Relativistic Physics in Arbitrary Reference Frames

TL;DR

This paper reviews the monad formalism for describing reference frames in relativistic physics, emphasizing its general covariance, applications to various fields, and comparison with other approaches, including practical examples and physical insights.

Contribution

It provides a comprehensive, covariant framework for reference frames in relativity, including applications to mechanics, electromagnetism, and gravity, with new solutions and comparisons to existing methods.

Findings

Unified covariant description of reference frames in relativity

New solutions illustrating physical phenomena in rotating frames

Comparison showing advantages of monad formalism over other approaches

Abstract

In this paper we give a review of the most general approach to description of reference frames, the monad formalism. This approach is explicitly general covariant at each step, permitting to use abstract representation of tensor quantities; it is applicable also to special relativity when non-inertial effects are considered in its context; moreover, it involves no hypotheses whatsoever thus being a completely natural one. For the sake of the reader's convenience, a synopsis of tensor calculus in pseudo-Riemannian space-time precedes discussion of the subject, containing expressions rarely encountered in literature but essentially facilitating the consideration. We give also a comparison of the monad formalism with the other approaches to description of reference frames in general relativity. In three chapters we consider applications of the monad formalism to general relativistic mechanics, electromagnetic and gravitational fields theory. Alongside of the general theory, which includes the monad representation of basic equations of motion of (charged) particles and of fields, several concrete solutions are provided to clarify the physical role and practical application of reference frames (e.g., cases when a rotating electrically charged fluid does not produce any electric field in its co-moving reference frame, or kinematic magnetic charges arise in a rotating frame). The cases are discussed when it is unnecessary to introduce a reference frame, and when such an introduction is essential. Special attention is dedicated to analogy between gravitation, electromagnetism and mechanics (e.g., the dragging phenomenon and existence in the Maxwell equations in rotating frames of terms of the same nature as that of the Coriolis and centrifugal forces).