PHY.5:4.2 - Locate the interactions and compare their scales

Follow the influence from preparation or input to the consequence. Identify what stores, transports, exchanges or dissipates the quantities involved. Include a boundary, contact, surrounding medium or measuring interaction when it carries an influence on that consequence.

Obtain the governing physical relations at the detail needed for this comparison. A studied theory, measured response or working hypothesis can supply them; retain which of these is being used. PHY.4 helps constrain an unresolved law. MMP.11 constructs its remaining mathematical family.

Derive characteristic sizes or rates from these relations and the proposed regime. Compare contributions to the same physical change. For time scales, compare relaxation with the fastest relevant forcing and with the interval of use. For spatial scales, compare a variation length with the scale of material structure or transport. An energy comparison may determine which states can be appreciably excited.

Inspect the coupled arrangement. A coupling can change a relaxation rate or create a collective mode. For a proposed rapidly adjusting state, ask whether small departures from its proposed response actually decay while the retained variables change. A response near loss of stability can become slow even though one component, considered alone, relaxes rapidly.

Scaling the equations as in PHY.1 makes these comparisons explicit. Keep the physical reason for each scale: a narrow gap, driving period or relaxation distance can matter more than the size of the whole apparatus.