# Fundamentals of Physics: Introduction to the Four-Vector

## Introduction to the Four-Vector

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