Time dilation becomes noticeable at speeds that are a significant fraction of the speed of light. According to special relativity, time dilation occurs as an object's velocity approaches the speed of light (299,792,458 meters per second in a vacuum).
The Lorentz factor, denoted as γ (gamma), quantifies the time dilation effect at a given velocity relative to an observer at rest. The Lorentz factor is given by the equation:
γ = 1 / √(1 - (v^2 / c^2))
where v is the velocity of the moving object and c is the speed of light.
As v approaches the speed of light (c), the Lorentz factor approaches infinity, indicating that time dilation becomes more significant. However, it's important to note that time dilation is a gradual effect that increases as velocity approaches the speed of light. Even at speeds significantly below the speed of light, time dilation can still be observed.
For example, at approximately 86.6% of the speed of light (0.866c), the Lorentz factor is approximately 2. This means that time will appear to pass at roughly half the rate for an object moving at that speed compared to a stationary observer. As the speed approaches the speed of light, the time dilation effect becomes more pronounced.
So, there is no specific threshold or percent of the speed of light at which time dilation becomes a problem. Instead, time dilation becomes increasingly significant as an object's velocity approaches the speed of light, with the Lorentz factor becoming larger and time appearing to slow down relative to a stationary observer.