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But every particle you shoot is in a way a time traveler. It reaches nearly the speed of light. It surely perceives time differently. Time is a personal matter.

This is almost a philosophical comment there. The particle is not conscious of anything... :)

It is true that special relativity effects impact the particle in an important way, as found out when we compared what is going on in the particle rest frame with what is going on in the lab frame. However, this does not change much with respect to the outcome of the experiment.

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