Special Relativity

Developed by Albert Einstein in 1905, Special Relativity is a foundational theory of physics that describes the relationship between space and time for objects moving at constant velocities. It is built upon two fundamental postulates: that the laws of physics are the same for all observers in uniform motion, and that the speed of light in a vacuum is constant for all observers, regardless of their motion or the motion of the light source. These principles lead to profound and counterintuitive consequences, including time dilation (moving clocks run slower), length contraction (moving objects appear shorter in their direction of motion), and the famous mass-energy equivalence, expressed by the equation E=mc².

1. Foundations of Relativity
   1. Historical Context
      1. Classical Physics Overview
         1. Newtonian Worldview
         2. Mechanical Universe Concept
         3. Deterministic Framework
      2. The Crisis in 19th Century Physics
         1. Incompatibility of Mechanics and Electromagnetism
         2. The Ether Problem
         3. Blackbody Radiation Issues
   2. Pre-Einstein Physics
      1. Newtonian Mechanics
         1. Newton's Laws of Motion
            1. First Law of Motion
            2. Second Law of Motion
            3. Third Law of Motion
         2. Absolute Space and Time
            1. Newton's Absolute Framework
            2. Universal Time Concept
            3. Absolute Reference Frame
         3. Determinism in Newtonian Physics
            1. Predictability of Motion
            2. Causal Relationships
      2. Galilean Relativity and Transformations
         1. Galilean Principle of Relativity
            1. Equivalence of Inertial Frames
            2. Invariance of Mechanical Laws
         2. Galilean Transformation Equations
            1. Coordinate Transformations
            2. Velocity Addition Formula
            3. Time Transformation
         3. Limitations of Galilean Transformations
            1. Failure with Electromagnetic Phenomena
            2. Speed of Light Problem
      3. The Principle of Inertia
         1. Definition and Implications
            1. Objects at Rest and in Motion
            2. Force-Free Motion
         2. Inertial vs Non-inertial Frames
            1. Characteristics of Inertial Frames
            2. Fictitious Forces in Non-inertial Frames
   3. Electromagnetism and the Ether
      1. Maxwell's Equations
         1. Unification of Electricity and Magnetism
            1. Electric Field Equations
            2. Magnetic Field Equations
            3. Electromagnetic Induction
         2. Prediction of Electromagnetic Waves
            1. Wave Equation Derivation
            2. Speed of Electromagnetic Waves
      2. The Predicted Speed of Light
         1. Light as an Electromagnetic Wave
            1. Wave Nature of Light
            2. Electromagnetic Spectrum
         2. Constancy of Light Speed in Maxwell's Theory
            1. Theoretical Prediction
            2. Experimental Confirmation
      3. The Luminiferous Ether Hypothesis
         1. Nature and Properties of the Ether
            1. Mechanical Properties Required
            2. Contradictory Characteristics
         2. Ether as a Medium for Light Propagation
            1. Wave Medium Necessity
            2. Absolute Reference Frame Concept
      4. The Michelson-Morley Experiment
         1. Experimental Setup
            1. Interferometer Design
            2. Measurement Principle
            3. Expected Results Based on Ether Theory
         2. Null Result and its Implications
            1. Failure to Detect Ether Wind
            2. Precision of Measurements
            3. Impact on Physics Community
         3. Subsequent Experiments and Reactions
            1. Repetitions and Refinements
            2. Alternative Explanations Attempted