Time dilation is not a linear relationship with speed because it is governed by the principles of special relativity, as described by Albert Einstein. According to special relativity, time dilation occurs due to the relative motion between two observers.
The key concept behind time dilation is that the passage of time is not absolute but is instead relative to the observer's frame of reference. When an object or observer is moving relative to another object or observer, their measurements of time can differ.
The relationship between time dilation and speed is governed by the Lorentz factor, which is a mathematical expression that accounts for the effects of special relativity. The Lorentz factor depends on the speed of the moving object relative to the speed of light (denoted as "c").
The equation for time dilation, known as the time dilation formula, is as follows:
Δt' = Δt / √(1 - (v^2 / c^2))
Where: Δt' is the dilated time experienced by the moving object or observer. Δt is the proper time experienced by a stationary object or observer. v is the velocity of the moving object or observer. c is the speed of light in a vacuum (approximately 299,792 kilometers per second).
As you can see from the time dilation formula, the Lorentz factor (√(1 - (v^2 / c^2))) is involved. The Lorentz factor causes time dilation to deviate from a linear relationship with speed. As the speed of the moving object approaches the speed of light (c), the Lorentz factor approaches infinity, and time dilation becomes more significant.
In essence, time dilation becomes more prominent at higher speeds, especially as an object or observer approaches the speed of light. This is why time dilation is non-linear and why it is a fundamental aspect of special relativity.