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Thomas Precession

What you are seeing: a gyroscope carried around a closed loop in SR returns rotated relative to its starting orientation. The vector at the gyroscope tip lags behind the orbital angle by (γ−1)(\gamma - 1) per revolution, the Thomas precession.

Figure 1. Orbit (cyan) and gyroscope axis (orange) accumulating Thomas precession.
β = v/c0.50

WHAT TO TRY

  • Raise beta = v/c toward 1: the gyroscope axis lags more per orbit, and the (gamma - 1) curve at the bottom steepens sharply. At low speed the precession is a tiny second-order relativistic effect.
  • Let several orbits accumulate: the lab-frame spin axis winds around by (gamma - 1) radians each revolution, a purely kinematic rotation with no torque applied.
  • Note where this bites in atoms: the same Thomas factor halves the spin-orbit coupling energy, which is why it matters for fine structure, not just orbiting gyroscopes.