Rapidity

Plate 29 speaks for itself: “Half plus half is four-fifths.”

The Physics

Velocities do not add in relativity, but rapidities do. Two boosts of 0.5c combine to 0.8c, and no number of boosts reaches c.

β = tanh η

• β: v/c, dimensionless
• η: rapidity, dimensionless

0.5c ⊕ 0.5c = 0.8c: rapidities add. η has no limit; β stays below 1.

Sources

• E. F. Taylor, J. A. Wheeler, Spacetime Physics, 2nd ed. (1992).

On the poster

Plate 029, “Rapidity”: the pixel-art plate with its slogan “Half plus half is four-fifths.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.