相关论文: From Kepler's laws to Newton's law: a didactical p…
An experimental formula, sometimes named as Newton-collision-formula, (v1-v2) = - e.(u1-u2) relating relative-velocities before & after impact of two bodies under linear-collision, is commonly used successfully for study of…
In non-Euclidean geometry, there are several known correspondings to Chapple-Euler Theorem. This remark shows that those results yield expressions corredponding to the well-known formula $d=\sqrt{R(R-2r)}$.
We summarise and discuss some of our previous results, which show that Bohr's theory of the one-electron atom may be derived from the theory underpinning Quantum ElectroDynamics (QED) or vice versa, and that General Relativity may also be…
We try to give a pedagogical introduction to Connes' derivation of the standard model of electro-magnetic, weak and strong forces from gravity.
Motivated by recent work on low energy unification, in this short note we derive corrections on Newton's inverse square law due to the existence of extra decompactified dimensions. In the four-dimensional macroscopic limit we find that the…
Kepler's rescaling becomes, when "Eisenhart-Duval lifted" to $5$-dimensional "Bargmann" gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted…
The gravitational effect of vacuum polarization in space exterior to a particle in (2+1)-dimensional Einstein theory is investigated. In the weak field limit this gravitational field corresponds to an inverse square law of gravitational…
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: The Axioms / Half-planes / Congruent triangles / Perpendicular…
Based on quantum origin of the universe, in this article we find that the universal wave function can be far richer than the superposition of many classical worlds studied by Everett. By analyzing the more general universal wave function…
The angular derivative of the standard form of the transfer equation is shown to have a non-zero value for the radiation normal incidence. This is demonstrated by a rigorous proof. The transfer equation for the starter intensity turned out…
Three decades ago, Ted Jacobson surprised us with a very appealing approach to classical gravity. According to him, the gravitational field equations are the consequence of the first law of thermodynamics applied to a Rindler observer.…
The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…
In this paper, we study the inverse surfaces in 3-dimensional Euclidean space $\mathbb{E}^{3}$. We obtain some results relating Christoffel symbols, the normal curvatures, the shape operators and the third fundamental forms of the inverse…
In this article we introduce a generalization of the Newton transformation to the case of a system of endomorphisms. We show that it can be used in the context of extrinsic geometry of foliations and distributions yielding new integral…
A modern elementary introduction to special relativity for advanced school children or first-year university students, in Russian. I try to demonstrate that relativity does not contradict common sense; on the contrary, it follows from…
We suggest a lecture on Newtonian gravity, discussing how the use of the scientific method allows to rule out some of the models for the shape of Earth leaving a spherical Earth as the only possibility, in agreement with empirical…
This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not…
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but based on the positive operator-valued…