Illustrated Special Relativity through its Paradoxes : a Fusion of Linear Algebra, Graphics, and Reality

Illustrated Special Relativity through its Paradoxes : a Fusion of Linear Algebra, Graphics, and Reality / illustrated by John dePillis, Jose Wudka.

Illustrated Special Relativity shows that linear algebra is a natural language for special relativity. It illustrates and resolves several apparent paradoxes of special relativity including the twin paradox and train-and-tunnel paradox. Assuming a minimum of technical prerequisites the authors intro...

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Bibliographic Details
Other Authors: Wudka, Jose
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 2014.
Series:Bibliografija "Spectrum."
Subjects:
Algebras, Linear.
Special relativity (Physics)
Algebras, Linear
Online Access:Click for online access
Table of Contents:
  • 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 ClockSynchronizing 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 MatrixPattern 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 TheoremInterpreting 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 ParadoxAn 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.

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