In this module, learners will derive length contraction and explain how measurements of distance depend on the observer’s motion. Learners will analyze the relativity of simultaneity and use spacetime diagrams to reason about “same time,” causal order, and common relativity paradoxes. By the end of this module, learners will be able to use Lorentz transformations to convert event coordinates between inertial frames and determine how time, position, and velocity measurements change between observers.

In this module, learners will interpret special relativity through spacetime geometry by using the invariant interval to identify what all inertial observers agree on. Learners will explain why classical definitions of momentum and energy break down at high speeds and apply relativistic expressions to solve conservation problems. By the end of this module, learners will be able to connect relativistic dynamics to spacetime structure and calculate relativistic momentum and energy in introductory applications.

In this module, learners will explain gravity as a consequence of spacetime curvature and use the equivalence principle to link gravitational effects to acceleration and free fall. Learners will derive and interpret gravitational time dilation and predict phenomena such as light bending and gravitational lensing. By the end of this module, learners will be able to explain how general relativity leads to black holes and gravitational waves and describe the observational signatures of these effects.

In this module, learners will apply basic gravity and symmetry assumptions to model an expanding universe and connect observations to cosmic expansion using Hubble’s law. Learners will derive how the universe’s contents change with time and relate the thermal history of the universe to key physical processes at different temperatures. By the end of this module, learners will be able to use simple cosmological equations to reason about the universe’s evolution and explain why inflation resolves the horizon problem.