Special relativity

In 1905 a young clerk at the Patent Office in Bern, Albert Einstein, started from a single postulate — Maxwell’s equations hold in every inertial reference frame — and derived astonishing consequences from it: time dilates, lengths contract, simultaneity is relative, mass and energy are the same thing. This chapter builds special relativity in terms of events and invariants, from the light clock all the way to $E=mc^2$, and finally opens onto general relativity and cosmology.

Sections

• Light and Galilean relativity
• Einstein’s postulates
• Time dilation
• Events and the spacetime invariant
• Natural units
• Relations between events: spacelike, timelike, lightlike
• The relativity of simultaneity
• Proper time is maximal
• The twin paradox
• Length contraction
• The simultaneity formula
• The train paradoxes
• The Lorentz transformations
• Relativistic Doppler effect
• Relativistic composition of velocities
• Mass and energy: E = mc²
• Introduction to general relativity
• Relativistic astrophysics: Hubble and cosmology

Reflections

• Invariance: the true heart of relativity
• From Galileo to Einstein: a conceptual turning point

Exercises

• All the chapter’s worked exercises