PHY.9:11 - SoTA-Echoing

The VIM definitions of measurement principle and measurand distinguish the phenomenon supporting a measurement from the quantity sought under specified conditions. JCGM GUM-6:2020, especially sections 7.2 and 9, explains theoretical, empirical and hybrid response models and effects of realizing a measurement.

Compare the two mass procedures in :5.1. Timing ideal free fall is simpler but supplies no mass distinction. A known-force comparison supplies it at the cost of a force reference and acceleration readout. Reversal adds another preparation only when separating the force offset matters. Neither a more accurate clock nor more identical falls supplies the missing physical dependence.

Degen, Reinhard and Cappellaro, Quantum Sensing, Reviews of Modern Physics 89 (2017), is a foundational synthesis of preparation, coupling, control and readout. Pezzè and Smerzi, Advances in multiparameter quantum sensing and metrology, 2025, extends the selection question to several parameters, incompatible optimal measurements and finite resources. The adopted contribution is the joint choice of probe, encoding and readout; a quantum sensitivity bound needs its own estimation and attainability assumptions.

For the phase question in :5.3, the same Hamiltonian with an eigenstate probe gives no observable phase, while a superposition and suitable readout do. Short interrogation resolves the wider range; longer interrogation can improve local sensitivity while requiring range information and adequate coherence. More complex entangled or adaptive arrangements require a comparison under the actual resource and uncertainty conditions, not an advantage inferred from their name.

The 2026 amendment to JCGM 100 explicitly addresses significant nonlinearity in both a measurement estimate and its uncertainty. It supports returning from a local sensitivity approximation when the receiving calculation depends on curvature. The applicable mathematical inference remains separate from construction of the physical coupling.

The numerical cases are constructed demonstrations under stated laws and idealizations. A changed material, interaction, preparation or readout range reopens the corresponding physical premise.