Detector and Instrument Validation Ledger

A detector or instrument model is credible only when separate tests challenge its response, normalization, complete positivity, spacetime support, energy balance, perturbative approximation, numerical convergence, and data lineage. Agreement with the same calculation used to design the model is not an independent validation.

Required background. Localized detector models defines the physical probe, and local measurement instruments defines the probability and update maps that must be tested.

Helpful background. Switching, smearing, and regularization supplies the regulator and limit-order checks.

Validation starts from a frozen protocol

Record the field theory and state, detector Hilbert space, trajectory or worldtube, switching $\chi$, smearing $F$, coupling, initial probe state, readout POVM, perturbative order, discretization, and software or analytic formula version. Calibration data and validation data should be distinguishable. If a parameter is tuned after seeing the test result, report that test as calibration and reserve an independent check.

The following checks answer different questions:

• Null: switched-off coupling or a symmetry-forbidden response vanishes within uncertainty.
• Normalization and positivity: probabilities sum to one and remain nonnegative; an instrument is CP on spectator extensions.
• Analytic benchmark: a vacuum or stationary response agrees with a known result in a shared convention.
• Causal support: changing an intervention outside the causal past does not change the marginal, within support-tail and numerical bounds.
• Convergence: time step, momentum cutoff, spatial grid, integration window, smearing scale, and perturbative order are varied independently.
• Energy balance: control work matches field plus probe energy change to the retained order.
• Cross-model: a second physical realization of the same intended effect exposes implementation-dependent disturbance.

Validation attaches tests to the stage where a failure can arise: coupling support, induced channel, readout calibration, or final inference. The diagram is schematic.

A benchmarked detector run

For a smeared inertial detector in the free-field vacuum, compute the leading response in two ways: direct integration of the pulled-back Wightman distribution and a spectral or stationary representation. Use identical $\chi$, $F$, gap, Fourier convention, and $i0$ prescription. Then run $\lambda=0$ and verify the excitation probability is consistent with the independently measured numerical floor.

Repeat over a refinement sequence. A useful acceptance quantity is

$$R_n=\frac{|P_{n+1}-P_n|}{\max(P_{n+1},P_{\mathrm{scale}})},$$

where $P_{\mathrm{scale}}$ prevents meaningless relative errors near a null. Estimate the perturbative remainder separately, for example through $\lambda$-scaling or an exactly solvable regulated comparison. A small quadrature residual does not bound omitted $O(\lambda^4)$ physics.

Seeded failures

A validation suite should demonstrate power by detecting known corruptions.

Support leak. Add a small switching tail that reaches the receiver’s causal past. The causal test should either detect the induced change or downgrade exact no signaling to a quantitative tail bound.

Quadrature bias. Shift integration nodes or perturb the detector gap. The analytic benchmark and grid-refinement sequence should identify the bias rather than absorb it into a fitted normalization.

Perturbative-order error. Insert one known fourth-order contribution while fitting only a quadratic law in $\lambda$. A multi-coupling scaling test should show structured residuals.

If a seeded failure passes, the corresponding unseeded claim is not validated. This fault-injection principle is especially important when several calculations share code or analytic simplifications.

The validation suite must challenge each independent failure branch. No single agreement test establishes ultraviolet control, causal locality, and inferential validity simultaneously. The map is schematic.

Evidence and provenance checklist

As assessed through 2026-08-09, a model-validation record should include input formulas and parameter units; source versions and hashes for generated data; random seeds where applicable; raw and transformed outputs; convergence tables; analytic references with matching conventions; failed and passed null tests; and the rule used to accept or downgrade the claim. Preserve negative results and seeded-failure outcomes. Validation supports the stated finite model and parameter range, not every detector or continuum limit.

The benchmark literature also supplies model-specific checks: smooth switching controls the transition response in Satz 2007, §§ 2–4, pp. 1722–1728, spatial smearing controls the pointlike limit in Louko and Satz 2006, §§ 3–5, pp. 6327–6339, and supported probe scattering supplies causal factorization in Fewster and Verch 2020, §§ 3–5.

References

• Fewster, C. J., and Verch, R. (2020). “Quantum Fields and Local Measurements.” Communications in Mathematical Physics 378, 851–889. DOI. Open PDF.
• Louko, J., and Satz, A. (2006). “How Often Does the Unruh–DeWitt Detector Click? Regularisation by a Spatial Profile.” Classical and Quantum Gravity 23, 6321–6344. DOI. Open PDF.
• Satz, A. (2007). “Then Again, How Often Does the Unruh–DeWitt Detector Click If We Switch It Carefully?” Classical and Quantum Gravity 24, 1719–1731. DOI. Open PDF.