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in one of issues of 'Scientific of American' explained that if space time was discrete then depending of the energy of light and since spacetime would be discrete the 'effective' space of light would not the same ,since in a discrete spacetime for short wavelength (high energy) the particle would note that space is discrete

another possiblity is that for a discrete space time lorentz invariance would not follow, so the fundamental group of Special relativity would not be the Lorentz group, but what more evidences are there ?