$gamma$ rays run on time. (arXiv:2208.02247v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Martinez_D/0/1/0/all/0/1">Daniel Beltrán Martínez</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Llanes_Estrada_F/0/1/0/all/0/1">Felipe J. Llanes-Estrada</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tejedor_Garcia_G/0/1/0/all/0/1">Gloria Tejedor-García</a> (Univ. Complutense de Madrid)
Significant absorption of radiation is usually accompanied by refraction.
This is not the case for $gamma$ rays travelling cosmic distances. We show
that the real and imaginary parts of the refraction index are indeed
commensurable, as they are related by dispersion relations, but when turning to
physical observables, the (finite) optical depth is way larger than the
(infinitesimal) time delay of the gamma rays relative to gravitational
radiation. The numerically large factor solving the apparent contradiction is
$E_gamma/H_0$ arising from basic wave properties (Bouguer-Beer-Lambert law)
and the standard cosmological model, respectively.
Significant absorption of radiation is usually accompanied by refraction.
This is not the case for $gamma$ rays travelling cosmic distances. We show
that the real and imaginary parts of the refraction index are indeed
commensurable, as they are related by dispersion relations, but when turning to
physical observables, the (finite) optical depth is way larger than the
(infinitesimal) time delay of the gamma rays relative to gravitational
radiation. The numerically large factor solving the apparent contradiction is
$E_gamma/H_0$ arising from basic wave properties (Bouguer-Beer-Lambert law)
and the standard cosmological model, respectively.
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