---
{
"id": "ASD-EXP-TESTS-DIRECTIONAL-ATOMIC-CLOCK-EN",
"path": "/en/tests/directional-atomic-clock",
"title": "Directional Clock Workbench",
"title_en": "Directional Clock Workbench",
"category": "Experimental Program",
"summary": "P1 · ASD-PRED-001. Fix the species, transition, background direction and transfer response before calculating a directional frequency shift.",
"template": "test",
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"updated": "2026-09-22",
"date_published": "2026-09-22",
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"path": "/en/tests/falsification",
"label": "Falsification",
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"path": "/en/tests/priority-experiments",
"label": "Priorities",
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"source_chapter": "Existing canonical module snapshots / 现有正式模块快照",
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"equations": [
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{
"label": "Ota et al. (2022), Nature Physics 18, 1436–1440",
"url": "https://www.nature.com/articles/s41567-022-01767-w",
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"label": "Wolf et al. (2006), Cold Atom Clock Test of Lorentz Invariance in the Matter Sector",
"url": "https://arxiv.org/abs/hep-ph/0601024",
"kind": "external-reference"
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{
"label": "BACON Collaboration (2021), optical frequency ratio network",
"url": "https://www.nist.gov/publications/frequency-ratio-measurements-18-digit-accuracy-using-network-optical-clocks",
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"outline": [
"From geometry to a frequency readout",
"Required apparatus response",
"Uncertainty budget and rejection region",
"Data, sources and reproduction"
],
"seo_title": "Directional Clock Workbench | ASD Predictions & Falsification v1.0",
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"mathematical_review": "INCOMPLETE",
"evidence_note": "No closed quantitative discriminator; planning/comparison only.",
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---
## From 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.
## Required 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](/open-problems/clock-response) addresses that gap.
## Uncertainty 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.
## Data, sources and reproduction
[Wolf et al.'s clock orientation test](https://arxiv.org/abs/hep-ph/0601024) is a comparison-research entry; [NIST/BACON clock ratios](https://www.nist.gov/publications/frequency-ratio-measurements-18-digit-accuracy-using-network-optical-clocks) 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.