The phenomenon of time dilation arises from the fundamental postulates of the theory of special relativity. One of these postulates states that the speed of light in a vacuum is constant for all observers, regardless of their relative motion. This means that the laws of physics should appear the same to all observers who are moving at a constant velocity relative to each other.
To maintain this constancy of the speed of light, other quantities, such as time and space, must be adjusted when an observer is in motion. In other words, the measurements of time and space made by one observer may appear differently to another observer who is moving relative to the first observer.
When two observers are in relative motion, their measurement of time is affected by the fact that the speed of light is constant. This leads to the phenomenon of time dilation.
To understand why a difference in velocity causes time dilation, let's consider a simple example: Imagine two observers, one stationary and one moving at a high velocity relative to the stationary observer. From the perspective of the stationary observer, time appears to pass at a normal rate.
However, from the perspective of the moving observer, who is also measuring the passage of time using their own clock, time appears to run slower. This means that if the two observers were to compare their clocks after some period of relative motion, they would find that the clock of the moving observer has ticked fewer times compared to the clock of the stationary observer.
This effect occurs because the moving observer experiences a distortion of both time and space due to their motion. The faster an object moves relative to another, the greater the time dilation effect becomes. As the relative velocity approaches the speed of light, time dilation becomes more pronounced, and time appears to slow down even more for the moving observer as observed by the stationary observer.
In summary, a difference in velocity causes time dilation because the constancy of the speed of light requires adjustments in the measurements of time and space between observers in relative motion. This effect is a fundamental consequence of the theory of special relativity and has been confirmed by numerous experimental observations.