Four-Vectors and Minkowski Spacetime
PHYS 401 · Module 5
This module introduces the geometric language of special relativity. Students learn four-vectors, the Minkowski metric, proper time, and four-momentum methods for collisions.
Lessons in this module
Four-vectors and notation
Four-vectors combine time and space components into objects that transform cleanly under Lorentz transformations. This lesson introduces position, velocity, and momentum four-vectors.
The Minkowski metric
The Minkowski metric defines spacetime intervals and inner products. This lesson explains metric signatures, invariant dot products, and the difference between Euclidean and spacetime geometry.
Proper time
Proper time is the time measured along a worldline by a clock traveling with the object. This lesson connects proper time to spacetime interval, four-velocity, and the geometry of aging.
Relativistic collisions using four-momentum
Four-momentum conservation provides a powerful method for analyzing relativistic collisions and particle reactions. This lesson explains invariant mass, threshold energy, and center-of-momentum reasoning.
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