Short Overview of Special Relativity based on Zangwill
Here is a summary of Section 22.1 (Special Relativity) of Zangwill’s Electrodynamics textbook .
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