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We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the…
Recently proposed ``table-top tests of quantum gravity'' involve creating, separating and recombining superpositions of masses at non-relativistic speeds. The general expectation is that these generate superpositions of gravitational fields…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
We discuss some effects induced by quantum field fluctuations on mass, inertia and gravitation. Recalling the problem raised by vacuum field fluctuations with respect to inertia and gravitation, we show that vacuum energy differences, such…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
Newton's inverse-square law of universal gravitation assumes constant mass. But mass increases with speed and perhaps with gravity. By SR, mass is increased over the rest mass by gamma. Rest mass is here postulated to increase under…
Whenever an alternative theory of gravity is formulated in a background Minkowski space, the conditions characterizing admissible coordinate systems, in which the alternative theory of gravity may be applied, play an important role. We here…
We generalize and unify the $f(R,T)$ and $f(R,L_m)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$, of the trace of the energy-momentum tensor $T$, and of the…
Complementing previous theoretical and experimental work, we explore new types of short-range modifications to Newtonian gravity arising from spacetime-symmetry breaking. The first non-perturbative, i.e., to all orders in coefficients for…
In this article the concept of mass is analyzed based on the special and general relativity theories and particle (quantum) physics. The mass of a particle (m=E(0)/c^2) is determined by the minimum (rest) energy to create that particle…
Within the weak-field approximation of general relativity, new exact solutions are derived for the gravitational field of a mass moving with arbitrary velocity and acceleration. A mass having a constant velocity greater than 3^-1/2 times…
We study the consequences of the $f(R/\Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the…
We give a definition and derive the equations of motion for the center of mass and angular momentum of an axially symmetric, isolated system that emits gravitational and electromagnetic radiation. A central feature of this formulation is…
An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
We derive a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity. This formulation is a generalization of the Newton-Cartan geometric formulation of Newtonian gravity. It involves several fields and…
Gravitation as a fundamental interaction that governs all phenomena at large and very small scales, but still not well understood at a quantum level, is a missing cardinal link to unification of all physical interactions. Problems of the…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is…