The particle will appear to live longer only to the outside, "from the point of view of the particle" the lifetime isn't altered.


By the way, Dreamworld:
some Russian mathematicians are warning that we might get more than we bargained for. Specifically, time-travellers: futurenauts using our ultra-duper atomsmasher to punch a hole in causality and hop back from the future.
This is a reason to use the LHC, not the contrary.