Final answer:
The question pertains to time dilation experienced by characters in the movie Interstellar due to proximity to a black hole. It illustrates how a shorter period spent near a black hole can equate to a much longer period having passed elsewhere, resulting in a substantial difference in experienced time for those at different distances from the black hole.
Step-by-step explanation:
The question revolves around the effects of time dilation experienced during interstellar travel near a black hole, as portrayed in the film Interstellar. In the movie, Cooper and Dr. Brand spend a brief amount of time on Miller's planet, which is in close proximity to a black hole, causing time to pass much more slowly for them than for people further away from the black hole, such as Dr. Mann. This phenomenon is a result of time dilation, a concept in relativity theory proposed by Albert Einstein, which states that time can pass at different rates depending on the strength of the gravitational field and the relative velocity compared to the observer.
While the exact period Cooper and Dr. Brand spend on Miller's planet is not provided in this text, the concept can be applied: if they were to spend an hour on Miller's planet, years could have passed outside of its gravitational influence. As such, the total time Dr. Mann spent without human contact would be significantly greater than the time spent by Cooper and Dr. Brand on the planet because time for Dr. Mann would be passing more quickly relative to them.