The Geometry of Time
1. Edition February 2005
XII, 241 Pages, Softcover
182 Pictures
Textbook
Short Description
The book describes the geometry of space-time that is in particular the theory of special relativity, with all the questions and issues which are difficult to comprehend when explained by way of formulas only. It shows that the geometry of space-time is indeed geometry, with actual constructions which we are familiar with from Euclidean geometry and which admit exact demonstrations and proofs. The relation to projective geometry is presented and used to illustrate the starting points of general relativity.
The book is not intended as a textbook with the aim to introduce the reader to the theory of relativity in order to enable him to calculate formally. Its aim is rather to show the connection with synthetic geometry. The formal mathematics behind the constructions is provided in the appendices.
The book is written at an introductory (undergraduate) level. The kind of presentation is new so that teaching staff will learn from it, too. In the many existing books on Special Relativity, the connection to elementary synthetic geometry is not used at all. In the present book, however, the formal introduction of these books is complemented with the (synthetic) geometric aspect.
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A description of the geometry of space-time with all the questions and issues explained without the need for formulas. As such, the author shows that this is indeed geometry, with actual constructions familiar from Euclidean geometry, and which allow exact demonstrations and proofs. The formal mathematics behind these constructions is provided in the appendices.
The result is thus not a textbook introducing readers to the theory of special relativity so they may calculate formally, but rather aims to show the connection with synthetic geometry. It presents the relation to projective geometry and uses this to illustrate the starting points of general relativity. Written at an introductory level for undergraduates, this novel presentation will also benefit teaching staff.
2 The World of Space and Time
2.1 Time-tables
2.2 Surveying space-time
2.3 Physical prerequisites of geometry
3 Reflection and Collision
3.1 Geometry and reflection
3.2 The reflection of mechanical motion
4 The Relativity Principle of Mechanics and Wave Propagation
5 Relativity Theory and its Paradoxes
5.1 Pseudo-Euclidean geometry
5.2 Einstein's mechanics
5.3 Energy
5.4 Kinematic peculiarities .
5.5 Aberration and Fresnel's paradox .
5.6 The net
5.7 Faster than light
6 The Circle Disguised as Hyperbola
7 Curvature
7.1 Spheres and hyperbolic shells .
7.2 The universe
8 The Projective Origin of the Geometries of the Plane
9 The Nine Geometries of the Plane
10 General Remarks
10.1 The theory of relativity .
10.2 Geometry and physics
A Reections
B Transformations
B.1 Coordinates
B.2 Inertial reference systems
B.3 Riemannian spaces, Einstein worlds
C Projective Geometry
C.1 Algebra .
C.2 Projective maps
C.3 Conic sections
D The Transition from the Projective to the Metrical Plane
D.1 Polarity
D.2 Reection
D.3 Velocity space
D.4 Circles and peripheries
D.5 Two examples
E The Metrical Plane
E.1 Classi_cation
E.2 The Metric
Exercises
References
Glossary
CHOICE
Professor of Theoretical Physics
Institute of Astrophysics
University of Potsdam, Germany
Dierck-Eckehard Liebscher studied physics at the Humboldt University, Berlin, and received two PhDs in 1966 and 1973, both on topics of general relativity. From 1967 to 1991, he worked at the Central Institute for Astrophysics of the former GDR. In 1992, he accepted a post as senior scientist at the Astrophysical Institute, Potsdam, where he still works. Professor Liebscher is the author of several books and numerous papers.
