Braginsky, Caves, and Thorne (Phys. Rev. D 15, 2047 (1977)) asked whether 'pure laboratory' experiments, with laboratory sources of post-Newtonian gravity and laboratory detectors both under the experimenter's control, could test relativistic gravity, and they identified the unresolved prerequisites: mechanical and electromagnetic quality factors far beyond demonstrated records (a torsion-suspension damping time of order 101310^{13} s, crystal-mode QQ of 101110^{11} and above, a superconducting microwave-cavity QQ near 5×10165\times10^{16} with relative frequency stability Δω/ω∼10−17\Delta\omega/\omega\sim10^{-17}), subtraction of mHz seismic rotation and tilt, suppression of Newtonian-gravity 'noise' to second order in apparatus imperfections, long-term cryogenic dimensional stability of sapphire-class monocrystals, and control of beam-particle backgrounds in storage-ring implementations. Neighboring components have progressed by other routes: the projected Eötvös precision was essentially reached by room-temperature rotating torsion balances (η≈2×10−13\eta\approx2\times10^{-13}) and surpassed in orbit (∼10−15\sim10^{-15}); G˙/G\dot G/G is bounded by lunar laser ranging rather than any laboratory torsion method; and the solenoid stress-gravity analysis was corrected theoretically. The core remains open: no laboratory experiment with a controlled source has ever detected a post-Newtonian gravitational effect, the key technology targets remain one to five orders of magnitude beyond demonstrated values, and the ultrarelativistic-matter thread has been explicitly revived in a 2025 proposal to measure the gravitational field of LHC proton bunches.

Background

Almost all precision tests of general relativity (GR) performed before 1977 used the Sun, Earth, or Moon as the source of gravity: light deflection, the Shapiro time delay, perihelion shifts, lunar laser ranging, and Eötvös–Dicke–Braginsky equivalence-principle experiments. In the weak-field, slow-motion limit, such tests are analyzed in the parametrized post-Newtonian (PPN) framework, in which the metric of any metric theory of gravity is expanded in powers of v/cv/c and characterized by dimensionless parameters (γ\gamma, β\beta, α1\alpha_1, α2\alpha_2, α3\alpha_3, ζw\zeta_w, and others); GR corresponds to γ=β=1\gamma=\beta=1 with all others zero. Among post-Newtonian phenomena, 'magnetic-type' gravity — the g0jg_{0j} metric components generated by mass currents (momentum density ρv⃗\rho\vec{v}), responsible for the dragging of inertial frames (the Lense–Thirring effect), spin–spin gravitational coupling between rotating bodies, and a gravitational analog of Faraday electromagnetic induction — is especially distinctive: in 1977 it had never been detected by any means, and its detection requires only that the source's rotation be modulated, since magnetic-type effects change sign with the sense of rotation while the Newtonian background does not.

Braginsky, Caves, and Thorne asked what would become possible with a new class of 'pure laboratory' experiments in which the source of post-Newtonian gravity is itself a controlled laboratory object. They proposed seven post-Newtonian experiments plus an improved Eötvös test: (i) a gravitational 'Ampère' experiment measuring spin–spin coupling between two rotating bodies with a torsion balance (a horizontal bar suspended from a thin fiber, whose twist measures torques far too small for any direct force measurement); (ii) a search for a time variation of the gravitational constant GG using a torsion balance whose restoring torque is dominated by the Newtonian gravity of large laboratory masses, for which ω˙/ω≃G˙/2G\dot\omega/\omega\simeq\dot G/2G; (iii) a test of whether magnetic stress gravitates, by modulating a 2×1052\times10^{5} G solenoid field at the balance eigenfrequency; (iv) a gravitational Faraday-induction experiment driving torsional oscillations of a sapphire crystal with a moving, rotating cylinder source; (v) searches for preferred-frame and preferred-orientation effects using rotating sources and rotating platforms; (vi) a measurement of the gravitational field of ultrarelativistic protons in a storage ring with a cryogenic dielectric-crystal detector, testing how gravity depends on Lorentz factor; and (vii) a laboratory frame-dragging experiment in which the rotation of standing-wave patterns in a superconducting toroidal microwave cavity reveals the dragging by a nearby rotating mass. For each they estimated signal sizes, typically (F/m)PN∼10−17(F/m)_{\mathrm{PN}}\sim10^{-17}–10−1810^{-18} cm/s², together with the dominant noise sources.

