According to the theory of special relativity, time dilation occurs as an object's velocity approaches the speed of light. However, the specific speed at which significant time dilation becomes noticeable depends on the frame of reference from which you are observing.
In the frame of reference of the moving object itself, there is no perception of time dilation. Time always appears to pass at a normal rate for an observer within the moving frame. It is when comparing the passage of time between two different frames of reference that time dilation becomes apparent.
For an observer in a stationary frame of reference, they would perceive time dilation in an object moving relative to them as its velocity increases. However, the effect becomes more significant as the object's velocity approaches a significant fraction of the speed of light, typically around 50% or more. At velocities significantly lower than the speed of light, the time dilation is negligible and not easily observable.
To provide a specific threshold, let's consider an example. Suppose you are observing an object moving relative to you. When the object's velocity reaches about 87% of the speed of light (0.87c), the time experienced by the moving object would be about twice as slow as the time experienced by the stationary observer.
As the velocity of the object continues to increase, the time dilation effect becomes more pronounced. At extremely high velocities approaching the speed of light, time dilation becomes more significant, and time can appear to slow down dramatically for the moving object compared to the stationary observer.
It's worth noting that time dilation is a gradual effect that occurs continuously as velocity increases. There is no sudden threshold at which time dilation starts or stops. Instead, the degree of time dilation increases progressively as the velocity approaches the speed of light, according to the principles of special relativity.