Special Relativity

  1. The Lorentz Transformations
    1. Mathematical Framework of Special Relativity
      1. Coordinate Systems and Events
        1. Spacetime Coordinates
          1. Event Representation
          2. Notation and Conventions
            1. Standard Coordinate Systems
              1. Velocity Notation
            2. Derivation of the Lorentz Transformations
              1. From the Postulates
                1. Linearity Requirements
                  1. Consistency with the Speed of Light
                    1. Light Signal Transformations
                      1. Invariance Conditions
                    2. The Lorentz Factor (Gamma)
                      1. Definition and Properties
                        1. Mathematical Expression
                          1. Velocity Dependence
                          2. Limiting Cases (Low and High Velocity)
                            1. Non-relativistic Limit
                              1. Ultra-relativistic Behavior
                          3. Comparison with Galilean Transformations
                            1. Differences in Space and Time Treatment
                              1. Coupled Space-Time Transformations
                                1. Time Transformation Necessity
                                2. Breakdown at High Velocities
                                  1. Galilean Approximation Limits
                                    1. Relativistic Corrections
                                  2. Lorentz Transformation of Coordinates
                                    1. Transformation of Space Coordinates
                                      1. Longitudinal Coordinate Transformation
                                        1. Transverse Coordinate Invariance
                                        2. Transformation of Time Coordinates
                                          1. Time Mixing with Space
                                            1. Simultaneity Changes
                                            2. Inverse Transformations
                                              1. Reciprocal Relationships
                                                1. Symmetry Properties
                                              2. Lorentz Transformation of Velocities
                                                1. The Relativistic Velocity Addition Formula
                                                  1. Derivation and Application
                                                    1. Mathematical Derivation
                                                      1. Physical Interpretation
                                                    2. Consequences for Light and Massive Particles
                                                      1. Light Speed Invariance
                                                        1. Velocity Limits for Massive Objects

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                                                    3. Kinematic Consequences of the Postulates

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                                                    5. Spacetime: The Geometric View