Directional Clock Workbench

01From geometry to a frequency readout

The worksheet defines $y(t)=\delta(f_1/f_2)/(f_1/f_2)$. Above, $Q(t)=(\hat n\cdot\hat b)^2-1/3$ is one symmetry-compatible planning basis, not an independently derived manuscript clock response. If $y=AQ+\sum_j a_jX_j$ is adopted, amplitude $A$, background direction and nuisance terms need physical sources and independent calibration. General directional responses may require other harmonics or tensors. Selecting a basis does not establish an ASD prediction.

The nominal planning sidereal day is 86164.0905 s. Real data require UTC/UT1, longitude and time-scale conventions. Horizontal azimuth runs eastward from north; right ascension/declination describe a user-selected background axis; the starting angle is local sidereal phase. Choosing a clock records a transition, but does not manufacture species-dependent coefficients.

02Required apparatus response

1. Calculate the transition-energy difference from atomic structure and field coupling, specifying how a scale change affects different levels.
2. Include quantization axis, polarization, reference clock and frequency-comb/transfer response.
3. Average over the actual measurement cycle and dead time; an instantaneous field is not a counted frequency.
4. Calculate the comparison model under the same protocol and test degeneracy with ordinary directional systematics.

These upstream inputs do not replace a full transition-specific shift calculation. OP-TIME-01 · Chinese original addresses that gap.

03Uncertainty budget and rejection region

General propagation uses $u^2=\mathbf J C\mathbf J^T$. The worksheet's sum of squares only applies to independent inputs in common units, already expressed as standard uncertainties. A real budget also needs Zeeman, blackbody, Stark, second-order Doppler, height, servo, transfer and sidereal/solar-day aliasing effects. The example is neither an instrument performance certification nor a required-precision estimate.

Fix a nonzero prediction, nuisance-parameter domain, sampling design and likelihood before declaring an exclusion rule. If $A$ is freely adjustable and includes zero, a null result constrains $A$ rather than excluding LVE.

04Data, sources and reproduction

Wolf et al.'s clock orientation test is a comparison-research entry; NIST/BACON clock ratios provide a frequency-metrology reference. Neither is an ASD fit performed here. Raw data are not imported. Templates specify ratios, axis angles, environment variables and covariance files.