The concept of the flow of time changing with speed is a fundamental consequence of Einstein's theory of special relativity. According to this theory, the laws of physics, including the behavior of time, depend on the relative motion between observers.
One of the key principles of special relativity is the constancy of the speed of light in a vacuum, denoted as "c." It states that the speed of light is the same for all observers, regardless of their relative motion. This principle has been verified by numerous experiments and observations.
To maintain the constancy of the speed of light, other quantities, such as time and space, must adjust when observers are in relative motion. The phenomenon known as time dilation arises from this adjustment.
Time dilation refers to the effect of time appearing to pass at different rates for observers in relative motion. Specifically, when two observers are moving relative to each other at a significant fraction of the speed of light, they will measure different amounts of time for the same events. The moving observer will perceive time passing more slowly compared to the stationary observer.
This effect can be understood in terms of the geometry of spacetime. Special relativity combines space and time into a four-dimensional framework called spacetime. When an object moves through spacetime, its trajectory traces a path called a worldline. The shape of this worldline affects the relative passage of time for the object.
As an object accelerates or moves at high speeds, its worldline becomes curved in spacetime. This curvature leads to time dilation, where time appears to slow down for the moving object relative to a stationary observer.
The magnitude of time dilation depends on the relative velocity between the observers. At everyday speeds, the effect is negligible and not noticeable. However, at speeds approaching the speed of light, time dilation becomes more pronounced. For example, if an observer were to travel in a spacecraft at a significant fraction of the speed of light and then return to Earth, they would find that less time has passed for them compared to the time experienced by people on Earth.
In summary, the flow of time changes with speed due to the principles of special relativity, which necessitate the constancy of the speed of light and the adjustment of time and space to maintain this constancy in the face of relative motion.