  A prominent effective description of particles interacting with the quantum
properties of gravity is through modifications of the general relativistic
dispersion relation. Such modified dispersion relations lead to modifications
in the relativistic time dilation. A perfect probe for this effect, which goes
with the particle energy cubed $E^3$ over the quantum gravity scale
$E_{\text{QG}}$ and the square of the particle mass $M^2$ would be a very light
unstable particle for which one can detect the lifetime in the laboratory as a
function of its energy to very high precision. In this article we conjecture
that a muon collider or accelerator would be a perfect tool to investigate the
existence of an anomalous time dilation, and with it the fundamental structure
of spacetime at the Planck scale.
