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 Schrödinger 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.
Characteristic interval, schr\"odinger equation, fundamental length
ROBERTS, MARK D.
"A characteristic particle length,"
Turkish Journal of Physics: Vol. 40:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/physics/vol40/iss1/3