Comment on "Time crystals made of electron-positron pairs"

Abstract

Direct reproduction of Bialynicki-Birula's quantum solutions using the authors' own equations and initial conditions reveals two fundamental flaws. First, the eigenfunctions exhibit divergence in the region $y<0$, contradicting the claimed decay behavior ($\abs{\phi}\to\infty$ as $y\to -10$) (Figs. 9--11). Second, the apparent parity symmetry displayed in Figures 9--11 is not supported by Equation (21); numerical solutions clearly show asymmetric wavefunctions. Furthermore, all quantum solutions presented in Section IV violate the boundedness requirements of quantum mechanics. These inconsistencies raise serious concerns about the physical validity of the quantum framework underlying the time crystal model.