According to the theory of special relativity, time dilation reaches its maximum value for an object traveling at the speed of light relative to a stationary observer. However, it's important to note that matter with mass cannot reach or exceed the speed of light.
According to special relativity, as an object approaches the speed of light, its relativistic mass increases, and time dilation effects become more pronounced. As the object's velocity approaches the speed of light, time dilation approaches infinity. This means that time would appear to stand still for the object moving at the speed of light, relative to a stationary observer.
However, it's crucial to emphasize that massive objects with rest mass cannot reach or exceed the speed of light. The theory of relativity states that as an object with mass accelerates towards the speed of light, its energy requirements increase infinitely, making it impossible to reach that speed.
Additionally, it's worth noting that time dilation is also influenced by gravitational forces. In the presence of a gravitational field, time dilation occurs even without high velocities. In general relativity, gravitational time dilation is observed when an object is in a region with a stronger gravitational field compared to another object. The closer an object is to a massive gravitational source, such as a black hole, the more pronounced the gravitational time dilation effects.
Therefore, in the absence of gravitational forces, time dilation would indeed be at its greatest for an object traveling at the speed of light, but it's important to acknowledge that matter with mass cannot attain or exceed that speed.