Freeze one observable
The initial measurement is the full beam-on minus beam-off force on a passive mirror. The external beam is normal to the ideal mirror; its force is perpendicular to a 0.10 m balance arm. At 1 W intercepted power, ideal F = 2P/c = 6.671 nN. Actual reflection, transmission, scatter, alignment and absorption must be measured. This is a new commissioning design point, separate from the earlier 10 W / 80% / ±30° lateral-force illustration.
| Subsystem | Provisional architecture | Acceptance evidence |
|---|---|---|
| Balance | Torsion balance, 0.10 m effective lever arm; illustrative inertia 0.002 kg·m² and 100 s period. | Measure inertia, lever arm, stiffness, damping, nonlinearity, creep and mechanical resonances. Final suspension design is open. |
| Force target | Passive reflective coupon; counterweight and trim; no graphene gate in first campaign. | Traceable dimensions and masses; measured optical power distribution and absorption. |
| Readout | Separate low-power optical lever and position detector; interferometric upgrade only if measured noise requires it. | Calibrate angle versus detector output; characterize beam-pointing drift and probe-beam recoil. A detector resolution is not force uncertainty. |
| Calibration | Independent electrostatic actuator and calibrated voltage/capacitance-gradient model; optical force used as the cross-check. | F = ½V² dC/dx, including fringe fields, patch/contact potentials and actual geometry. Do not calibrate with the same optical prediction being tested. |
| Vacuum | Approximately 400 mm internal chamber diameter to be checked against drawings; dry-backed turbo candidate. | Provisional pressure sweep 10⁻¹ to 10⁻³ Pa where attainable; require a measured force plateau, adequate gauges and outgassing control. Reaching a pressure alone is not a pass. |
| Thermal / mechanical | Thermal shield, sample/mount/chamber temperature channels, matched heater and vibration-isolated pump connection. | Measure temperature-to-force transfer functions and pump/tilt sensitivity; include thermal lag and reassembly. |
| Source and containment | 1064 nm source capable of the 1 W operating point; external attenuation and monitored power. | Qualified laser enclosure, interlocks, beam stops and wavelength-specific protection before operation. Freeze spot size and sensor limits. |
Calculate the readout scale before choosing hardware
For the illustrative inertia and period, κ = 4π²I/T² = 7.896 × 10⁻⁶ N·m/rad. A 6.671 nN force at 0.10 m gives 84.49 µrad static deflection; a 1 m optical lever gives approximately 169.0 µm reflected-spot displacement. This estimates range, not sensitivity. Suspension thermal noise, measured loss/Q, environmental tilt and readout drift still set the attainable floor.
The settling time is not the pendulum period
For a lightly damped viscous model, the amplitude ring-down time is QT/π. At T = 100 s and an illustrative Q = 100, this is roughly 3,183 s. Structural loss or feedback changes the response. Measure the transfer function before choosing modulation, dwell time or averaging; 280 independent windows cannot be translated into a campaign duration without that evidence.
A budget that must be earned
Target an expanded uncertainty below 10% of the 1 W ideal reference: 0.667 nN. The allocations below combine to u = 0.276 nN and U = 0.552 nN at coverage factor k = 2 if independent. Adding an illustrative thermal/mechanical correlation of 0.6 raises U to 0.602 nN. Actual coverage and covariance must be evaluated from the instrument; unknown effects cannot be assigned zero.
| Contribution | Allocation | Evidence status |
|---|---|---|
| Optical prediction | 0.10 nN | Proposed standard-uncertainty allocation |
| Force calibration | 0.10 nN | Proposed standard-uncertainty allocation |
| Statistical mean difference | 0.12 nN | Proposed standard-uncertainty allocation |
| Thermal residual | 0.15 nN | Proposed standard-uncertainty allocation |
| Electrostatic residual | 0.08 nN | Proposed standard-uncertainty allocation |
| Gas residual | 0.08 nN | Proposed standard-uncertainty allocation |
| Mechanical residual | 0.08 nN | Proposed standard-uncertainty allocation |
Use enough independent data
For a full on/off difference with equal allocation, u = 2σ/√N. If qualified window noise is 1 nN, 280 total independent windows give 0.120 nN statistical standard uncertainty. This is a planning calculation, not a demonstration of independence or a substitute for prospective detection-power analysis. Recalculate when measured drift, autocorrelation and settling are available.
| Gate | Proposed pass criterion | If it fails |
|---|---|---|
| G0 · design review | Experimental lead and independent reviewer accept the observable, mechanical model, optical layout, hazards, uncertainty model and interface drawings. | Do not purchase integrated hardware. |
| G1 · reference calibration | Independent reference recovered over the selected range; pre/post drift stays within the 0.10 nN calibration allocation at the test point. | Repair calibration or relax the experiment’s scope. |
| G2 · nuisance controls | Residual effects and their uncertainties fit the allocated budget; each state-correlated contribution is measured or defensibly bounded. | Add controls or stop that configuration. |
| G3 · optical closure | Signed force agrees with measured optical momentum within the combined k=2 interval; expanded uncertainty ≤0.667 nN at the 1 W reference. Check 0.25/0.5/1 W scaling and an appropriate reversal/null configuration. | Report discrepancy; do not reinterpret it as new physics. |
| G4 · repeatability | The closure and controls repeat across at least three days and a controlled reassembly using a frozen analysis. | Investigate instability before materials integration. |
| G5 · graphene entry | Independent optical/thermal characterization predicts a resolvable state difference at a demonstrated safe operating point. | Keep graphene in optical characterization; no forced transfer to the balance. |
Review roles and missing engineering
Christopher Hill owns program priorities. A qualified experimental lead must own mechanical and optical design; a metrologist must review calibration and uncertainty; an independent physicist must challenge the interpretation. These roles remain unfilled. Fabrication drawings, suspension material/dimensions, actuator geometry, control law, measured environmental spectra and installation requirements are still required before procurement.