In the context of relativity, time dilation is a fundamental consequence of the theory that arises from the principle that the speed of light in a vacuum is constant for all observers. Time dilation is a result of the relative motion between observers and is an essential part of the theory of special relativity.
In your scenario where you are isolated in space and a clock flies by you at half the speed of light, you correctly point out that you would perceive the clock ticking at a slower rate compared to your own reference frame. This is due to time dilation. From your perspective, the moving clock experiences time passing more slowly.
However, it's important to note that the concept of "who's moving" is relative in relativity. In the theory of special relativity, there is no absolute frame of reference to determine who is truly at rest or in motion. Instead, it is the relative motion between observers that determines the observed effects, including time dilation.
From the perspective of the clock itself or an observer moving with the clock, it would perceive its own time to be passing normally. It would see you as the one moving and experiencing time dilation.
So, while you can indeed observe the clock ticking at a slower rate, the important point is that both you and the clock observe the other to be in motion and experiencing time dilation. This is consistent with the principles of relativity, where the laws of physics are the same for all observers, regardless of their relative motion.
The concept of time dilation helps reconcile the observations of different observers in relative motion and is a key aspect of Einstein's theory of relativity.