  This work demonstrates that quantum diffractive collisions, those that result
in very small momentum and energy transfer, are universal. Specifically, the
cumulative energy distribution transferred to an initially stationary sensor
particle by a quantum diffractive collision follows a universal function that
depends only on the sensor particle mass and the thermally-averaged, total
collision cross section. The characteristic energy scale corresponds to the
localization length associated with the collision-induced quantum measurement,
and the shape of the universal function is determined {\it only} by the
analytic form of the interaction potential at long range. Using cold $^{87}$Rb
sensor atoms confined in a magnetic trap, we observe experimentally the
universal function specific to van der Waals collisions, and realize a
\emph{self-defining} particle pressure sensor that can be used for any ambient
gas. This provides the first primary and quantum definition of the Pascal,
applicable to any species and therefore represents a key advance for vacuum and
pressure metrology. The quantum pressure standard realized here was compared
with a state-of-the-art orifice flow standard transferred by an ionization
gauge calibrated for N$_2$. The pressure measurements agreed at the 0.5\%
level.
