Temperature-Distance Relations in Casimir Physics

The Casimir-Lifshitz force arises from thermal and quantum mechanical fluctuations between classical bodies and becomes significant below the micron scale. We explore temperature-distance relations based on the concepts of Wick and Bohr arising from energy-time uncertainty relations. We show that temperature-distance relations similar to those arising from the uncertainty principle are found in various Casimir interactions, with an exact relation occurring in the low-temperature regime when the zero point energy contribution cancels the thermal radiation pressure contribution between two plates.