I am a little confused by the terminology here. Initially synchronised atomic clocks do lose their synchronisation if one is put on a jet plane and flown around the world a few times and then brought back to the other clock. A twin travelling at relativistic speeds and returning home would age less than the twin that stayed at home. The decay rate of particles travelling at relativistic speeds is time-dilated, allowing us to detect muons here on Earth that should decay at the edge of the atmosphere.

If the rate at which particles decay is time-dilated by relativistic speed, surely we can say that time does change. If the twin who travelled at relativistic speeds comes home again and has indeed aged less than the twin who stayed at home, surely it is not just the perception of time that changes - they actually experienced time passing at different rates, didn't they? Am I still missing something here?