Special Relativity

Special Relativity is a fundamental theory in physics formulated by Albert Einstein in 1905, which describes the behavior of objects moving at constant high speeds, particularly close to the speed of light. The theory introduces key concepts such as the relativity of simultaneity, time dilation, and length contraction, demonstrating that measurements of time and space are relative to the observer's state of motion. It fundamentally altered the understanding of space and time, establishing that the laws of physics are the same for all observers, regardless of their relative motion, and leading to the famous equation E=mc², which expresses the equivalence of mass and energy.

1. Introduction to Special Relativity
   1. Historical Context
      1. Pre-Einstein Physics
         1. Classical Mechanics
            1. Newtonian Framework
               1. Absolute Space and Time
               2. Limitations encountered at high velocities
            2. Applicability and Success in Low-Speed Regimes
         2. Electromagnetism
            1. Maxwell's Equations
               1. Unified Theory of Electricity and Magnetism
               2. Predicted Consistent Speed of Light in a Vacuum
            2. Challenges to Classical Mechanics
               1. Need for a Rest Frame for Light
         3. Michelson-Morley Experiment
            1. Objective to Detect the "Aether"
            2. Null Result
               1. Inconsistencies with Aether Hypothesis
               2. Implications for Stationary Medium
      2. Einstein's Breakthrough in 1905
         1. Annus Mirabilis Papers
            1. Development of Theory of Special Relativity
            2. Abandonment of Aether Concept
         2. Radical Re-envisioning of Space and Time
            1. Foundations for Modern Physics
            2. Focus on Observers and Light Propagation
   2. Core Principles
      1. Invariance of Physical Laws
         1. Equivalence of Physical Laws in All Inertial Frames
            1. Basis in Galileo's Principle of Relativity
         2. Mathematical Consistency and Universality
      2. Constancy of the Speed of Light
         1. Uniform Speed for All Observers Regardless of Motion
            1. Connection to Maxwell’s Equations
            2. Empirical Validation through Experimentation
            3. Departure from Common Intuitions of Velocity Addition
         2. Consequences for Simultaneity and Time