Can the same gravitational interaction yield a reproducible difference when it is measured mechanically and when it is balanced electrostatically? Measurement Quantization (MQ) predicts a small separation between those measurement routes. A planned experiment will test that prediction by alternating two modes in one carefully characterized apparatus, with the analysis and acceptance conditions fixed before the result is revealed.

The starting point is the method difference reported in the NIST redetermination using the BIPM torsion balance. Its free-deflection results were higher than its electrostatic-servo results in both material configurations. Chapter 7 of The Rules Beneath Reality develops the connection to MQ and explains why a dedicated follow-up is needed. The proposed work turns that discussion into an engineering program—contactless suspension, independent readout, controlled reversals and physical tests of the mechanisms that could imitate a mode gap. [1] [2]

One instrument, two measurement routes

The Newtonian gravitational constant, G in conventional experimental notation, relates a gravitational force or torque to independently measured source masses and geometry. It is different from local gravitational acceleration. Balancing a test body against Earth’s gravity alone does not independently determine this constant.

In free deflection, a torsion balance responds mechanically to the attraction of the source masses. In electrostatic servo, an applied counter-torque holds the balance near its reference angle. The same gravitational geometry is examined through different calibration and response models. Their distinct systematic effects make a paired comparison especially useful. The 2026 NIST measurements provide the four determinations shown in Table 1. [1]

The copper free-minus-servo difference is 56.7889 ± 29.4252 parts per million (ppm), using the published differential covariance. Chapter 7’s covariance-aware four-pair BIPM/NIST analysis gives 60.994 ± 26.930 ppm. That common-gap estimate is 2.265 standard uncertainties from zero under the stated model, with a two-sided probability of 0.0235. These are suggestive comparisons, with unresolved instrumental effects still relevant. They do not uniquely identify the MQ value. [2]

The fixed MQ prediction

MQ describes the Internal Frame as a discrete count configuration and the System Frame as its continuous relational representation. The Frames mapping connects the two. The Informativity differential is the proposed non-Lorentz length contraction associated with this realization of discrete measure. It is count dependent rather than a contraction caused by relative velocity. The Informativity differential and frames of reference pages develop these ideas in detail. [6]

Let n_L be the separation count in fundamental lengths and Q_L the residual given by the unit-count right-triangle construction. Their exact geometric relation is

The dimensionless factor 2Q_Ln_L tends to unity at the upper count limit. At the finite electromagnetic interaction count, it remains below unity. In MQ notation, upright G denotes the upper-count gravitational realization and italic G denotes the finite-count electromagnetic realization. The proposed relation is

For the input set used in Chapter 7, the finite-count value is 6.6738448362 × 10⁻¹¹ and the upper-count value is 6.6740779428 × 10⁻¹¹, both in m³ kg⁻¹ s⁻². Their predicted midpoint is 6.6739613895 × 10⁻¹¹ in those units. These are the numerical realizations retained in the supplied historical comparison, rather than newly fitted values.

Define δ_MQ as the fractional upper-minus-finite separation normalized to the finite-count value. The fixed prediction used for the proposed mode comparison is 34.9284 ppm, written to the reporting precision adopted in Chapter 7.

The same typography distinguishes the companion reduced Planck quantities—italic ℏ at the electromagnetic demarcation and upright ħ at the upper count limit. These are realization labels, not a claim that a single experiment has already measured both constants. The gravitational-constant discussion provides the broader derivation and input dependencies.

A midpoint agreement is a different test

A historical population midpoint asks where two classified groups are centered. A paired-mode test asks how far the measurement routes separate. The supplied comparison in Figure 1 keeps those questions distinct. Table 2 records the midpoint results and Table 3 records the mode-gap comparison, so their numerical roles remain clear. [2]

The midpoint agreement motivates further work, but cannot establish two physically distinct branches. Likewise, the current mode-gap sample cannot select 34.9284 ppm uniquely over every other positive separation. A prospective experiment must determine both the sign and magnitude under a predeclared measurement model.

A precision advance built into the experimental design

The planned science assembly replaces the conventional measurement-axis torsion fiber with a contactless niobium magnetic suspension. The aim is to reduce a major source of mechanical response uncertainty while measuring the remaining restoring torque, other-axis motion and magnetic history independently. The magnetic bearing provides lift; that alone does not establish sufficiently free angular motion or stability in every coordinate. [3]

The preliminary science rotor has a nominal moving mass of 2 kg, two 0.5 kg sapphire end masses at ±0.500 m, and a symmetric silicon beam or truss. The stationary niobium tube has a 40.0 mm outer radius; a moving sleeve starts at 40.1 mm inner radius with a 200 mm active length and approximately 1 mm wall. This creates a nominal 100 µm radial clearance. The initial persistent-circuit concept uses 8,000 equivalent axial ampere-turns. These are engineering specifications awaiting finite-geometry electromagnetic, mechanical and thermal qualification.

