  By analyzing trajectories of solid hydrogen tracers in superfluid $^4$He, we
identify tens of thousands of individual reconnection events between quantized
vortices. We characterize the dynamics by the minimum separation distance
$\delta(t)$ between the two reconnecting vortices both before and after the
events. Applying dimensional arguments, this separation has been predicted to
behave asymptotically as $\delta(t) \approx A(\kappa |t-t_0|)^{1/2}$, where
$\kappa=h/m$ is the quantum of circulation. The major finding of the
experiments and their analysis is strong support for this asymptotic form with
$\kappa$ as the dominant controlling feature, although there are significant
event to event fluctuations. At the three-parameter level the dynamics may be
about equally well-fit by two modified expressions: (a) an arbitrary power-law
expression of the form $\delta(t)=B|t-t_0|^{\alpha}$ and (b) a
correction-factor expression $\delta(t)=A(\kappa|t-t_0|)^{1/2}(1+c|t-t_0|)$. In
light of possible physical interpretations we regard the correction-factor
expression (b), which attributes the observed deviations from the predicted
asymptotic form to fluctuations in the local environment and in boundary
conditions, as best describing our experimental data. The observed dynamics
appear statistically time-reversible, which suggests that an effective
equilibrium has been established in quantum turbulence on the time scales
investigated. We discuss the impact of reconnection on velocity statistics in
quantum turbulence and, as regards classical turbulence, we argue that forms
analogous to (b) could well provide an alternative interpretation of the
observed deviations from Kolmogorov scaling exponents of the longitudinal
structure functions.
