Geometry of Minkowski Space-Time

Front Cover
Springer Science & Business Media, May 7, 2011 - Science - 116 pages

This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.

The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions.

The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.

Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 Introduction
1
2 Hyperbolic Numbers
3
3 Geometrical Representation of Hyperbolic Numbers
25
4 Trigonometry in the Hyperbolic Minkowski Plane
33
5 Equilateral Hyperbolas and Triangles in the Hyperbolic Plane
57
6 The Motions in Minkowski SpaceTime Twin Paradox
73
7 Some Final Considerations
97
The Presentday Meaning of Geometry
101
Conclusions
111
Reference
112
Index
113
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information