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Photonic time-varying systems have attracted significant attention owing totheir rich physics and potential opportunities for new and enhancedfunctionalities. In this context, the duality of space and time in wave physicshas been particularly fruitful to uncover interesting physical effects in thetemporal domain, such as reflection/refraction at temporal interfaces andmomentum-bandgaps in time crystals. However, the characteristics of thetemporal/frequency dimension, particularly its relation to causality and energyconservation ($\hbar \omega$ is energy, whereas $\hbar \boldsymbol{k}$ ismomentum), create challenges and constraints that are unique to time-varyingsystems and are not present in their spatially varying counterparts. Here, weoverview two key physical aspects of time-varying photonics that have onlyreceived marginal attention so far, namely temporal dispersion and externalpower requirements, and explore their implications. We discuss how temporaldispersion, an inherent property of any causal material, makes the fieldsevolve continuously at sharp temporal interfaces and may limit the strength offast temporal modulations and of various resulting effects. Furthermore, weshow that changing the refractive index in time always involves large amountsof energy. We derive power requirements to observe a time-crystal response inone of the most popular material platforms in time-varying photonics, i.e.,transparent conducting oxides, and we argue that these effects are almostalways obscured by less exotic nonlinear phenomena. These observations andfindings shed light on the physics and constraints of time-varying photonics,and may guide the design and implementation of future time-modulated photonicsystems.

$\hbar \omega$ versus $\hbar \boldsymbol{k}$: Dispersion and Energy Constraints on Time-Varying Photonic Materials and Time Crystals