In special relativity, time dilation occurs when there is a relative motion between two observers. Time dilation states that the passage of time appears to be slower for an observer in motion relative to a stationary observer. This effect becomes more significant as the velocity of the moving observer approaches the speed of light.
When considering the scenario where light travels a shorter distance compared to the observer, it's important to note that in the framework of special relativity, the speed of light is always constant and invariant for all observers, regardless of their relative motion. The speed of light in a vacuum is approximately 299,792,458 meters per second.
If an observer is moving relative to a source of light and they perceive that the light has traveled a shorter distance compared to a stationary observer, this discrepancy would not directly affect the time dilation itself. Time dilation is primarily determined by the relative velocity between the two observers and not by the specific distances traveled by light or other objects.
In other words, if two observers are moving relative to each other, and one observer measures the light to have traveled a shorter distance due to their relative motion, both observers would still experience time dilation effects based on their relative velocities. The observer in motion would perceive time to be passing more slowly compared to the stationary observer.
It's worth noting that time dilation and the constancy of the speed of light are well-established principles in the theory of special relativity and have been confirmed by numerous experiments and observations.