4 Special Relativity

Special relativity is the phenomenon of physical events in space and time as measured by observers in uniform relative motion.

An event is an occurrence at a definite place and time. An observer is a system of clocks and rulers that records when and where events happen.

Special relativity is related to electromagnetism because the speed of light in vacuum is independent of which inertial frame is used.

4.1 Topics

1. Principle of Relativity
   1. Relativity Principle
   2. Constancy of the Speed of Light
   3. Reference Frames
      1. Frame
      2. Inertial Frame
         1. Inertial Reference Frames
      3. Non-Inertial Frames
2. Minkowski Space
   1. Spacetime
      1. Visualization of Spacetime
   2. Events
   3. Spacetime Interval
   4. Minkowski Metric
   5. Worldlines
   6. Light Cone
   7. Proper Time
   8. Proper Length
3. Lorentz Transformations
   1. Lorentz Factor
   2. Coordinate Transformations
   3. Simultaneity
   4. Velocity Addition
   5. Rapidity
4. Time Dilation
   1. Proper Time
   2. Moving Clocks
   3. Twin Paradox
5. Length Contraction
   1. Proper Length
   2. Contracted Length
6. Relativistic Momentum and Energy
   1. Four-Momentum
   2. Relativistic Momentum
   3. Kinetic Energy
      1. Derivation of Kinetic Energy Formula
         1. Derivation of Newtonian Kinetic Energy Formula
         2. Derivation of Relativistic Kinetic Energy Formula
   4. Potential Energy
      1. Derivation of Potential Energy Formula
         1. Derivation of Gravitational Potential Energy Formula
         2. Derivation of Elastic Potential Energy Formula
   5. Total Energy
   6. Energy-Momentum Relation
   7. Massless Particles
   8. Photon Energy
7. Mass-Energy Equivalence
   1. Rest Energy
   2. Particle Creation
   3. Annihilation
   4. Nuclear Energy
8. Relativistic Electrodynamics
   1. Electromagnetic Field Transformations
   2. Magnetism as a Relativistic Effect
   3. Field Tensor
   4. Four-Potential
   5. Four-Current

4.2 References

1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — events, observers, and the invariance of the speed of light.
2. Feynman, R. P., Leighton, R. B., & Sands, M. The Feynman Lectures on Physics, Vol. I. — uniform relative motion and the same speed of light in every inertial frame.

• Annihilation
• Constancy of the Speed of Light
• Contracted Length
• Coordinate Transformations
• Derivation of Elastic Potential Energy Formula
• Derivation of Gravitational Potential Energy Formula
• Derivation of Kinetic Energy Formula
• Derivation of Newtonian Kinetic Energy Formula
• Derivation of Potential Energy Formula
• Derivation of Relativistic Kinetic Energy Formula
• Electromagnetic Field Transformations
• Energy-Momentum Relation
• Events
• Field Tensor
• Four-Current
• Four-Momentum
• Four-Potential
• Frame
• Inertial Frame
• Inertial Reference Frames
• Kinetic Energy
• Length Contraction
• Light Cone
• Lorentz Factor
• Lorentz Transformations
• Magnetism as a Relativistic Effect
• Mass-Energy Equivalence
• Massless Particles
• Minkowski Metric
• Minkowski Space
• Moving Clocks
• Non-Inertial Frames
• Nuclear Energy
• Particle Creation
• Photon Energy
• Potential Energy
• Principle of Relativity
• Proper Length
• Proper Time
• Rapidity
• Reference Frames
• Relativistic Electrodynamics
• Relativistic Momentum
• Relativistic Momentum and Energy
• Relativity Principle
• Rest Energy
• Simultaneity
• Spacetime
• Spacetime Interval
• Time Dilation
• Total Energy
• Twin Paradox
• Velocity Addition
• Visualization of Spacetime
• Worldlines