Suppose spaceships A and B with clocks A and B move along the same straight line at uniform speeds differing by 161 miles per second. At the moment when B passes A, their clocks both read noon. Shortly after they meet, at 2 o'clock according to A's clock, spaceship B passes space station C.
Furthermore, suppose that spaceship B has a computer monitor that is programmed to display the time according to clock B plus the word "yes" if spaceship B has already passed space station C or the word "no" if spaceship B has not yet passed space station C (according to B's perspective). Assume that spaceship A can see this computer monitor at all times from where it is.
Then according to the special theory of relativity, from A's point of reference, B's computer monitor will change from "no" to "yes" when as soon as it displays 1 o'clock.
But by symmetry, from B's point of reference, B's computer monitor will change from "no" to "yes" when as soon as it displays 2 o'clock.
Did I make a mistake, or is it a consequence of special relativity that two people can perceive completely different realities from completely different perspectives, A seeing the monitor change from "no" to "yes" at 1 o'clock and B seeing the monitor change from "no" to "yes" at 2 o'clock?