Defense of the Standard Quantum Limit for Free-Mass Position

Measurements of the position $x$ of a free mass $m$ are thought to be governed by the standard quantum limit (SQL): In two successive measurements of $x$ spaced a time $\tau$ apart, the result of the second measurement cannot be predicted with uncertainty smaller than ${\left(\frac{\hslash \tau }{m}\right)}^{\frac{1}{2}}$. Yuen has suggested that there might be ways to beat the SQL. Here I give an improved formulation of the SQL, and I argue for, but do not prove, its validity.