Orbiting Gyroscopes as Torsion Sensors: Frame Couplings and the Gravity Probe B Bound

Gravity Probe B flew four ultra-precise gyroscopes in Earth orbit to measure how the planet's mass and rotation shape the spacetime around it, and its final drift measurements agree with general relativity's geodetic and frame-dragging predictions within their uncertainties. Any additional agent that torques a gyroscope — and an axial torsion background is such an agent, in the class of theories where torsion couples to a body's total angular momentum — would have appeared as an anomalous drift. This paper converts the mission's residuals into torsion bounds. Taking the frame-dragging channel's residual ceiling of 7.8 milliarcseconds per year, an anomalous precession of 1.20e-15 radians per second, the corresponding axial torsion background is bounded at 4.00e-24 per metre; the geodetic channel at a conservative 20 milliarcseconds per year gives 1.02e-23 per metre. The frame-dragging figure is the tightest background-torsion bound obtainable from a gravitational experiment, and it lies a factor of about 84 below the 3.36e-22 per metre that Earth's rotation would source if bulk rotation counted as spin density — so the mission already excludes, at useful depth, the naive picture in which a rotating planet wraps itself in torsion. In Einstein-Cartan theory proper, where torsion couples to intrinsic spin density rather than to a macroscopic rotor's angular momentum, the gyroscopes are predicted to show no torsion drift at all, and none was seen. Computed from stated assumptions, not measured.