The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference

Abstract

We report an observer effect in an Einstein solid, a quantum-mechanical system, induced by fluctuations of an observer’s frame of reference; which has been studied so far under the assumption that the observer’s frame of reference remains constant throughout the performance of a measurement, thus, what is actually measured throughout the performance of a measurement is an unresolved problem during which the observer’s frame of reference is assumed to fluctuate. We investigate the average energy and molar specific heat at constant volume of an Einstein solid measured by an observer with fluctuating frame of reference. The Einstein solid consists of N identical non-interacting simple harmonic oscillators per mole, where N is the Avogadro’s number at temperature T. The average energy and molar specific heat at constant volume of the Einstein solid are formulated for two types of fluctuations of the observer’s frame of reference in order to consider pedagogical and experimental demonstrations. The average energy of the Einstein solid is formulated from the definition of canonical ensemble average and the molar specific heat at constant volume of it is calculated by differentiating the average energy with T. The molar specific heat at constant volume of the Einstein solid exhibits novel features at low temperatures according to the distribution of fluctuations of the observer’s frame of reference: 0 and 3R at T = 0 K for square-wave and sawtooth-wave fluctuations, respectively, where R is the gas constant.