Gravity Probe Spin: Prospects for measuring general-relativistic precession of intrinsic spin using a ferromagnetic gyroscope

Abstract

An experimental test at the intersection of quantum physics and general relativity is proposed: measurement of relativistic frame dragging and geodetic precession using intrinsic spin of electrons. The behavior of intrinsic spin in spacetime dragged and warped by a massive rotating body is an experimentally open question, hence the results of such a measurement could have important theoretical consequences. Such a measurement is possible by using mm-scale ferromagnetic gyroscopes in orbit around the Earth. Under conditions where the rotational angular momentum of a ferromagnet is sufficiently small, a ferromagnet's angular momentum is dominated by atomic electron spins and is predicted to exhibit macroscopic gyroscopic behavior. If such a ferromagnetic gyroscope is sufficiently isolated from the environment, rapid averaging of quantum uncertainty via the spin-lattice interaction enables readout of the ferromagnetic gyroscope dynamics with sufficient sensitivity to measure both the Lense-Thirring (frame dragging) and de Sitter (geodetic precession) effects due to the Earth.

Ferromagnetic gyroscopes for tests of fundamental physics

“…Qualitative and quantitative differences are observed in the precession dynamics of the FG in the two cases. In relation to tests of fundamental physics, FGs have recently been proposed as tools to measure general-relativistic precession [39]; here we extend this discussion to show how FGs can be used in other searches for new physics.…”

“…To better understand the dynamics of an FG, we model a freely floating FG in space subjected to a constant magnetic field B, similar to the modelling in reference [39]. A weak magnetic field causes precession of the FG with Larmor frequency…”

“…where we defined the following dimensionless vectors: the unit spin n ≡ S/S, the rotational angular momentum ≡ L/S, and the total angular momentum j = n + . Equations ( 6) and ( 7) are derived from Landau-Lifshitz-Gilbert equations under the assumption that the spin vector is locked to the easy axis, as was done in the modelling of the FG in [35,39]. Solving for j(t) and n(t), figure 1 shows the different kinds of motions of a freely floating FG in an external magnetic field.…”

Gravitomagnetic Stern--Gerlach Force

“…In Equation (35), the difference in the energy of a spin-1/2 particle polarized vertically up and down relative to the surface of the Earth is given by Ω ⊕ ≈ 10 −19 eV and Ω P ≈ 10 −29 eV. For recent attempts to measure the spin-gravity term, see [61,62]. Furthermore, the gravitomagnetic field depends upon position; therefore, there exists a gravitomagnetic Stern-Gerlach force −∇(Ω P • S) on a spinning particle that is independent of its mass and hence violates the principle of equivalence and the universality of free fall.…”

Quantum sensitivity limits of nuclear magnetic resonance experiments searching for new fundamental physics

“…[17,18,19]). Another early use of NMR methods to test fundamental physics was in a series of experiments searching for couplings between intrinsic spin and gravity [20,21,22,23,24], and experiments along these lines are still being actively pursued [25,26,27,28]. The existence of "new" spin-0 or spin-1 bosons may imply the existence of exotic spin-dependent interactions [29,30,31], which can also be searched for using NMR.…”