Validity of lorentz invariance at extremely high energies

Experimental data on the distribution of times of arrival of electrons (and muons) in extensive air showers produced by cosmic rays in the energy range 10¹²–10¹⁹ eV have been examined to see if there is any evidence for a departure of the velocity of ultra-high energy particles from that of light as suggested by the model proposed by Pavlopoulos. No evidence for such a departure has been found. An upper limit to the “fundamental length” occurring in the theory is obtained as ～10^?21 cm.