In special relativity (SR), movement can indeed affect time dilation. Time dilation refers to the phenomenon where time appears to pass differently for two observers relative to their relative motion. It is a consequence of the constancy of the speed of light in all inertial reference frames.
According to special relativity, the passage of time is not absolute but depends on the relative motion between two observers. When two observers are in relative motion to each other, they will measure different time intervals for the same event.
The equation that describes time dilation in special relativity is given by:
Δt' = Δt √(1 - (v^2 / c^2))
where Δt' is the time interval measured by the moving observer, Δt is the time interval measured by the stationary observer (in their frame of reference), v is the relative velocity between the two observers, and c is the speed of light.
This equation shows that as the relative velocity (v) between the observers increases, the term (v^2 / c^2) becomes larger, approaching 1. As a result, the square root term approaches zero, causing the measured time interval (Δt') for the moving observer to become larger compared to the time interval (Δt) measured by the stationary observer.
In other words, an observer who is moving relative to another observer will perceive time to be passing more slowly for the stationary observer. This effect becomes more significant as the relative velocity increases, approaching the speed of light (c). At speeds much slower than the speed of light, the effect of time dilation is negligible in everyday situations, but it becomes more noticeable as the velocity approaches relativistic speeds.
It's important to note that time dilation is a real physical effect that has been experimentally verified. It has practical implications for phenomena such as the operation of GPS satellites, particle accelerators, and the synchronization of clocks in high-speed transportation systems.