Figure 2 separates the intended science geometry from the rigid-dummy pilot discussed below. In the science baseline, the beam lies along x, the bearing axis is y, and z is vertical. The science coordinate is pitch about the bearing axis. Earlier concept artwork should not override this coordinate definition.

Opposing guarded electrodes provide electrostatic torque. Independent optical readouts track the moving assembly and reference structure, while synchronized acquisition retains waveform timing and channel delays. The rotor’s floating potential, electrode geometry, magnetic current paths, residual gas, optical recoil and temperature gradients all enter the qualification program. A cryostat bath reading cannot substitute for a measured levitated-body temperature.

The measured quantity is a difference of reversals

Let S_F and S_E denote source-reversal torques measured in free-deflection and electrostatic-null modes. Each is the difference between the indicated torques in the positive and negative source states. Let D_FE denote their complete mode contrast.

A mode offset independent of source state cancels from this contrast. A source-correlated change of gain, stiffness, pose or thermal history can survive. The experiment therefore needs matched six-coordinate trajectories, measured settling, balanced reversal order and an estimator validated on reserved records. The 20 aN·m suspension requirement applies to the complete contrast, not to one reading or one diagnostic channel.

Current precision estimates—and what they are relative to

MQ predicts a mode separation of 34.9284 ppm of the reference gravitational measurement. For the page’s torque conversion, the retained 217.083649 nN·m source reversal is taken as the electromagnetic/servo reference. Applying the MQ fractional separation gives a predicted mode-gap torque of 7.58238 pN·m. The final experimental estimator must preserve this reference convention. This conversion changes the reporting denominator; it does not change the source model or the absolute uncertainty estimates.

The target is a combined standard uncertainty below 5 ppm of the MQ-predicted mode gap. On the reference just defined, that corresponds to less than 37.9119 aN·m. The current combined estimate is 23.0274 aN·m, or 3.03695 ppm, which is below the target. Every engineering uncertainty column labeled “ppm of MQ-predicted gap” below uses the same 7.58238 pN·m denominator. Historical NIST ppm values remain relative to the gravitational constant and must not be compared directly with these gap-relative ppm values. Additional common-scale precision metrics are in development.

Table 4 transcribes the current dashboard’s 15 systematic contributions. Here u denotes estimated standard uncertainty and k the coverage factor; the quoted standard uncertainties use k = 1. For rows other than K06, the underlying dashboard converts rectangular planning allocations to standard uncertainties. K06 instead propagates uncertain mechanical inputs through a beam model. Table 4 contains standard uncertainties only. Allocation ranges and conservative model intervals are not additional uncertainty contributions and are excluded from this table.

The covariance model matters as much as the individual allocations. Residuals within each C group are treated as fully correlated; different groups and random noise are assumed independent. Contributions are summed within each group before group totals are combined in quadrature. Figure 3 shows the resulting variance shares. C03 deformation accounts for 97.5%, making independent elastic and readout-transfer qualification the central engineering priority.

K06 has a predicted bias of −155.04 aN·m (about −20.44739 ppm of the MQ-predicted gap). The displayed uncertainty assumes that this modeled bias is corrected. Its 22.73 aN·m uncertainty reflects uncertain geometry, scalar modulus and root position. Elastic inertia is already counted in K06; independent bearing and rigid-inertia errors remain in their other rows. A correction is useful only if its residual uncertainty and transfer to the real apparatus are independently justified.

The retained system-level budget

Table 5 gives the current standard uncertainty budget. The random component assumes 150 useful science days and an unmeasured noise model. Under the retained covariance assumptions, systematic and random components combine to 3.03695 ppm of the MQ-predicted gap. This total satisfies the less-than-5-ppm planning target; it remains an estimate awaiting physical qualification.

The next experiment is a two-route pilot

Baseline 1.22 proposes a rigid-dummy pilot before a loaded cold comparison. A monolithic silicon bar, 200 × 30 × 20 mm, carries small optical targets on a centrally supported stage. Its independent optical frame can move separately. The purpose is to expose optical and mechanical transfer errors with physical motion, rather than to simulate a successful gravitational measurement.

Route A places a calibration carrier on the optical frame. Route B places it on the dummy while reproducing the same relative target-to-head trajectory. If the inferred response changes, relative angle alone has not captured all relevant laboratory-path effects. Additional common rotation changes the beam geometry while leaving relative motion unchanged. Independent laser, receiver and phase-processing chains, fixed references, receiver swaps and measured stage trajectories support the comparison.

The main acquisition has 3,072 sixty-second records, including its explicit closure reserve, for 51.2 acquisition hours. Path and roll injections increase the counted acquisition to 91.2 hours; structural mapping and settling bring the planned useful total to about 107.2 hours. The baseline allows at least ten calendar days, with additional diagnostic work able to extend it. These are prospective schedules, not completed observations.

