14. Introduction to the Four-Vector

For more information about Professor Shankar’s book based on the lectures from this course, Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics, visit

Fundamentals of Physics (PHYS 200)

The four-vector is introduced that unifies space-time coordinates x, y, z and t into a single entity whose components get mixed up under Lorentz transformations. The length of this four-vector, called the space-time interval, is shown to be invariant (the same for all observers). Likewise energy and momentum are unified into the energy-momentum four-vector.

00:00 – Chapter 1. Recap—Consequences of the Lorentz Transformations
06:25 – Chapter 2. Causality Paradoxes: “Killing the Grandmother”
15:22 – Chapter 3. A New Understanding of Space-Time
25:51 – Chapter 4. Introducing the Fourth Dimension and Four-Vector Algebra
44:09 – Chapter 5. The Space-Time Interval, or “Proper Time”
51:47 – Chapter 6. Deriving the Velocity and Momentum Vectors in Space-Time
01:04:40 – Chapter 7. The New Energy-Mass Relation

Complete course materials are available at the Yale Online website: online.yale.edu

This course was recorded in Fall 2006.

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