The link between speed and mass in causing time dilation arises from Einstein's theory of special relativity. According to this theory, the passage of time is not absolute but depends on the relative motion between observers.
One of the key principles of special relativity is that the speed of light in a vacuum is constant and the same for all observers, regardless of their relative motion. This principle implies that the laws of physics, including the behavior of time, must be the same for all inertial observers.
When an object moves at a high velocity relative to an observer, the effects of time dilation come into play. Time dilation refers to the phenomenon where time appears to pass slower for a moving object compared to a stationary observer. In other words, time seems to "dilate" or stretch out for the moving object.
The link between speed and time dilation can be understood through the Lorentz transformation equations, which describe how time, space, and other quantities change between different reference frames moving relative to each other. These equations show that as an object's velocity increases, its time dilation factor also increases. This means that the faster an object moves, the more dilated time becomes for that object from the perspective of a stationary observer.
Mass, on the other hand, is related to time dilation through the concept of gravitational time dilation, which is described by Einstein's theory of general relativity. According to general relativity, the presence of mass and energy curves the fabric of spacetime, and this curvature affects the passage of time. In regions of stronger gravitational fields, such as near massive objects like black holes, time dilation occurs.
The relationship between mass and time dilation can be understood by considering that mass warps spacetime, and this warping influences the flow of time. In the presence of a massive object, time runs slower compared to a region with weaker gravity. As a result, an observer closer to the massive object will experience time passing slower than an observer further away.
Therefore, both speed and mass can cause time dilation, but they operate through different mechanisms. Speed affects time dilation due to the relativistic effects of special relativity, while mass influences time dilation through the gravitational effects of general relativity.