Yes, a clock on a spaceship would be affected if it were traveling at an extremely high speed, according to the principles of special relativity. Special relativity is a theory proposed by Albert Einstein that describes how objects and observers in relative motion experience time, space, and other physical quantities.
One of the key concepts in special relativity is time dilation, which states that the passage of time for an object moving at a significant fraction of the speed of light relative to another stationary observer will appear to pass more slowly from the perspective of the stationary observer.
To put it simply, if you were to observe a clock on a spaceship moving at an extremely high speed relative to you, the clock on the spaceship would appear to tick slower than a clock that is stationary relative to you. This effect becomes more pronounced as the speed of the spaceship approaches the speed of light.
Time dilation has been experimentally confirmed and is a critical factor to consider in modern physics, particularly in scenarios involving high-speed travel or relativistic particles like those encountered in particle accelerators.
It's worth noting that this effect is only significant at speeds close to the speed of light, and in most everyday scenarios, the differences in time due to relative motion are too small to be noticeable. However, in the realm of extremely high-speed space travel or particle physics, these relativistic effects become crucial to consider.