Education Is the Single Most Factor in the Development of Country
THE SPECIAL THEORY OF RELATIVITY
Lecture Notes prepared by
J D Cresser Department of Physics Macquarie University
July 31, 2003
CONTENTS
1
Contents
1 Introduction: What is Relativity? 2 Frames of Reference 2.1 2.2 A Framework of Rulers and Clocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 5 7 7 9 9
Inertial Frames of Reference and Newton’s First Law of Motion
3 The Galilean Transformation 4 Newtonian Force and Momentum 4.1 4.2 Newton’s Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . .
Newton’s Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . 10 10 11 13 14 16
5 Newtonian Relativity 6 Maxwell’s Equations and the Ether 7 Einstein’s Postulates 8 Clock Synchronization in an Inertial Frame 9 Lorentz Transformation 9.1 9.2 9.3 9.4
Length Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Simultaneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Transformation of Velocities (Addition of Velocities) . . . . . . . . . . . . . 24 27
10 Relativistic Dynamics
10.1 Relativistic Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 10.2 Relativistic Force, Work, Kinetic Energy . . . . . . . . . . . . . . . . . . . . 29 10.3 Total Relativistic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.4 Equivalence of Mass and Energy . . . . . . . . . . . . . . . . . . . . . . . . 33 10.5 Zero Rest Mass Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 11 Geometry of Spacetime 35
11.1 Geometrical Properties of 3 Dimensional Space . . . . . . . . . . . . . . . . 35 11.2 Space Time Four Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 11.3 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 11.4 Properties of Spacetime Intervals . . . . . . . .
Lecture Notes prepared by
J D Cresser Department of Physics Macquarie University
July 31, 2003
CONTENTS
1
Contents
1 Introduction: What is Relativity? 2 Frames of Reference 2.1 2.2 A Framework of Rulers and Clocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 5 7 7 9 9
Inertial Frames of Reference and Newton’s First Law of Motion
3 The Galilean Transformation 4 Newtonian Force and Momentum 4.1 4.2 Newton’s Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . .
Newton’s Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . 10 10 11 13 14 16
5 Newtonian Relativity 6 Maxwell’s Equations and the Ether 7 Einstein’s Postulates 8 Clock Synchronization in an Inertial Frame 9 Lorentz Transformation 9.1 9.2 9.3 9.4
Length Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Simultaneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Transformation of Velocities (Addition of Velocities) . . . . . . . . . . . . . 24 27
10 Relativistic Dynamics
10.1 Relativistic Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 10.2 Relativistic Force, Work, Kinetic Energy . . . . . . . . . . . . . . . . . . . . 29 10.3 Total Relativistic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 10.4 Equivalence of Mass and Energy . . . . . . . . . . . . . . . . . . . . . . . . 33 10.5 Zero Rest Mass Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 11 Geometry of Spacetime 35
11.1 Geometrical Properties of 3 Dimensional Space . . . . . . . . . . . . . . . . 35 11.2 Space Time Four Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 11.3 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 11.4 Properties of Spacetime Intervals . . . . . . . .