# 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**

- Principle of Relativity - [TBD]
- Michelson-Morely
Experiment

**Chapter 2 - Relativistic Kinematics**

- Time Dilation -
Derivation of time dilation. A light clock is used to facilitate the
derivation
*.* - Lorentz Contraction - Derivation of Lorentz contraction relation
- Lorentz Contraction - Second Version
- Lorentz Contraction - Third Version

- Lorentz Transformation - Derivation of the Lorentz Transformation equations
- Velocity Transformation Rules - Transformation of velocity and g from S to S'
- Acceleration Transformation Rules - Transformation of acceleration from S to S'
- Spacetime - Explains the concept of spacetime, events, world-lines etc.
- Spacetime Diagram - Example
of a spacetime diagram [Under Construction]

- Relativistic Optics - The transformation of the reflection angle of a beam of light off a mirror is calculated
- Uniformly Accelerating Particle - The trajectory of a uniformly accelerating particle is derived

**Chapter 3 - Relativistic Dynamics**

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

**Chapter 4 - Energy in Special ****Relativity**

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