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Time-varying materials bring an extra degree of design freedom compared totheir conventional time-invariant counterparts. However, few discussions havefocused on the underlying physical difference between spatial and temporalboundaries. In this letter, we thoroughly investigate those differences fromthe perspective of conservation laws. By doing so, the building blocks ofoptics and electromagnetics such as the reflection law, Snell's law, andFresnel's equations can be analogously derived in a temporal context, but withcompletely different interpretations. Furthermore, we study the unique featuresof temporal boundaries, such as their nonconformance to energy conservation andcausality.

Fundamental asymmetries between spatial and temporal boundaries in electromagnetics