Comment on "Quantum Raychaudhuri equation"

TL;DR

This paper critically examines the derivation and physical implications of the quantum Raychaudhuri equation proposed by Das, highlighting significant issues in its mathematical foundation and physical relevance.

Contribution

It provides a detailed critique of the derivation and conclusions of the quantum Raychaudhuri equation, questioning its validity and physical significance.

Findings

Identifies flaws in the derivation of the quantum Raychaudhuri equation

Argues the physical implications of the equation are invalid

Highlights issues with the mathematical correctness of the formalism

Abstract

We address the validity of the formalism and results presented in [ S. Das, Phys. Rev. {\bf D89} 084068 (2014)] with regard to quantum Raychaudhuri equation. The author obtained the so called quantum Raychaudhuri equation by replacing classical geodesics with quantal trajectories arising from Bhommian mechanics. The resulting modified equation was used to draw some conclusions about the inevitability of focussing and the formation of conjugate points and therefore singularity. We show that the whole procedure is full of problematic points, on both physical relevancy and mathematical correctness. In particular, we illustrate the problems associated with the technical derivation of the so called quantum Raychaudhuri equation, as well as its invalid physical implications.