Terrell Rotation

Plate 28 speaks for itself: “Contracted, but it looks turned.”

The Physics

A fast object is Lorentz contracted, but a photograph does not show the squash. Light from the far side left earlier, so a small object seen side-on appears rotated instead.

sin φ = β

• φ: apparent rotation angle, °
• β: v/c, dimensionless
• γ: Lorentz factor 1/√(1 − β²), dimensionless

β = 0.9: γ ≈ 2.29, φ ≈ 64°. Terrell; Penrose, 1959.

Honest caveat: The simple rotation picture holds for small objects at small angular size.

Sources

• J. Terrell, Phys. Rev. 116, 1041 (1959).
• R. Penrose, Proc. Camb. Phil. Soc. 55, 137 (1959).

On the poster

Plate 028, “Terrell Rotation”: the pixel-art plate with its slogan “Contracted, but it looks turned.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.