front cover -- copyright page -- Contents -- I. A FIRST PASS -- Preface -- Exposition and Paradoxes -- Organization of this Book -- Introduction to the Paradoxes -- Aristotle vs. Galileo -- Frames of Reference -- Straight-Line Trajectories in 3-Space -- Galilean Relativity -- Special Relativity: A First Pass -- A Symmetry Principle -- Lorentzian Relativity -- The Ubiquitous Shrinkage Constant -- Paradox: The Accommodating Universe -- Paradox: Time and Distance Asymmetry -- Paradox: The Traveling Twin -- Paradox: The Train in the Tunnel -- Paradox: The Pea-Shooter -- Paradox: The Bug and Rivet -- Exercises -- Clocks and Rods in Motion -- The Perfect Clock -- Synchronizing Clocks within a Single Frame -- Moving Clocks Run Slow, Moving Rods Shrink -- Exercises -- The Algebra of Frames -- Inertial Frames of Reference -- Vector Space Structure of Frames -- Several Parallel Moving Frames -- Six Rules for Frames -- Exercises -- The Graphing of Frames -- The Filmstrip Model of Spacetime -- Constant Velocities in Spacetime -- Worldlines are Parallel to the Home Frame Time Axis -- Simultaneous and Static Events -- Linearity of Line-of-Sight Functions -- Exercises -- II. GALILEAN TRANSFORMATIONS OF FRAMES -- Galilean Transformations -- Key Ideas -- Galilean Spacetime Diagrams -- The Galilean Matrix -- Pattern of the Galilean Matrix -- Addition of Speeds via Matrices -- Addition of Speeds via Areas -- III. The SPEED OF LIGHT IS CONSTANT -- Constant c in Spacetime -- Minkowski Spacetime Diagrams -- Constant c and Simultaneity -- How Constant c Destroys Simultaneity -- Exercise -- IV. LORENTZ TRANSFORMATIONS OF FRAMES -- Lorentz Transformations -- The Lorentz Matrix -- Pattern of the Lorentz Matrix -- The Lorentz Sum of Speeds -- Addition of Speeds via Matrices -- Addition of Speeds via Areas -- Exercises -- The Hyperbola of Time-Stamped Origins.

Invariance of Minkowski Length -- The Time-Stamped Origins Theorem -- Interpreting the Time-Stamped Origins Theorem -- Tangent Lines of Simultaneity -- Exercises -- V. GRAPHIC RESOLUTION OF THE PARADOXES -- The Accommodating Universe Paradox -- Preview -- Setup for the Minkowski Diagram -- Resolving the Accommodating Universe -- Exercises -- The Length-Time Comparison Paradoxes -- An Overview of the Paradoxes -- Resolving the Mutual Length-Time Paradoxes -- Summary -- Exercises -- The Twin Paradox -- An Overview of the Paradox -- A Simplifying Assumption -- Setup for the Minkowski Diagram -- Resolving the Twin Paradox -- General Relativity Confirmation -- Exercises -- The Train-Tunnel Paradox -- An Overview of the Paradox -- A Distance Lemma -- The Train-Tunnel Minkowski Diagram -- Explaining Mutual Contraction -- Resolving the Train-Tunnel Paradox -- Exercises -- The Pea-Shooter Paradox -- An Overview of the Paradox -- The Fizeau Experiment: Adding Speeds -- Exercises -- The Bug-Rivet Paradox -- The Minkowski Diagram -- Coordinates in the Minkowski Diagram -- The Slinky Connection -- Exercises -- VI. ENERGY AND MASS -- E = mc2 -- How We Came to This Place -- Speed-Dependent Mass: an Intuitive View -- Equivalence of Mass and Energy -- A Numerical Example -- Exercises -- VII. THE MATHEMATICS OF WAVES AND LIGHT -- The Nature of Waves -- Propagated Waves -- Speed of Rope Wave is Constant -- Shapes Traveling in One Dimension -- The Wave Equation in One Dimension -- Wave Propagation: The Skipping Stone Model -- The Doppler Effect in Spacetime -- Exercises -- Measuring the Speed of Light -- Early Thoughts on the Speed of Light -- Rømer: The Speed of Light is Finite -- Fizeau Measures the Speed of Light -- de Sitter: c Independent of Source Speed -- Michelson-Morley's Happy Failure -- Exercises -- VIII. MAXWELL'S EQUATIONS -- Maxwell's Mathematical Toolkit.

Preface -- Language and Proportionality -- 1D Lengths & 2D Areas as 3D Vectors -- Orientations of Lines and Surfaces -- Vectors Modeling Reality -- Inner and Cross Products -- Riemann Sums and Integrals -- Integrals of the Inner Product -- Exercises -- Electric and Magnetic Fields -- Background -- Electric Forces: Coulomb's Law -- Electric Fields -- Magnetic Fields -- Magnetic Forces: Lorentz Forces -- How Thomson Discovers the Electron -- Electricity and Magnetism: Gauss' Laws -- Flux of Vector Fields -- Electric and Magnetic Flux -- Gauss' Law for Electricity -- Gauss' Law for Magnetism -- Exercises -- Towards Maxwell's Equations -- Biot-Savart Law: Magnetism from Electricity -- Quantitative Results for Biot-Savart -- Ampère's Law -- Maxwell Adds to Ampère's Law -- Faraday's Law: Electricity from Magnetism -- Lentz's Law: The Positive Side of Negativity -- Maxwell's Four Equations -- Exercises -- Electromagnetism: A Qualitative View -- Magnetic Waves from an Infinite Wire -- Wave Propagation -- The Geometry of Electromagnetism -- Electromagnetism: A Quantitative View -- Quantitative Preliminaries -- A Quantitative View of Propagation -- Theoretical Speed of Wave Propagation -- Maxwell's Calculation of c -- Mathematical Hits -- Exercises -- IX. FINAL THOUGHTS -- Epilogue: Final Thoughts -- A Coming of Age -- Einstein's Annus Mirabilis -- Comparing Relativities -- Against Conventional Wisdom -- Some Experimental Results -- Bad Assumption, Good Result -- A Limited Reality -- PIES Reality -- Exercises -- X. APPENDICES -- Linear Algebra Overview -- Mathematics as a Conduit to Reality -- Vector Spaces -- Functions -- Linear Functions and Matrices -- Eigenvectors and Eigenvalues -- Hyperbolic Functions -- Overview -- Even and Odd Functions -- Invariant Areas of Transformed Hyperbolas -- Exercises -- Deconstructing a Moving Train -- Motion Alters Age.

Minkowski Diagram for a Moving Train -- Exercises -- XI. SUPPLEMENTAL MATERIAL -- Dimensional Analysis -- Unitless Quotients of Dimensions -- Dimensions in Fractions -- Exercises -- Rings of Functions and Square Matrices -- Associative, Binary Operations -- Rings over the Real Numbers -- The Ring of Matrices -- Exercises -- The Scientific Method -- Reality of the Unseen -- If-then Sentences -- Property Lists -- The Four-Step Scientific Method -- Is X a Duck? Applying the Scientific Method. -- Whence the Scientific Method? -- The Logical Implication -- Induction vs. Deduction -- Necessary vs. Sufficient -- Uncertainty, Popper, and Derrida. -- Popper Logic -- Exercises -- Logic of the Scientific Method -- Implications Built from P, Q -- Equivalence of Implications -- Proof by Contradiction -- Exercises -- Bibliography -- Index.