UNIVERSITY OF NEVADA, LAS VEGAS Getting the Measure of Einstein’s Space and Time An Introduction to Special Relativity Len Zane 12/12/2014 The space and time introduced by Albert Einstein in 1905 is explained by examining a series of simple thought or “gedanken” experiments. The development makes extensive use of spacetime diagrams to help readers appreciate the full extent of these changes. Table of Contents Introduction ................................................................................................................................................ 4 Chapter One: Space and Time Before 1905 ............................................................................................ 6 Speed and Velocity ................................................................................................................................ 6 The Experimenters are Introduced ...................................................................................................... 6 The First Set of Experiments: Earth-Based ........................................................................................ 8 The Second Set of Experiments: Bus-Based ..................................................................................... 11 Bev and Anne Carefully Observe the Experiment Done on the Bus ............................................ 12 The Addition of Velocities Formula .................................................................................................. 15 A Picture is Worth a Thousand Words ............................................................................................. 17 The Galilean Transformation Equations ........................................................................................... 22 Summary of Chapter One ................................................................................................................... 26 The Principle of Relativity and the Isotropy of Space................................................................. 26 Space and Time pre-1905 ................................................................................................................ 27 Chapter Two: The Speed of Light ......................................................................................................... 28 Chapter Three: Space and Time After 1905 ......................................................................................... 31 A New Set of Experiments are Proposed.......................................................................................... 31 New Stop Watches are distributed .................................................................................................... 31 Anne and Bev Measure the Speed of Light ...................................................................................... 31 The Super Bus Rolls into the Story .................................................................................................... 34 Anne and Bev Observe the Light Flash on the Bus: I ..................................................................... 36 Anne and Bev Observe the Light Flash on the Bus: II .................................................................... 41 The Effect of Motion on Space ............................................................................................................ 48 The Effect of Motion on Time ............................................................................................................. 51 Light Moves through Space and Time in a Very Strange Way ..................................................... 54 Chapter Four: Generalizing the Observations .................................................................................... 56 Defining the New Problem ................................................................................................................. 57 Finding the Shrinkage Factor ............................................................................................................. 58 The Ticking Rate of Moving Clocks .................................................................................................. 62 1 Quantifying the Disagreement over Synchronization .................................................................... 63 Testing the Theory ............................................................................................................................... 66 A Question about Synchronization ................................................................................................... 68 Global Positioning System (GPS) ....................................................................................................... 70 Chapter Five: The Relationship between Bus and Earth Observers ................................................ 72 Combining Spacetime Graphs ........................................................................................................... 72 Bev Generalizes Chuck’s Spacetime Diagram ................................................................................. 79 A Simple Example for Dean ............................................................................................................... 83 The Revised Equation for the Addition of Velocities ..................................................................... 84 Chapter Six: Chuck Suggests an Experiment and Anne has a Dream ............................................ 89 Experiment I.......................................................................................................................................... 90 Experiment II ........................................................................................................................................ 93 Answers for Experiment I ................................................................................................................... 97 Answers for Experiment II ............................................................................................................... 100 Anne has a Dream about a Superluminal Pigeon ......................................................................... 104 Chapter Seven: The Bus and the Garage ........................................................................................... 108 Anne’s Proposal ................................................................................................................................. 115 The Collision between Theory and Reality .................................................................................... 116 R.I.P. Super Bus .................................................................................................................................. 118 Chapter Eight: The Solar System and Beyond .................................................................................. 120 Synchronizing Watches Separated by Large Distances ................................................................ 121 Chapter Nine: Chuck and Dean Travel to Alpha Centauri ............................................................. 123 May 1, Thirteen Years Later.............................................................................................................. 124 Using the Lorentz Equations ............................................................................................................ 130 Looking at a Moving Watch – The Doppler Effect ........................................................................ 132 Chapter Ten: Space Travel ................................................................................................................... 136 The Equivalence Principle ................................................................................................................ 136 Designing the Space Adventure ...................................................................................................... 139 The Results of Chuck’s Calculations ............................................................................................... 143 2 How does a Rocket Accelerate? ....................................................................................................... 148 Bonus Topic: A Peek at General Relativity ..................................................................................... 152 Chapter Eleven: Does it Really Happen? ........................................................................................... 154 The Far-Away Observer (FAO) ........................................................................................................ 154 A Dynamic Explanation for the Behavior of Watches and Rulers .............................................. 158 A Model for a Hydrogen Atom ........................................................................................................ 159 Chapter Twelve: E = mc2 ...................................................................................................................... 162 Appendix A: Graphing ......................................................................................................................... 169 Appendix B: Scientific Notation.......................................................................................................... 172 Appendix C: The Light Clock .............................................................................................................. 173 Appendix D: The Gravitational Clock Effect ...................................................................................