  It is argued that there are characteristic intervals associated with any
particle that can be derived without reference to the speed of light $c$. Such
intervals are inferred from zeros of wavefunctions which are solutions to the
Schr\"odinger equation. The characteristic length is
$\ell=\beta^2\hbar^2/(8Gm^3)$, where $\beta=3.8\dots$; this length might lead
to observational effects on objects the size of a virus.
