 Originally Posted by Xei
Doesn't make much sense to me...
Say the particle is 'watching' a clock. It normally lives for one minute, say from 12.00 to 12.01. However at near light speeds, the time of its surroundings goes faster; it still experiences itself as living for one minute, however it sees the clock go from 12.00 to say 13.00 in this minute. Therefore external observers see the particle for a whole hour.
The particle will only see one hour pass on that clock, if said clock is moving with the particle, ie. moving just as fast.
The atomic watch that we sent into space, to prove the theory of relativity, counted "slower" because time was going slower for it, and for the vessel it was carried within.
If the proton we're gonna shoot through the LHC is sentient, or atleast able to perceive time (think of this as a hypothetical situation, seing as it is impossible), the proton would measure time to be slower and, from its perspective, it would take longer to go around the LHC, than from our perspective.
Lets say we put a human into LHC. He flies around, and takes a look on his watch and he's been in there for an hour. Once he gets out, he talks to the scientists, and they say he was in there for 30 minutes.
So in very simple words, from his perspective and according to his measuring gear, he was going around in there at half the speed of light, but to the scientists and according to their measuring gear, he was moving at the speed of light. Or atleast 99,9999999999%. Once again, this is a hypothetical situation by the way 
I hope this helped you out a bit at understanding relativity.
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