Unit 3097: Special Relativity

1. Introduction to Special Relativity

• Historical background
  • Development before Einstein: Michelson-Morley experiment, classical mechanics conflicts
  • Einstein’s 1905 paper and the motivation for special relativity
• Key concepts and principles
  • Principle of relativity: physical laws are the same in all inertial frames
  • Constancy of the speed of light in vacuum
  • Inertial reference frames and simultaneity

2. Lorentz Transformation

• Derivation of Lorentz transformations
  • Coordinates in different inertial frames
  • Mathematical form of Lorentz transformations
• Physical significance
  • Invariance of spacetime interval
  • Relation to Galilean transformations

3. Time Dilation

• Conceptual explanation
  • Moving clocks run slower from the viewpoint of a stationary observer
• Mathematical formulation
  • Deriving time dilation formula
  • Examples and problem solving

4. Length Contraction

• Explanation of length contraction phenomenon
  • Objects moving relative to an observer appear shorter along the direction of motion
• Mathematical expression and derivation
  • Application examples

5. Relativistic Momentum and Energy

• Classical vs relativistic momentum
  • Derivation of relativistic momentum formula
• Relativistic energy
  • Total energy and kinetic energy relations
  • Mass-energy equivalence: derivation and implications of E=mc²

6. The Twin Paradox

• Description of the thought experiment
• Analysis using time dilation and inertial frames
• Resolution of the paradox and its implications for time and simultaneity

7. Relativistic Doppler Effect

• Classical Doppler effect refresher
• Modification under special relativity
  • Frequency and wavelength shifts for approaching and receding sources
• Mathematical derivation and applications

8. Spacetime Diagrams

• Introduction to Minkowski diagrams
• Representation of events, worldlines, and simultaneity
• Visualizing time dilation and length contraction

9. Relativistic Electrodynamics

• Effects of special relativity on electric and magnetic fields
  • Unification of electric and magnetic fields as components of the electromagnetic tensor
• Relativistic addition of velocities
  • Formula and examples

10. Applications of Special Relativity

• GPS satellite technology and time corrections
• Particle accelerators and relativistic particle behavior
• Nuclear energy and mass-energy conversion
• Other modern physics applications