Table of Contents

Part I - Space-time Geometry

• Introduction
• Why Special Relativity Is Interesting
• Summary of Important Results
• The Idea of Space-Time is Pretty Simple
• Example Histories
• Grids Measure Motion
• Grids Measure Time With Many Sensors, Not One
• A Camera Is Not A Grid
• Inertial Grid
• Inertial Grid Family
• Invariants: What Family Members Agree On
• What Does Relative Mean?
• Rule Zero: The Rule About All The Other Rules
• The Problem Of Language
• Invariant #1: Speed Limit
• Examples of Fast Objects
• Geometric Points Have No Speed Limit
• ct Is Better Than t
• Invariant #2 - The Space-Time Interval
• Light-like, Time-like, and Space-like
• Cause And Effect
• Surfaces With Constant s²
• Measure Rel-Time Dilation
• Standard Configuration Of Two Grids
• Rel-time Intervals Are Relative, Not Invariant
• Reverse The Perspective
• Warp Factor
• Measuring Intervals With Only A Single Sensor
• An Object's Wristwatch Measures The Interval
• Rel-Time Dilation Revisited
• Three Weeks To The Pleiades
• Moving Children Age More Slowly
• Rule For Uniform Motion
• Action Principles
• Boost Transformation - Overview
• Boost Transformation - Details
• Active Versus Passive Boosts
• Time Order Can Change
• Pancake Effect (Rel-Length Contraction)
• Why Rel-Size Decreases
• Does It Really Dilate/Contract?
• Invariant #3: Volumes in Space-Time
• Time Machines and Wormholes
• The Here-And-Now Is Stretched Out
• Is Rel-Time The Fourth Dimension?
• Space-Time Geometry Constrains The Rules
• Electrodynamics Pops Out Of Special Relativity
• Boosted Rel-Velocity
• Core Items Are Dimensionless
• Avoid Common Pitfalls
• How Special Relativity Relates to Other Parts of Physics
• Four Time Dimensions
• Questions To Ask Of An Author

Part II - Optics and Signals

• Grids, Sensors, and Signals
• Signals: Energy And Direction
• Light-Slice and Time-Slice
• Photon Signals
• Events On The Light Cone With Constant ct
• Direction: Aberration
• Aberration Preserves Angles
• Frequency: Doppler Effect
• Two Variations for the θ Angle
• Optical Effects as Non-Mysterious Prototypes
• Doppler Factor
• Brightness: Beaming Effect
• The Appearance of a Sky Full of Stars
• Angular Size
• Geometric Outline
• Apparent Velocity
• Astrophysical Jets

Animations

Warning: sometimes screens can subtly distort images. For example, the author has seen small but measurable distortions in some angles, when a screen is not using its default resolution.

Animations - Part I:

• Example Histories
• The Slowness of c In Astronomical Contexts
• Beta, Gamma, and Interval
• Inertial Grid Family
• Boost Transformation - Events
• Boost Transformation - Histories
• Boost Velocity

Animations - Part II:

• Light Cone Boost
• Aberration as Boost of Rel-Speed=1
• Doppler Effect
• Doppler Factor
• Doppler Effect and Aberration Together
• Stars From a Travelling Spacecraft (this one is especially interesting)
• Apparent Velocity as Intersection Point
• Apparent Velocity
• Apparent Magnitude
• Astrophysical Jets

Other Pages

• Terms Used, and Terms Avoided
• Resources and References
• Collected Formulas
• Version History and Errata
• Notes on Groups
• Software - Relativistic Starfield
• The github repository for this entire site.

Author