相关论文: Can physics laws be derived from monogenic functio…

The aim of this paper is to create a large geometrical background on the dual 1-jet space J^{1*}(T,M) for a multi-time Hamiltonian approach of the electromagnetic and gravitational physical fields. Our geometric-physical construction is…

A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…

A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of…

In a recent publication the I showed how the geometric algebra ${G}_{4,1}$, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper…

This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…

Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…

The ``geometry'', in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG), along with resulting, thereby, potential physical…

It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…

Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…

The reader surely knows what particles physics is about: finding building blocks of nature that appear elementary at a given time and study their interactions - so why in the world this essay? The problem is how to arrive at a fundamental…

We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a…

Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…

We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that…

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 find equations of particle motion from the point of view of observer on a rotating disk, and demonstrate that a particle moving along a rotating disk is influenced by forces arising from geometry. They can be considered as analogs of the…

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of…

A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…

The main purpose of this paper is to seek a mechanical interpretation of gravitational phenomena. We suppose that the universe may be filled with a kind of fluid which may be called the $\Omega (0)$ substratum. Thus, the inverse-square law…