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14. Introduction to the Four-Vector

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 Shankar, Ramamurti

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14. Introduction to the Four-Vector
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24
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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