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Strategies intended to resolve the problem of time in quantum gravity bymeans of emergent or hidden timefunctions are considered in the arena ofrelational particle toy models. In situations with `heavy' and `light' degreesof freedom, two notions of emergent semiclassical WKB time emerge; these arefurthermore equivalent to two notions of emergent classical`Leibniz--Mach--Barbour' time. I futhermore study the semiclassical approach,in a geometric phase formalism, extended to include linear constraints, andwith particular care to make explicit those approximations and assumptionsused. I propose a new iterative scheme for this in the cosmologically-motivatedcase with one heavy degree of freedom. I find that the usual semiclassicalquantum cosmology emergence of time comes hand in hand with the emergence ofother qualitatively significant terms, including back-reactions on the heavysubsystem and second time derivatives. I illustrate my analysis by taking itfurther for relational particle models with linearly-coupled harmonicoscillator potentials. As these examples are exactly soluble by means outsidethe semiclassical approach, they are additionally useful for testing thejustifiability of some of the approximations and assumptions habitually made inthe semiclassical approach to quantum cosmology. Finally, I contrast theemergent semiclassical timefunction with its hidden dilational Euler timecounterpart.Comment: References Update

Emergent semiclassical time in quantum gravity: I. Mechanical models