Related papers: Relativistic Diffusion in G\"odel's Universe
Stochastic diffusion equation, which attained prominence with Einstein's work on Brownian motion at the beginning of the twentieth century, was first formulated by Laplace a century earlier as part of his work on Central Limit Theorem.…
In 1919 A. Einstein suspected first that gravitational fields could play an essential role in the structure of elementary particles. In 1937, P.A.M. Dirac found a miraculous link between the properties of the visible Universe and elementary…
Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement…
The theory of relativity was built up on linear Lorentz transformation. However, in his fundamental work "Theory of Space, Time and Gravitation" V.A.Fock shows that the general form of the transformation between the coordinates in the two…
.This article reexamines the genesis of special relativity by situating the contributions of Lorentz, Poincare, and Einstein within the scientific, documentary, and editorial context of the years 1895--1913. It emphasizes the rapid…
We show that Kompaneetz equation describing photon diffusion in an environment of an electron gas, when linearized around its equilibrium distribution, coincides with the relativistic diffusion discussed in recent publications. The model of…
Exactly one hundred years ago, in May 1922, Alexander Friedmann discovered that General Relativity (GR) predicts non-stationary Universe. His equation describing the evolution of the Universe is now named after him. In this paper we briefly…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
We discuss the superluminal problem in the diffusion of ultra high energy protons with energy losses taken into account. The phenomenological solution of this problem is found with help of the generalized J\"uttner propagator, originally…
We consider reversible diffusions in random environment and prove the Einstein relation for this model. It says that the derivative of the effective velocity under an additional local drift equals the diffusivity of the model without drift.…
Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim…
We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised…
Einstein's genius and penetrating physical intuition led to the general theory of relativity, which incorporates gravity into the geometry of spacetime. However, the theory of general relativity leads to perspectives which go far beyond the…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
Einstein's Special Theory of Relativity was proposed a little over a hundred years back. It remained a bedrock of twentieth century physics right up to Quantum Field Theory. However, the failure over several decades to provide a unified…
The foundations of Einstein's first (1907) principle of equivalence are explored and their consequences are stated in terms of invariance under generalized Lorentz transformations, first explored by Hessenberg.
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
The nature of space-time and surrounding matter objects was and persists to be a one of the most intriguing and challenging problems facing the mankind and natural scientists especially. As we know one of the most brilliant inventions in…
In 1908, Minkowski put forward the idea that invariance under what we call today the Lorentz group, $GL(1,3, {\bf R})$, would be more meaningful in a four-dimensional space-time continuum. This suggestion implies that space and time are…