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Non-relativistic model of the laws of gravity and electromagnetism, invariant under the change of inertial and non-inertial coordinate systems

Arkady Poliakovsky

Abstract

Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravity. Moreover, in the frames of our model, we obtain that the laws of Non-relativistic Quantum Mechanics also invariant under the change of inertial or non-inertial cartesian coordinate system.

Non-relativistic model of the laws of gravity and electromagnetism, invariant under the change of inertial and non-inertial coordinate systems

Abstract

Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravity and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravity. Moreover, in the frames of our model, we obtain that the laws of Non-relativistic Quantum Mechanics also invariant under the change of inertial or non-inertial cartesian coordinate system.

Paper Structure

This paper contains 136 sections, 45 theorems, 3066 equations.

Table of Contents

  1. Introduction
  2. A new look to the Newtonian Gravity
  3. Variational principle for the solution of the Cauchy-problem for Hamilton-Jacobi type equation \ref{['MaxVacFull1ninshtrgravortghhghgjkgghklhjgkghghjjkjhjkkggjkhjkhjjhhfhjhklkhkhjjklzzzyyyhjggjhgghhjhNWNWNWNWNWBWHWPPN222int']}.
  4. Non-relativistic model of Electrodynamics
  5. Local gravitational time and Maxwell equations
  6. Motion of the particles in the gravitational and electromagnetic fields and invariance of Shrödinger and Pauli equations
  7. Unified gravitational-electromagnetic field and conservation laws in the case of the Newtonian-type gravity
  8. Transformations of general scalar and vector fields under the change of cartesian coordinate system
  9. Genuine gravity and inertia
  10. Lagrangian of the unified Gravitational-Electromagnetic field in the case of some possible alternative model of the gravity
  11. Covariant formulation of the physical laws in the four-dimensional non-relativistic space-time
  12. Four-vectors, four-covectors and tensors in the four-dimensional non-relativistic space-time
  13. Pseudo-metric tensors of the four-dimensional space-time
  14. Maxwell equations in covariant formulation
  15. Covariant formulation of Lagrangian of motion of a classical charged particle in the external gravitational and electromagnetic fields
  16. ...and 121 more sections

Key Result

Theorem 1.1

Consider that the change of some non-inertial cartesian coordinate system $(*)$ to another cartesian coordinate system $(**)$ is given by noninchgravortbstrjgghguittu2int. Next, assume that in the coordinate system $(**)$ we observe a validity of the Second Law of Newton in the form: where $\mathbf{x}':=\mathbf{x}'(t')$, $\mathbf{u}':=\mathbf{u}'(t')=\frac{d\mathbf{x}'}{dt'}(t')$ and $m'$ are the

Theorems & Definitions (118)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Remark 1.1
  • Theorem 1.4
  • Definition 1.1
  • Proposition 1.1
  • Proposition 1.2
  • Definition 1.2
  • Proposition 1.3
  • ...and 108 more