Yes, if you were traveling at near-light speeds relative to another observer, your clock would appear to be ticking slower compared to the observer's clock. This phenomenon is a result of the time dilation effect predicted by Einstein's theory of special relativity.
According to special relativity, as an object approaches the speed of light, its relative velocity with respect to other objects has a profound effect on the passage of time. Time dilation occurs, and the moving object's clock appears to run slower from the perspective of a stationary observer.
This effect becomes more significant as the relative velocity between the two objects increases. As you approach the speed of light, the time dilation effect becomes more pronounced, and your clock would appear to be ticking slower than the clocks of observers who are stationary or moving at a slower velocity relative to you.
It's important to note that this time dilation effect is mutual. From your perspective, you would also observe the clocks of stationary or slower-moving observers to be ticking slower than your own clock. This phenomenon is known as the relativity of simultaneity, where the perception of time depends on the relative motion of observers.
The time dilation effect at high velocities has been experimentally verified, and it has important implications for understanding the nature of time and space in relativistic scenarios.