Published online by Cambridge University Press: 31 October 2025
Thermal and zero-point fluctuations of charges and electromagnetic fields give rise to fluctuation-induced forces, known as dispersion forces. To understand these forces, we first discuss the properties of stationary stochastic fields and derive fluctuation–dissipation theorems for both fields and sources. Fluctuating sources give rise to Johnson noise in resistors and to blackbody radiation and heat transfer. For a pair of polarizable particles, we derive the Casimir–Polder potential and evaluate it for short and large separations, which renders the Van der Waals and the Casimir force, respectively. For a particle moving in a thermal field, we find a viscous force, referred to as vacuum friction. We show that zero-point fluctuations are responsible for shot noise in optical power measurements and for radiation pressure shot noise exerted on irradiated objects. Shot noise is responsible for measurement imprecision and radiation pressure shot noise for measurement backaction, the disturbance of an object by the measuring optical field. We show that imprecision and backaction noise set a limit to measurement accuracies, known as the standard quantum limit, and that their product is fundamentally bound by the so-called Heisenberg limit.
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