Meissner effect cannot be explained classically

Abstract

The Meissner effect is an important characteristic of superconductivity and is critical to distinguishing superconductivity from simply the absence of electrical resistance (perfect conductivity). In a recent paper published in American Journal of Physics, Ess\'en and Fiolhais claimed that the Meissner effect is explained by classical physics. [Am. J. Phys. {\textbf{80}} 164, (2012).] We claim it cannot be understood by classical mechanics and point out that their derivation of the Meissner effect by classical physics is based on an inadequate treatment of the magnetic field energy. A correct treatment of the magnetic field energy clarifies the need for quantum mechanics to understand the Meissner effect. We stress that Meissner effect is energetically favorable due to the energy of condensation of the Cooper pairs. The condensation of electrons into Cooper pairs is best understood as a quantum mechanical phenomenon.