Feynman paradox induced by vacuum and thermal fluctuations

Abstract: A charged particle initially at rest in an external magnetic field starts to rotate when the magnetic field is switched off. This is a variant of the Feynman disc paradox, where the conservation of angular momentum is seemingly violated. The paradox is understood by realizing that angular momentum is initially stored in the electromagnetic field and is transferred to the particle when the magnetic field is removed. In a classical description, no rotation occurs if the particle is uncharged, as the initial angular momentum is zero in this case. We show that electromagnetic fluctuations in thermal equilibrium can induce a quantum analog of the Feynman paradox, where a nonreciprocal particle without charge starts to rotate when the source of nonreciprocity is removed. This paradox is due to persistent energy fluxes arising in nonreciprocal systems at equilibrium, leading to angular momentum stored in the electromagnetic field. We demonstrate that the contribution of vacuum fluctuations to persistent energy fluxes dominate over thermal fluctuations at finite temperature, so vacuum fluctuations dominate the equilibrium angular momentum as well. Observation of the induced motion would thus provide a means of detecting persistent energy fluxes and offer further evidence for the physical reality of vacuum fluctuations.