Related papers: Basel problem: a physicist's solution
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
We present a physical-optics based theory of the physical mechanism for aberration of starlight. We apply non-relativistic and relativistic theories for wavefront image formation and include the effects of optically transmitting media…
We explore the possibility to give a classical explanation to the specifics and physical sense of de Broglie matter waves when studying the microparticle as an object of non zero size, from the point of view of the special theory of…
Amongst a number of modified theories of gravity, the Rastall theory has been propounded to address some shortcomings of the standard theory of general relativity. Our purpose is to investigate this framework's capacity to analyse stellar…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
If the fine structure constant $\alpha =e^2/(\hbar c)$ were to change, then a number of interpretations would be possible, attributing this change either to variations in the electron charge, the dielectric constant of the vacuum, the speed…
Physical properties of stars such as luminosity, surface temperature, distance, or mass are measured from observations. These physical properties are of paramount importance to understand how stars are born, live, and die in the universe…
The relation between the pole quark mass and the $\overline{MS}$-renormalized mass is governed by an infrared renormalon singularity, which leads to an ambiguity of order $\Lambda_{QCD}$ in the definition of the pole mass. We use the…
The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball,…
We tackle the problem of the accelerating universe by reconsidering the most general form of the metric when the speed of light is allowed to evolve with time in a homogeneous and isotropic universe. A new varying speed of light (VSL) model…
We propose a cosmological model which could explain, in a very natural way, the apparently periodic structures of the universe, as revealed in a series of recent observations. Our point of view is to reduce the cosmological…
The Euler equation has been accepted as the basic postulate of stellar physics long before the plasma physics was developed. The existence of electrical interaction between particles of interstellar plasma poses the question, how this…
An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system…
Naturalness problems such as the hierarchy problem and the origin of dark energy remain significant challenges in modern cosmology. This paper develops a rigorous mathematical framework where each observer defines their own universe, and…
In this paper I present three new results of astronomical interest concerning the theory of Abel inversion. 1) I show that in the case of a spatial emissivity that is constant on toroidal surfaces and projected along the symmetry axis…
In this paper, the notion of complexity factor and its implication is extended to the framework of non-conserved Rastall theory of gravity. First of all, the field equations governing a static spherical geometry associated with the…
The Euler equation has been accepted as the basic postulate of stellar physics long before the plasma physics was developed. The existence of electrical interaction between particles of interstellar plasma poses the question, how this…
Based on experimental discovery that the mass-square of neutrino is negative, a quantum equation for superluminal neutrino is proposed in comparison with Dirac equation and Dirac equation with imaginary mass. A virtual particle may also be…
A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl…
The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…