First-year university special relativity
Study first-year university special relativity through an ordered core sequence, optional derivations and links to modern-physics practice.
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Before you begin
UY1 special relativity is about frame discipline: tie every measured quantity to a stated observer frame. Most mistakes come from mixing proper and observed quantities without saying which frame each symbol belongs to.
Learning goals
- Distinguish events, reference frames, invariants, and frame-dependent measurements.
- Derive and interpret time dilation, length contraction, and relativity of simultaneity.
- Use Lorentz transformations while checking low-speed limits and frame conventions.
Lessons
Work through them in order.
- The principle of relativityExplain why no experiment in an inertial frame can detect absolute rest.
- Einstein’s postulates and inertial framesState Einstein's two postulates and explain why classical velocity addition fails for light.
- Simultaneity and relativity of timeDistinguish observation delay from frame-dependent simultaneity.From GCE A-Level H3 Physics
- Lorentz transformationsTransform an event forward and back between inertial frames with consistent space and time coordinates.From GCE A-Level H3 Physics
- Comparing events between inertial framesApply Lorentz event differences using simultaneity and proper-measurement conditions.From GCE A-Level H3 Physics
- Time dilationIdentify proper time and derive the moving-clock relation.From GCE A-Level H3 Physics
- Length contractionIdentify proper length and enforce simultaneous endpoint measurements.From GCE A-Level H3 Physics
- Relativistic velocity additionCombine collinear velocities without exceeding c.From GCE A-Level H3 Physics
Practise and check
Topic reference
Checking a result
Check every result against the low-speed classical limit.
Deeper derivations
H3 Physics covers the full derivations if your course needs them.
- H3 special relativity — Full derivations.
- Twin paradox — Worldline reasoning.