The obstacles they identified are of two kinds. First, dissipation: thermal (Brownian) fluctuation forces are set by the quality factor QQ, the number of oscillation cycles over which the stored energy decays (equivalently, the damping time τ∗=Qτ0/π\tau^{*}=Q\tau_0/\pi for eigenperiod τ0\tau_0). The proposals required torsion-suspension damping times τ∗∼1013\tau^{*}\sim10^{13} s (Q≈3×109Q\approx3\times10^{9} at τ0=104\tau_0=10^{4} s) versus roughly 101010^{10} s achieved in 1977; sapphire crystal-mode QQ of 101110^{11} and above versus 5×1095\times10^{9} then measured (with a theoretical pristine-sapphire limit near 3×10153\times10^{15}); and a superconducting cavity Q≈5×1016Q\approx5\times10^{16} (mirror reflection deficiency 1−R∼2×10−141-\mathcal{R}\sim2\times10^{-14}, about 1000 times better than the state of the art) together with relative frequency stability Δω/ω∼10−17\Delta\omega/\omega\sim10^{-17} over the 10510^{5} s cavity damping time, versus 6×10−166\times10^{-16} achieved by superconducting-cavity oscillators. Second, backgrounds: Newtonian gravitational forces exceed the post-Newtonian signals by c2/v2∼1011c^{2}/v^{2}\sim10^{11}, so the Newtonian coupling at the signal frequency must be made second order in apparatus imperfections, requiring geometric and mass-distribution tolerances at the 10−610^{-6}–10−710^{-7} level on kilogram-scale rotating sources; seismic rotation and tilt at the millihertz eigenfrequencies must be suppressed or subtracted (seismic-rotation effects were estimated about 10610^{6} times larger than the frame-dragging signal, motivating paired-resonator subtraction schemes whose achievable rejection was never analyzed); sapphire aging at cryogenic temperature was uncharacterized and would mimic G˙/G\dot G/G; and beam-induced particles near a storage ring were impossible to assess without dedicated experimental tests. Their conclusion was that all the experiments 'stretch the limits of current technology' and that detailed feasibility and design studies should begin.

Problem Statement

Determine whether the pure laboratory tests of relativistic gravity proposed by Braginsky, Caves & Thorne (1977) can be realized — that is, whether a laboratory experiment with a controlled laboratory source and a laboratory detector can detect at least one of the targeted relativistic-gravity effects, at the sensitivity the source projected for that effect: magnetic-type gravity (spin–spin coupling between rotating bodies, dragging of inertial frames, or gravitational Faraday induction), the gravity produced by stress (with the corrected general-relativistic prediction, e.g. in the vacuum region inside a current-carrying solenoid), the velocity or Lorentz-factor dependence of the gravity of ultrarelativistic matter, preferred-frame or preferred-orientation effects, or a time variation of GG. Realization means meeting, for the chosen experimental branch, the technology and systematic-control prerequisites the source identified for that branch — the conditions that make that projected sensitivity attainable: torsion-suspension damping time τ∗\tau^{*} of order 101310^{13} s (Q≈3×109Q\approx3\times10^{9} at a 10410^{4} s eigenperiod) for the spin–spin Ampère and magnetic-stress torsion-balance experiments (i) and (iii); dielectric-crystal mode QQ of 101110^{11} and above for the gravitational Faraday-induction crystal experiment (iv); superconducting toroidal microwave-cavity QQ near 5×10165\times10^{16} with relative frequency stability Δω/ω∼10−17\Delta\omega/\omega\sim10^{-17} over the 10510^{5} s cavity damping time for the frame-dragging resonator; suppression and subtraction of seismic rotation and tilt at millihertz frequencies and Newtonian-gravity 'noise' made second order in apparatus imperfections (geometric and mass-distribution tolerances at the 10−610^{-6}–10−710^{-7} level on kilogram-scale rotating sources) for the rotating-source experiments (i), (iv), (v) and (vii); long-term cryogenic dimensional stability against aging of sapphire-class monocrystals for the G˙/G\dot G/G search; and control of beam-particle backgrounds for the storage-ring implementation. A branch is one proposed experiment with its own prerequisite set, so that where a single targeted effect class (for example, magnetic-type gravity) spans several apparatuses, each apparatus is a separate branch required to meet only the prerequisites listed against it. The number of branches in scope is seven — the seven proposed experiments (i)–(vii) — and the top-level question is existential over them. Three of the prerequisites above — suppression and subtraction of seismic rotation and tilt, long-term cryogenic dimensional stability against aging of sapphire-class monocrystals, and control of beam-particle backgrounds — the source identified only as capabilities, without fixing a target level; for those branches the required level is itself part of the question and must be determined from the quoted signal and noise estimates. Realizability is to be assessed for a concrete specified design — whether that design can attain the branch's prerequisite technology and systematic-control levels (this is a forward-looking feasibility judgement, not a claim that the experiment has already been performed).

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