Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

On the experimental foundation of Maxwell’s equations 305
5.1. DISPERSION
The search for a dispersion in light propagation amounts to a search
for a difference in the time–of–arrival for a specific signal when observed
in different frequency windows. For the interpretation of such observations
one has to be very careful, since matter like interstellar gas
may interact with the light and then lead to a dispersive behaviour
of the propagation of light. Therefore, one has to know very well the
properties of the interstellar gas. A first treatment of this approach
with taking interstellar matter into account has been carried through
by Feinberg [34]. Fortunately, this is only relevant for low energy photons.
High energy photons are not influenced by interstellar matter.
The best results have been obtained recently by Schaefer [35] leading to
In terms of a photon mass this
means
5.2. HIGH ENERGY COSMIC RAYS
High energy cosmic rays and in particular high energy photons are
especially well suited for searches for quantum gravity induced modifications
of the dispersion relation (13). Since new aspects enter the
discussion, we treat this case in an extra subsection.
First, also here one searches for dispersion effects. An analysis of this
kind has been carried through by Biller and coworkers [36]: A short
signal of about 280 sec emitted from Mkn 421, which is
112 Mpc away arrived, when decomposed into two frequency
windows, at earth at the same time. From this analysis one
arrives at and correspondingly, at
However, another aspect of high energy cosmic rays may be of much
more importance: Based on the conventional dispersion relation
it can be shown that the high energy photons react with the infrared
background what results in the creation of massive particles. Therefore
high energy photons have a finite free path only, which can be calculated
to be of the order of 100 Mpc, [38, 39]. This applies to photons with