Convert timing error into the quantity being tested
For a phase comparison, a delay δt contributes δφ = 2πfδt. At 250 kHz, a 10 ns delay corresponds to 0.9 degrees. This is an illustrative phase calculation, not a measured SPHERE tolerance. A constant delay need not bias an independently estimated stationary frequency; changing delay, mismatched windows and chirped signals can affect comparisons.
For a slowly drifting frequency, a window offset δt produces an approximate mismatch (df/dt)δt. Measure df/dt in the pilot, allocate a tolerable comparison error, then derive the permissible offset. “Exactly the same time” should become a measured skew specification with uncertainty.
Source: NI: Sample Clock SynchronizationProposed uncertainty register
| Contribution | Characterization | Control |
|---|---|---|
| Temperature | Calibrate df/dT per sphere and mode | Multiple calibrated sensors; record gradients and lag |
| Mounting / handling | Repeat removal, reseating and sham moves | Controlled fixture; measured settling criterion |
| Clock and trigger | Common-signal skew and drift tests | Shared timing; log lock and dropped samples |
| Optical geometry | Beam angle, reflectivity and alignment tests | Document target point and signal quality |
| Excitation / crosstalk | Drive one object at a time in calibration | Check coupling before simultaneous excitation |
| Mode identification | Track mode shape and nearby peaks | Fixed estimator and mode-selection rule |
| Electromagnetic pickup | Source on/off and shielding tests | Separate electrical artifacts from mechanical response |
Do not combine unlike frequency measurements
Mechanical resonance from a vibrometer and electrical/RF response from a network analyzer are different observables. They need separate mode definitions, excitation paths, calibration, and statistical endpoints. Shared timing permits correlation studies but does not make their spectra interchangeable.
Four objects do not create six independent replications
Four objects produce six unique pairwise comparisons, but pairs sharing an object are correlated. The clock-network study explicitly accounted for covariance between comparisons sharing a clock. Plan analysis at the trial/block level and model shared noise rather than inflating the effective sample size.
Source: A lab-based test of the gravitational redshift with a miniature clock network (2023)Ratios cancel selectively
A proposed diagnostic is rᵢ(t) = fᵢ(t)/f₁(t), followed by a randomized A-versus-B contrast. This can suppress shared fractional timebase drift. It does not necessarily suppress additive offsets or unequal thermal responses. Shared references can also fail together: include independent diagnostic checks and publish reference health logs.
What a credible result would say
Report an effect estimate, uncertainty or confidence interval, the preregistered smallest effect of interest, and the tested conditions. A null result can bound effects within those conditions. A nonzero residual calls for artifact investigation; it does not establish a unique cause. Avoid universal requirements such as a fixed shielding attenuation or thermal target unless derived from the measured error budget.
Public questions
Which systematic would you prioritize first? Have you seen a sensor swap move an apparent effect with the instrument rather than the object? Explain the diagnostic you used and what you would do differently.
Continue the design review
- Synchronized measurement research hub
- Does Earth’s motion affect resonance measurements?
- Synchronized four-object frequency measurement protocol
- What a miniature clock network teaches SPHERE about synchronized measurements
- Earth rotation and resonator tests: what SPHERE can learn
- Hardware for synchronized resonance measurements
- Community review: how would you improve the experiment?
- Current draft LOC-1 protocol