  Recently a series of analyses on the flight time of cosmic photons and
neutrinos suggests that the speed of light \emph{in vacuo} takes the
energy-dependent form $v(E)\simeq 1-E/E_{\text{LIV}}^{\gamma }$ with
$E_{\text{LIV}}^{\gamma }\approx 3.6\times 10^{17}~\text{GeV}$, and meanwhile
the speed of neutrinos is proposed to be $v(E)\simeq 1\pm E/E_{\text{LIV}}^{\nu
}$ with $E_{\text{LIV}}^{\nu }\approx 6.5\times 10^{17}~\text{GeV}$ and $\pm
{}$ representing the helicity dependence. This novel picture immediately urges
us to provide a satisfactory theoretical explanation. Among all the attempts to
predict the speed variations from quantum gravity, we find that loop quantum
gravity can serve as a good candidate for explaining the aforementioned picture
consistently.
