Reading assignment: 39.1-39.3
The Galilean velocity transformation equation, Eqn 39.2 (8th
edition), is simple--much simpler than its name implies. It's also
sometimes called the "classical velocity addition" formula. It's "obviously"
true. Use it to answer this question: A pickup truck is traveling forward at 5 m/s. A
man standing in the back of the truck throws a ball forward at 10 m/s (relative
to himself). How fast will someone on the ground measure the ball to be
traveling? What is the faulty assumption on which the equation
15 m/s. The faulty assumption is that all observers will agree on what time it is at any given instant: t' = t for all observers.
Explain in your own words (in language that your non-physics-major
roommates could understand) how the Galilean velocity
transformation equation and the 2nd postulate of special
relativity are at odds with each another. Einstein said (2nd postulate) that all observers will measure a given light wave to travel at 3x10^8 m/s, regardless of the observers' own velocities. This contradicts the normal velocity addition formula, because if the truck is traveling at (for example) 0.5c, and the man turns on a flashlight with photons traveling at c, then someone on the ground would measure the photons' speed to be 1.5c. That's too fast! And impossible, according to Einstein.