To what real-world problem from time is the narrator referring?

The real-world problem from time that the narrator is referring to is the phenomenon of time dilation. Time dilation is the difference in the elapsed time measured by two observers, especially for observers moving relative to each other. This means that time can pass at different rates for different observers, depending on their relative motion. This phenomenon has been confirmed by numerous experiments, and it is one of the key predictions of the theory of relativity.