Special Relativity

  1. Kinematic Consequences of the Postulates
    1. The Relativity of Simultaneity
      1. Definition and Conceptual Basis
        1. Observer-Dependent Simultaneity
          1. Breakdown of Absolute Time
          2. Thought Experiment: The Moving Train
            1. Description of the Experiment
              1. Lightning Strikes Setup
                1. Observer Positions
                2. Analysis from Different Frames
                  1. Platform Observer Perspective
                    1. Train Observer Perspective
                  2. Dependence of Simultaneity on the Observer's Frame
                    1. Mathematical Relationship
                      1. Physical Interpretation
                      2. Synchronization of Clocks
                        1. Einstein Synchronization Procedure
                          1. Clock Synchronization Problems
                        2. Time Dilation
                          1. Moving Clocks Run Slower
                            1. Mathematical Expression of Time Dilation
                              1. Time Dilation Factor
                                1. Proper Time vs Coordinate Time
                              2. The Light Clock Thought Experiment
                                1. Setup and Analysis
                                  1. Vertical Light Path
                                    1. Diagonal Light Path in Moving Frame
                                    2. Derivation of Time Dilation Formula
                                      1. Geometric Analysis
                                        1. Pythagorean Theorem Application
                                      2. Proper Time
                                        1. Definition and Calculation
                                          1. Time Measured in Rest Frame
                                            1. Invariant Time Interval
                                          2. Experimental Evidence
                                            1. Muon Decay in the Atmosphere
                                              1. Cosmic Ray Muons
                                                1. Extended Lifetime Observation
                                                2. Atomic Clocks in Flight
                                                  1. Hafele-Keating Experiment
                                                    1. GPS Satellite Corrections
                                                    2. Particle Accelerators
                                                      1. High-Speed Particle Lifetimes
                                                        1. Accelerator Measurements
                                                    3. Length Contraction
                                                      1. Moving Objects Appear Shorter
                                                        1. Mathematical Expression of Length Contraction
                                                          1. Contraction Factor
                                                            1. Proper Length vs Contracted Length
                                                          2. Contraction in the Direction of Motion
                                                            1. Longitudinal Contraction Only
                                                              1. Transverse Dimensions Unchanged
                                                              2. Proper Length
                                                                1. Definition and Calculation
                                                                  1. Length in Rest Frame
                                                                    1. Invariant Length Measurement
                                                                  2. Experimental Evidence
                                                                    1. High-Energy Particle Experiments
                                                                      1. Indirect Confirmations
                                                                    2. The Twin Paradox
                                                                      1. Statement of the Paradox
                                                                        1. Symmetric Time Dilation Problem
                                                                          1. Apparent Contradiction
                                                                          2. The Role of Acceleration
                                                                            1. Non-inertial Phases
                                                                              1. Departure Acceleration
                                                                                1. Turnaround Acceleration
                                                                                  1. Return Deceleration
                                                                                2. Resolution of the Paradox
                                                                                  1. Asymmetry in the Twins' Experiences
                                                                                    1. Inertial vs Non-inertial Motion
                                                                                      1. Proper Time Calculations
                                                                                      2. Spacetime Diagrams and Analysis
                                                                                        1. World Line Representations
                                                                                          1. Geometric Interpretation

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                                                                                    2. The Postulates of Special Relativity

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                                                                                    4. The Lorentz Transformations