit in his 1916 field equations, that inertial mass, even in its appearance as energy, is equivalent to active gravitational mass and therefore is a source of gravity allows revising the field equations…
At the level of the Planck scale, the spacetime metric has to be considered a quantum variable. Conformal quantum fluctuations of the metric tensor are studied here. They lead to an extra term in the Einstein equations which can be…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
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…
A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…
Some of the assumptions of cosmology, as based on the simplest version of General Relativity, are discussed. It is argued that by slight modifications of standard gravitation theory, our notion of the sources of gravity {the right hand side…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
We generalize Einstein's Lagrangian in a non-polynomial (in R) way. The usual Lagrangian (linear in R) is the zero $\alpha'$ limit of our theory, where $\alpha'$ is a parameter that is interpreted as the inverse cosmological costant before…
Einstein's Brownian motion of a quantum particle in a classical environment is studied via virial and equipartition theorems. The effect of continuous measurement in a strongly dissipative environment is accounted for and a quantum…