Special Relativity: A Heuristic Approach

Cover
Special Relativity:
A Heuristic Approach
Copyright
Dedication
Preface
List of Symbols, Phrases, and Acronyms
Note to the Reader
1 Qualitative Relativity
	1.1 It Began With Maxwell
		1.1.1 Einstein and Signal Velocity
	1.2 Relativity of Simultaneity
		1.2.1 Simultaneity in a Single RF
		1.2.2 Simultaneity in Different RFs
	1.3 Relativity of Length
	1.4 Problems
2 Relativity of Time and Space
	2.1 Time Dilation
		2.1.1 Proper Time
	2.2 Length Contraction
	2.3 Relativisticity
	2.4 The Twin Paradox
	2.5 Problems
3 Lorentz Transformation
	3.1 \"Derivation\" of Euclidean Distance
		3.1.1 Coordinate Transformation
	3.2 Spacetime Distance
	3.3 Lorentz Transformation
	3.4 Examples of the Use of LT
	3.5 Relativistic Law of Addition of Velocities
	3.6 Problems
4 Spacetime Geometry
	4.1 Plane Spacetime Geometry
		4.1.1 Events and Worldlines
		4.1.2 Light Cone
	4.2 Rules of Spacetime Geometry
		4.2.1 Invariant Distance
		4.2.2 The Rules
	4.3 Examples of Spacetime Diagrams
		4.3.1 Simultaneity Revisited
		4.3.2 The Train and the Tunnel
		4.3.3 The Doppler Effect
		4.3.4 Time Travel?
	4.4 Lorentz Transformation Revisited
		4.4.1 Lorentz Transformation and Time Travel
	4.5 Curved Worldlines
		4.5.1 The Spacetime Triangle Inequality
		4.5.2 The Twin Paradox Revisited
	4.6 Problems
5 Spacetime Momentum
	5.1 Spacetime Velocity
	5.2 Spacetime Momentum
		5.2.1 Relativistic Energy
		5.2.2 No Mass at Light Speed
		5.2.3 Invariant Length of Spacetime Momentum
		5.2.4 No Velocity-Dependent Mass
	5.3 Conservation of Momentum
		5.3.1 The Classical Case
		5.3.2 The Relativistic Case
	5.4 Problems
6 Relativity in Four Dimensions
	6.1 Four-Vectors
	6.2 Lorentz Transformation in 4D
	6.3 General Velocity Addition Formula
		6.3.1 Aberration
			Aberration of Starlight
	6.4 General Doppler Effect
	6.5 Global Positioning System
	6.6 Four-Velocity
	6.7 Four-Momentum
	6.8 Second Law of Motion
		6.8.1 Four-Acceleration
		6.8.2 Four-Force
		6.8.3 Weirdness of Velocity-Dependent Mass
	6.9 Problems
7 Relativistic Photography
	7.1 History
	7.2 Physics of Photography
	7.3 Photograph of Two Points
	7.4 Photograph of a Rod
	7.5 Photograph of a Cube
		7.5.1 Capturing Length Contraction With a Camera
	7.6 Photograph of a Sphere at the Origin
		7.6.1 Cone Construction via Aberration Formula
		7.6.2 Cone Construction via Relativistic LAV
		7.6.3 Cone Construction via LT of Emission Events
	7.7 Photograph of a Sphere off the Origin
		7.7.1 Stationary Sphere
		7.7.2 Moving Sphere
	7.8 Problems
8 Relativistic Interactions
	8.1 Center of Mass and Lab Frames
		8.1.1 Lorentz Transformation of CM
	8.2 Two-Particle Collision
		8.2.1 Minimum Two-Particle Production Energy
		8.2.2 Minimum Multi-Particle Production Energy
	8.3 Decays
	8.4 Special Relativity, Spin, and Antimatter
		8.4.1 Dirac Equation
		8.4.2 Discovery of Antimatter
	8.5 Problems
9 Interstellar Travel
	9.1 Massive Particle Propulsion
	9.2 Photon Propulsion
		9.2.1 Uniform Depletion
		9.2.2 Laser Propulsion
	9.3 Ground-Based Propulsion
		9.3.1 The Physics
		9.3.2 The Equation of Motion
		9.3.3 The Formal Solution
		9.3.4 Numerical Examples
		9.3.5 Nonrelativistic Limits
	9.4 Problems
10 A Painless Introduction to Tensors
	10.1 From Boldface to Indices
		10.1.1 Dot and Cross Products
		10.1.2 Proof of Note 7.6.2
	10.2 Index Management in Special Relativity
	10.3 Invariance of the Elemental 4-Volume
	10.4 Problems
11 Relativistic Electrodynamics
	11.1 Transformation of Ē and B̄
		11.1.1 Transformation of Ē
		11.1.2 Transformation of B̄
	11.2 Field of a Uniformly Moving Charge
	11.3 Electromagnetic Field Tensor
		11.3.1 Lorentz Force Law
		11.3.2 The Cyclotron
		11.3.3 Maxwell\'s Equations
	11.4 Problems
12 Early Universe
	12.1 Photon Gas
	12.2 Friedmann Equation
	12.3 The Densities
	12.4 Evolution of the Universe
		Matter Dominance
		Radiation Dominance
		Dark Energy Dominance
	12.5 Cosmic Background Radiation
	12.6 Cosmic Genesis
		The First Epoch 1015 K