We evaluated the emission of a low-mass particle in the system (atomic) transition for the case when the particle Lorentz factor is $10^{18}$ and found that the angular distribution of emission in the laboratory inertial system is strongly affected by the directional variation of the maximum attainable speed of the particle. We show that for a photon mass consistent with the experimental limit, $m_{ph} leq 10^{-18}$ eV, due to the experimentally known absence of a significant anisotropy of the photon emission by an atom, the anisotropy of the one-way speed of light, $Delta c_1/c$, is $10^{-37}$ or less. This is many orders of magnitude smaller than previously reported and the limit becomes even stronger for the lower mass of the photon.
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