- Title Pages
- Dedication
- Foreword
- Book 1 Space, time, and gravity in Newton’s theory
- Part I Kinematics
- 1 Cartesian coordinates
- 2 Vector geometry
- 3 Curvilinear coordinates
- 4 Differential geometry
- Part II Dynamics
- 5 Equations of motion
- 6 Dynamics of massive systems
- 7 Conservation laws
- 8 Lagrangian mechanics
- 9 Hamiltonian mechanics
- 10 Kinetic theory
- Part III Gravitation
- 11 The law of gravitation
- 12 The Kepler problem
- 13 The N-body problem
- 14 Deformations of celestial bodies
- 15 Self-gravitating fluids
- 16 Newtonian cosmology
- 17 Light in Newtonian theory
- Book 2 Special relativity and Maxwell’s theory
- Part I Kinematics
- 1 Minkowski spacetime
- 2 The kinematics of a point particle
- 3 The kinematics of light
- 4 The wave vector of light
- 5 Accelerated frames
- Part II Dynamics
- 6 Dynamics of a point particle
- 7 Rotating systems
- 8 Fields and matter
- 9 The classical scalar field
- 10 The Nordström theory
- Part III Electromagnetism
- 11 The Lorentz force
- 12 The Maxwell equations
- 13 Constant fields
- 14 The free field
- 15 Electromagnetic waves
- 16 Waves in a medium
- Part IV Electrodynamics
- 17 The field of a moving charge
- 18 Radiation by a charge
- 19 The radiation reaction force
- 20 Interacting charges I
- 21 Interacting charges II
- 22 Electromagnetism and differential geometry
- Book 3 General relativity and gravitation
- Part I Curved spacetime and gravitation
- 1 The equivalence principle
- 2 Riemannian manifolds
- 3 Matter in curved spacetime
- 4 The Einstein equations
- 5 Conservation laws
- Part II The Schwarzschild solution and black holes
- 6 The Schwarzschild solution
- 7 The Schwarzschild black hole
- 8 The Kerr solution
- 9 The physics of black holes I
- 10 The physics of black holes II
- Part III General relativity and experiment
- 11 Tests in the solar system
- 12 The post-Newtonian approximation
- 13 Gravitational waves and the radiative field
- 14 Gravitational radiation
- 15 The two-body problem and radiative losses
- 16 The two-body problem: an effective-one-body approach
- Part IV Friedmann–Lemaître solutions and cosmology
- 17 Cosmological spacetimes
- 18 Friedmann–Lemaître spacetimes
- 19 The Lambda-CDM model of the hot Big Bang
- 20 Inflationary models of the primordial universe
- 21 Cosmological perturbations
- 22 Primordial quantum perturbations
- Part V Elements of Riemannian geometry
- 23 The covariant derivative and the curvature
- 24 Riemannian manifolds
- 25 The Cartan structure equations
- Index

# Minkowski spacetime

# Minkowski spacetime

- Chapter:
- (p.179) 1 Minkowski spacetime
- Source:
- Relativity in Modern Physics
- Author(s):
### Nathalie Deruelle

### Jean-Philippe Uzan

- Publisher:
- Oxford University Press

This chapter presents the main features of the Minkowski spacetime, which is the geometrical framework in which the laws of relativistic dynamics are formulated. It is a very simple mathematical extension of three-dimensional Euclidean space. In special relativity, ‘relative, apparent, and common’ (in the words of Newton) space and time are represented by a mathematical set of points called events, which constitute the Minkowski spacetime. This chapter also stresses the interpretation of the fourth dimension, which in special relativity is time. Here, time now loses the ‘universal’ and ‘absolute’ nature that it had in the Newtonian theory.

*Keywords:*
Minkowski spacetime, relativistic dynamics, three-dimensional Euclidean space, special relativity, fourth dimension, time

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .

- Title Pages
- Dedication
- Foreword
- Book 1 Space, time, and gravity in Newton’s theory
- Part I Kinematics
- 1 Cartesian coordinates
- 2 Vector geometry
- 3 Curvilinear coordinates
- 4 Differential geometry
- Part II Dynamics
- 5 Equations of motion
- 6 Dynamics of massive systems
- 7 Conservation laws
- 8 Lagrangian mechanics
- 9 Hamiltonian mechanics
- 10 Kinetic theory
- Part III Gravitation
- 11 The law of gravitation
- 12 The Kepler problem
- 13 The N-body problem
- 14 Deformations of celestial bodies
- 15 Self-gravitating fluids
- 16 Newtonian cosmology
- 17 Light in Newtonian theory
- Book 2 Special relativity and Maxwell’s theory
- Part I Kinematics
- 1 Minkowski spacetime
- 2 The kinematics of a point particle
- 3 The kinematics of light
- 4 The wave vector of light
- 5 Accelerated frames
- Part II Dynamics
- 6 Dynamics of a point particle
- 7 Rotating systems
- 8 Fields and matter
- 9 The classical scalar field
- 10 The Nordström theory
- Part III Electromagnetism
- 11 The Lorentz force
- 12 The Maxwell equations
- 13 Constant fields
- 14 The free field
- 15 Electromagnetic waves
- 16 Waves in a medium
- Part IV Electrodynamics
- 17 The field of a moving charge
- 18 Radiation by a charge
- 19 The radiation reaction force
- 20 Interacting charges I
- 21 Interacting charges II
- 22 Electromagnetism and differential geometry
- Book 3 General relativity and gravitation
- Part I Curved spacetime and gravitation
- 1 The equivalence principle
- 2 Riemannian manifolds
- 3 Matter in curved spacetime
- 4 The Einstein equations
- 5 Conservation laws
- Part II The Schwarzschild solution and black holes
- 6 The Schwarzschild solution
- 7 The Schwarzschild black hole
- 8 The Kerr solution
- 9 The physics of black holes I
- 10 The physics of black holes II
- Part III General relativity and experiment
- 11 Tests in the solar system
- 12 The post-Newtonian approximation
- 13 Gravitational waves and the radiative field
- 14 Gravitational radiation
- 15 The two-body problem and radiative losses
- 16 The two-body problem: an effective-one-body approach
- Part IV Friedmann–Lemaître solutions and cosmology
- 17 Cosmological spacetimes
- 18 Friedmann–Lemaître spacetimes
- 19 The Lambda-CDM model of the hot Big Bang
- 20 Inflationary models of the primordial universe
- 21 Cosmological perturbations
- 22 Primordial quantum perturbations
- Part V Elements of Riemannian geometry
- 23 The covariant derivative and the curvature
- 24 Riemannian manifolds
- 25 The Cartan structure equations
- Index