The Geometry of Time

  • ID: 2180208
  • Book
  • 253 Pages
  • John Wiley and Sons Ltd
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A description of the geometry of space–time, in particular the theory of special relativity, with all the questions and issues explained without relying solely on formulas. The author shows that the geometry of space–time is indeed geometry, using actual constructions with which we are familiar from Euclidean geometry, and which admit exact demonstrations and proofs. He also uses the relation to projective geometry to illustrate the starting points of general relativity.

This is not intended as a textbook aimed at introducing readers to the theory of relativity so they may calculate formally, but rather its aim is to show the connection with synthetic geometry –– a first in books on special relativity.

The book is written at an introductory (undergraduate) level, with the formal mathematics behind the constructions provided in the appendices. The novel presentation allows teaching staff to learn from it, too.

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1 Introduction

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

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Dierck–Ekkehard Liebscher
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