  Theoretical models and experimental observations suggest that gamma-ray
bursts (GRB) and high-energy neutrino bursts travelling through the
interstellar space may reach the Earth at different speeds. We propose and
study in details the mechanism i), which always exists, where GRB are slowed
down due to the dispersion of light in the interstellar medium. In addition to
the standard media such as electrons and photons as CMB, we consider the medium
with invisible axions. The amount of GRB delays in different media are
calculated in details utilizing a novel technique in QFT by using the hitherto
known or estimated densities of particles in the space without introducing any
arbitrary parameter. Previously, the GRB delays have been interpreted as a sign
of Lorentz invariance violation by modifying the dispersion relation of Special
Relativity, which relates the energy, the momentum and the mass of a particle,
based on different mechanisms ii), such as a stringy spacetime foam, coming
from a quantum gravity effect and using an adjustable parameter. Obviously, all
the above-mentioned mechanisms i) and ii) are induced (seeming) Lorentz
invariance violations but not an intrinsic (genuine) one. The amount of GRB
delay due to the two aforementioned interpretations can be distinguished by
observing the time of arrival of light with different frequencies. Namely,
dispersion of light i) predicts that the higher energy GRB arrive the Earth
earlier, while in the other interpretations ii), they arrive later. We notice
that the needed amount for delay due to the dispersion of light shall have the
potential power to shed additional light on the microstructure of interstellar
media with respect to the densities of constituent particles and the origins of
their sources. Finally, we indicate the ways to detect the intrinsic Lorentz
invariance violation and to interpret them theoretically.
