Short Overview of Special Relativity based on Zangwill

Here is a summary of Section 22.1 (Special Relativity) of Zangwill’s Electrodynamics textbook [1].

Basic Points of Special Relativity

• There are different observers.
• One observer moves with a constant velocity with respect to the other observer.
  • A velocity vector has a direction & a magnitude, so a constant velocity means that the moving observer’s direction & speed (magnitude of velocity) do not change.
  • An observer is associated with a coordinate system.
• In special relativity, focus is placed on an event.
• General relativity is for arbitrary motion, which can include acceleration.
• Special relativity is connected to electromagnetism.
• Einstein thought about the possibility of traveling at the speed of light, $c$.
  • Light properties can be deduced from Maxwell’s equations.
  • Einstein pondered the question of “can light have a speed of $0$ if the observer is moving fast enough in the same direction as the light.
  • These considerations led to the “concept of the relativity of simultaneity.”
• Adopting special relativity means abandoning Newtonian dynamics.
• Relative motion between two observers might not occur along one Cartesian axis.
• Relativity has postulates.
• Relativity involves the Lorentz transformation.
• Point particles are used in special relativity.
  • A particle may or may not have spin.
  • Similarly, a particle may or may not have charge.
  • A particle can have a velocity relative to something else.
• Term: Lorentz tensor
• Term: Covariant representation of Maxwell’s equations
• Term: Covariant representations of conservation laws for electrodynamics
• Related: Dielectric and magnetic matter

References