The universe from the perspective of an EECR

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If an extreme energy cosmic ray (EECR) is traveling at nearly the speed of light,
then it experiences significant time dilation and can, from its perspective,
observe essentially the entire universe in the direction it is traveling, and thus the
universe would appear to be small and there would be no barrier beyond which the EECR could
not detect the end of the universe. No?

If a particle could travel at the speed of light, then the entire universe would immediately
in front of the particle and would reach the end of the universe instantly. Correct?