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

TL;DR

This paper critically examines the quantum solutions of a time crystal model, revealing fundamental flaws such as divergence and symmetry violations that question its physical validity.

Contribution

It provides a detailed critique of previous quantum solutions, highlighting inconsistencies and mathematical issues that challenge the model's validity.

Findings

Eigenfunctions diverge in certain regions

Wavefunctions lack expected symmetry

Solutions violate quantum boundedness requirements

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.