The Impossible Effects of an Infinite Past

Time travel movies make it seem like you could go into the past and remain on the same timeline. But something can be impossible even if it seems possible at first. An infinite past is impossible not because the infinite past itself is impossible, but because an infinite past would allow impossible things to happen. If we imagine a Hilbert's hotel that is built at the rate of one room every year, each room is equipped with a device that creates an immortal guest who then checks into the hotel.