Related papers: A new approach in theoretical physics based on the…
The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein's general relativity could alleviate the different problems associated with it that result…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
We suggest that not only quanta may have played a role in Einstein's ideas on relativity, but that they themselves may be related to the dynamical and relativistic behaviour of the electromagnetic field exhibited in a Poincar\'e's 1900…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
In the first part of this work we apply Bohr (old or naive quantum atomic) theory for analysis of the remarkable electro-dynamical problem of magnetic monopoles. We reproduce formally exactly some basic elements of the Dirac magnetic…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
The possibility of a modification of special relativity with an invariant energy scale playing the role of a minimum energy is explored. Consistency with the equivalence of different inertial frames is obtained by an appropriate choice of a…
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective…
The fundamental Einstein-Hopf work that convinced the most part of physicists, since it had appeared, to take quantum ideas seriously, is reanalysed in this paper. We have studied the genesis of the work and have found the conclusion made…
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…
We derive the quantum Einstein equations (which are the quantum generalisation of the Einstein equations of classical gravity) from Bohmian quantum gravity. Bohmian quantum gravity is a non-classical geometrodynamics (in the ADM formalism)…
We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
Solutions of Einstein's equations are discussed in which the ``gravitational force" is balanced by an electrical force, and which can serve as models for the Cavendish experiment.
The present work aims to search for an implementation of new symmetries in the space-time in order to enable us to find a connection between electrodynamics and gravitation, from where quantum principles naturally emerge. To do that, first…
The Einstein static universe has played a central role in a number of emergent scenarios recently put forward to deal with the singular origin of the standard cosmological model. Here we study the existence and stability of the Einstein…