Introduction to the Four-Vector in Special Relativity - Lecture 14

Delve into the fundamental concepts of special relativity in this comprehensive lecture from Yale University's Fundamentals of Physics course. Explore the unification of space-time coordinates through the introduction of the four-vector, a powerful mathematical tool that combines x, y, z, and t into a single entity. Discover how Lorentz transformations affect these components and learn about the invariant space-time interval. Examine causality paradoxes and gain a new understanding of space-time. Investigate four-vector algebra, the concept of proper time, and derive velocity and momentum vectors in space-time. Conclude with an exploration of the revolutionary energy-mass relation. This 73-minute lecture provides a deep dive into the mathematical foundations of special relativity, offering valuable insights for students and enthusiasts of physics.

- Chapter 1. Recap—Consequences of the Lorentz Transformations.
- Chapter 2. Causality Paradoxes: "Killing the Grandmother".
- Chapter 3. A New Understanding of Space-Time.
- Chapter 4. Introducing the Fourth Dimension and Four-Vector Algebra.
- Chapter 5. The Space-Time Interval, or "Proper Time".
- Chapter 6. Deriving the Velocity and Momentum Vectors in Space-Time.
- Chapter 7. The New Energy-Mass Relation.