Its impossible, maybe with no physical activity one can survive 100 days, but climbing upstairs??? I only fasted for max 5 days in a row, and by the end of 5th day it was quite difficult to go up and down in the mountains. also, i am sorry to tell you this, but these time-travellers you've discovered - they were ghosts of someone who died, while climbing this infinite stairs. Thats why( bc they had died) they were able to time-travel. I am not saying that living creatures cant potentially travel in time, but they would need some type of a vehicule to do that. Only pure energy (meaning with no physical representation) can travel by its own will with no devices. I don't have evidence for that , but I am pretty sure.