Final answer:
The correct statement regarding time during high-speed space travel is that time for the pilot of a spacecraft would pass slower than for an observer on Earth. This outcome results from time dilation, where relative motion affects the measurement of time intervals without changing the speed of light.
Step-by-step explanation:
The correct statement regarding time for the pilot and the observer is that time for the pilot would pass slower than for the observer. This is due to the effects of time dilation, a concept in relativity theory developed by Albert Einstein. When a spacecraft flies past Earth at a speed approaching the speed of light, the astronaut within the spacecraft and the Earth-bound observer experience time differently. Although the astronaut's clock runs at the same rate from their perspective, the observer on Earth would see the astronaut's clock running slower. This effect is based on the principles of special relativity, where the speed of light is constant in all reference frames (c), and relative motion affects the measurement of time intervals. Importantly, no matter the motion of the source or observer, the speed of light remains constant. Therefore, the other options regarding the speed of light being greater or smaller for the observer are incorrect, as the speed of light does not change due to relative motion.