A Novel Approach to Relativistic Dynamics: Integrating Gravity, Electromagnetism and Optics

A new mathematical model that unifies gravity, electromagnetism, optics, and quantum behavior is presented. The model is based on an extension of the Principle of Inertia and visualized through plotting the action function. It provides a simple and physically meaningful way to understand the geometries of different fields and their interactions. The model is accessible to students with standard courses in multivariable calculus and linear algebra and can be used to compute phenomena such as Mercury's precession, light deflection, Shapiro time delay, binary star relativistic motion, and gravitational waves.

Format: Hardback
Length: 196 pages
Publication date: 19 February 2023
Publisher: Springer International Publishing AG

This groundbreaking monograph presents a mathematically concise and physically meaningful framework that seamlessly integrates gravity, electromagnetism, optics, and even certain quantum phenomena. The authors achieve simplicity by employing an inertial observer framework and utilizing a physically meaningful least action principle. They introduce an extension of the Principle of Inertia, resulting in a straightforward, physically meaningful action function. Visual representations of the geometry are generated through plotting the action function, offering valuable insights into the similarities and differences between various field types. Furthermore, a novel understanding of a field's energy-momentum emerges through these visualizations.

The relativistic dynamics derived herein accurately depict the motion of massive and massless objects under the influence of gravitational and/or electromagnetic fields, as well as in the presence of isotropic media. The reader will gain proficiency in computing Mercury's precession, light deflection, and the Shapiro time delay. Additionally, the book covers relativistic motion of binary stars, encompassing gravitational wave generation, the derivation of Snell's Law, and a relativistic description of spin. We derive a complex-valued prepotential for an electromagnetic field, akin to the wave function in quantum mechanics. The mathematics presented here is accessible to students after completing standard courses in multivariable calculus and linear algebra. For those unfamiliar with tensors and the calculus of variations, these topics are developed in rigorous detail within the opening chapters.

The unified model presented herein holds immense potential for upper undergraduate and graduate students, as well as seasoned researchers. Its simplicity and comprehensive nature make it a valuable resource for advancing our understanding of fundamental physics and its interdisciplinary applications.

Weight: 489g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031252136
Edition number: 1st ed. 2023