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

[1] Andrew Zangwill. Modern Electrodynamics (Section 22.1). Cambridge University Press. 2012.

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