Table 6 reproduces the new pilot estimates. Their conservative sum covers any covariance among the listed terms, but remains incomplete. They estimate the ability of the qualification instrument to test transfer; they are not new physical science errors to add to Table 4.

The independent cold-trajectory qualification allocation, Q12, therefore stays at 0.750 aN·m. Q12 is a qualification-test identifier and is distinct from science-budget entry K12. The stricter design ceiling for a future Q12 result is below 0.559 aN·m with useful margin. Neither the pilot subtotal nor warm dummy agreement establishes that limit. Longer averaging alone cannot remove model, geometry, optical-path or loaded-cold transfer errors.

Conditional forecasts remain qualification targets

The dashboard retains the prior forecast for a much smaller combined standard uncertainty if all required gates pass—3.9485 aN·m, or 0.52075 ppm of the MQ-predicted gap. That is an important design objective, but it has not replaced the current 23.0274 aN·m estimate.

A 5.83-fold conditional reduction in modeled uncertainty

Figure 4 compares those two combined standard uncertainties on the same absolute torque scale and under the retained group assumptions. The ratio is 5.83, rounded from the baseline calculations. This is a forecast of the improvement available if the required gates pass, not a measured gain over the NIST apparatus. Figure 5 and Table 7 retain the separate guarded-screen values.

Joint compliance, real force footprints, transient leakage and covariance still require qualification. Even a nominal screen below 20 aN·m does not establish adequate coverage across all operating histories. Acceptance requires independent finite bounds, held-out combined-disturbance tests and a total that includes correlated residuals without double counting overlapping diagnostics.

A result that can challenge the prediction

The purpose of the follow-up is to make the mode assignment prospective. The apparatus definition, source states, uncertainty model, corrections, exclusions and data-release procedure should be fixed before unblinding. Independent calibration and reserved validation records must remain separate from the data used to fit response coefficients. The planned university partnership will provide an institutional setting for this work; no partner or completed installation is being announced here.

Chapter 7 notes that a differential uncertainty near 7 ppm of the gravitational measurement would place a 34.9284 ppm separation near five standard uncertainties from zero, if the prediction were realized and the uncertainty model were complete. A result near zero with sufficiently small uncertainty would challenge the proposed realization law. A different stable positive gap would require revisiting its magnitude or mode assignment. A result consistent with the fixed MQ value would become persuasive only after the apparatus mechanisms capable of imitating that difference were independently bounded.

The next milestone is therefore physical qualification, followed by a blinded comparison with a defensible uncertainty. The current estimates make the engineering priorities visible. They do not yet constitute an experimental demonstration of non-Lorentz contraction.

Sources and related reading

[1] S. Schlamminger and collaborators, “Redetermination of the gravitational constant with the BIPM torsion balance at NIST,” Metrologia 63, 025012 (2026). Published paper. The paired modes, material configurations and their covariance are the experimental source; MQ interpretations and the four-pair synthesis are attributed separately.

[2] Jody A. Geiger, The Rules Beneath Reality, Chapter 7, “The Experiment I Had Nothing to Do With,” supplied manuscript revision 02. Source of the historical population constructions, four-pair synthesis, chronology and prospective test discussion. The supplied MQ midpoint comparison is retained in Figure 1.

[3] Jody A. Geiger / Informativity Institute, Magnetic Suspension Qualification Design Baseline, ED MSQ 001, version 1.22, 21 October 2026, and Mode-Gap Uncertainty Budget, planning dashboard 1.22. Design calculations and allocations; no measured qualification results. Sections 221–230 govern the new pilot; earlier appended worksheets remain design history. This webpage retains the absolute torque estimates but renormalizes engineering uncertainty reports to the MQ-predicted gap, replacing the dashboard’s 60 ppm sizing denominator.

[4] T. R. Armstrong and M. P. Fitzgerald, “New Measurements of G Using the Measurement Standards Laboratory Torsion Balance,” Physical Review Letters 91, 201101 (2003). Published paper.

[5] M. P. Fitzgerald and T. R. Armstrong, “The measurement of G using the MSL torsion balance,” Measurement Science and Technology 10, 439–444 (1999). Published paper.

[6] Jody A. Geiger, “Measurement quantization,” International Journal of Geometric Methods in Modern Physics 20, 2350069 (2023). Published paper. Earlier development includes “Measurement Quantization Unites Classical and Quantum Physics” (2018). The numerical values in the historical report are Chapter 7 calculations using its stated input set.

[7] E. Goetz and R. L. Savage, “Calibration of the LIGO displacement actuators via laser frequency modulation.” Published article and source record. A precedent for physical frequency-based displacement calibration, not a certificate for this proposed pilot.

[8] M. S. Hartig, S. Schuster and G. Wanner, studies of geometric tilt-to-length coupling and non-geometric tilt-to-length coupling in precision interferometry. Relevant mechanisms include beam geometry, wavefronts and detector response.