Final answer:
The student's question is about gravitational time dilation, a concept from physics. Time does run slightly faster at higher altitudes due to this effect, but the difference is too minute to notice without precision instruments and cannot account for being 5 minutes late to a meeting.
Step-by-step explanation:
The student's question relates to the concept of time dilation, which is a part of Einstein's theory of relativity. In physics, time dilation occurs when two observers are in different gravitational potentials or moving relative to each other at high speeds. This effect is very subtle and can only be measured with precise instruments, such as atomic clocks.
In this scenario, your friend has suggested that time runs faster at the top of the Empire State Building compared to its base. Technically, due to gravitational time dilation, time does indeed run slightly faster at a higher altitude, but the difference is so small—a few nanoseconds—that it could never account for a 5-minute discrepancy in a casual meeting. Therefore, this excuse is not a reasonable explanation for your friend's tardiness.
While it's an interesting concept, the effect of gravitational time dilation at the height of the Empire State Building is incredibly minute and not perceivable in everyday life. In practical terms, both you and your friend would experience time at essentially the same rate, regardless of your positions in the building.