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The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…
In this paper we discuss some aspects of the theory of wave packets. We consider a popular non-covariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic…
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations…
Some versions of quantum theory treat wave function collapse as a fundamental physical phenomenon to be described by explicit laws. One motivation is to find a consistent unification of quantum theory and gravity, in which collapse prevents…
The assumption that wave function collapse is induced by correlating interactions of the kind that constitute measurements leads to a stochastic collapse equation that does not require the introduction of any new physical constants and that…
We investigate the dephasing suffered by a nonrelativistic quantum particle within a conformally fluctuating spacetime geometry. Starting from a minimally coupled massive Klein-Gordon field, the low velocity limit yields an effective…
In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…
For a class of viable cosmological models in $f(R)$ gravity which deviation from the Einstein gravity decreases as a inverse power law of the Ricci scalar $R$ for large $R$, an analytic solution for density perturbations in the matter…
This article is a brief survey of some approaches to implementing the suggestion that collapse of the wave function is mediated by gravity. These approaches include: a possible connection between the problem of time and problem of quantum…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
We incorporate non-local gravitational self-energy, motivated by string-inspired T-duality, into the Schr\"odinger-Newton equation. In this framework spacetime has an intrinsic non-locality, rendering the standard linear superposition…
Both the additional non-linear term in the Schr\"odinger equation and the additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localisation and decoherence of macro-objects, resp., contain the same Newtonian…
We present the third-order analytic solution of the matter density fluctuation in the proper-time hypersurface of nonrelativistic matter flows by solving the nonlinear general relativistic equations. The proper-time hypersurface provides a…
Cosmic observations strongly support a time varying scenario for matter/space. On the other hand, so far, observations at solar system scale failed to identify any time variation on matter/space characteristics. To explain both results it…
Upcoming surveys of cosmic structures will probe scales close to the cosmological horizon, which opens up new opportunities for testing the cosmological concordance model to high accuracy. In particular, constraints on the squeezed…
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of…
We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there…
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…