Zero Mass Limit and Its Experimental Test

TL;DR

This paper challenges Sancho's claim that the zero-mass limit interpretation of Brownian particle experiments is physically invalid, providing a more complete analysis that supports the zero-mass limit's validity.

Contribution

It offers a comprehensive mathematical and physical analysis demonstrating that the zero-mass limit is a valid interpretation of Brownian motion experiments, countering prior incomplete arguments.

Findings

Zero-mass limit is a valid interpretation for Brownian particles.

Sancho's analysis was incomplete and excluded the zero-mass limit.

The paper provides both mathematical and physical justification for the zero-mass limit.

Abstract

J. M. Sancho [Phys. Rev. E 84, 062102 (2011)] analyzed two stochastic interpretations on a recent experiment [Phys. Rev. Lett. 104, 170602 (2010)] of Brownian colloidal particles. The author asserted that the stochastic interpretation "obtained by simply setting the acceleration equal to zero" should not be taken and that the zero-mass limit interpretation of the experimental data would not be physically correct. In this Comment we show that Sancho's analysis is incomplete in that it pre-excludes zero mass limit and hence his assertions are incorrect. Our reasoning will be both mathematical and physical.