Special Relativity

Back to Special Relativity

What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing but an electric field - Albert Einstein (1952)

Chapter 1 -Introduction

  1. Principle of Relativity - [TBD]
  2. Michelson-Morely Experiment - Description of the experiment and theory of operation of the Michelson-Morely interferometer.

Chapter 2 - Relativistic Kinematics

  1. Time Dilation - Derivation of time dilation. A light clock is used to facilitate the derivation.
  2. Lorentz Contraction - Derivation of Lorentz contraction relation
  3. Lorentz Contraction - Second Version
  4. Lorentz Contraction - Third Version
  5. Lorentz Transformation - Derivation of the Lorentz Transformation equations
  6. Velocity Transformation Rules - Transformation of velocity and g from S to S'
  7. Acceleration Transformation Rules - Transformation of acceleration from S to S'
  8. Spacetime - Explains the concept of spacetime, events, world-lines etc.
  9. Spacetime Diagram - Example of a spacetime diagram [Under Construction]
  10. Relativistic Optics - The transformation of the reflection angle of a beam of light off a mirror is calculated
  11. Uniformly Accelerating Particle - The trajectory of a uniformly accelerating particle is derived

Chapter 3 - Relativistic Dynamics

  1. Lorentz 4-Vectors - The Lorentz 4-vector is defined using the position 4-vector as a prototype.
  2. Lorentz Tensor - Definition of Lorentz tensor
  3. Force Transformation - The transformation rules for the xyx components is derived
  4. Inertial Mass - The concept of mass is defined and discussed as it pertains to special relativity
  5. Invariant Mass - The concept of invariant mass is defined for both single particles and systems of particles.
  6. Longitudinal and Transverse Mass - The relationship between force and longitudinal and transverse mass is derived.
  7. Energy-Momentum Tensor - Describes the stress-energy-momentum tensor T.
  8. Inertial Energy vs. Mass - An example is given where E/c2 does not equal p/c.
  9. Conservation of mass - The principle of the conservation is derived from the conservation of momentum law as a corollary. 
  10. Center of mass - The center of mass is defined and explained for a discrete and continuous mass distributions.
  11. Conservation Laws - The angular and linear momentum conservation theorems are derived 

Chapter 4 - Energy in Special Relativity

  1. Relativistic Energy - Calculate the total energy of a relativistic particle using Lagrangian methods
  2. Work Energy Theorem in Special Relativity - The expression for the kinetic energy and inertial energy are derived
  3. Mass Energy Equivalence - Derivation of the Einstein's famous equation E = mc2.
  4. Energy and Momentum Transformation Rules - Mass, energy and momentum transformation rules are derived
  5. Einstein's Box - Derives the inertia of energy from utilizing the center of mass theorem
  6. Mass of a Rotating Cylinder - The rest mass of a rotating cylinder is found as a function of its non-rotating rest mass.
  7. Rindler Article - Physics Today article in which Wolfgang Rindler spells out the benefits of velocity.
  8. Einstein's 1905 Error - Discusses the error regarding transverse mass in Einstein's 1905 error.
  9. Rindler-Denur Paradox - The Rindler-Denur paradox is described and then used to give an example of a radiating body.
  10. Nuclear Fission - Example of conservation of mass during fission of Uranium.
  11. Cyclotron - Calculate the trajectory of a charged particle moving in a uniform magnetic field. 
  12. Weight of a Moving Particle in SR - The weight of a moving body is derived using special relativity.