The concept that time slows down as objects move faster is derived from the theory of relativity, specifically the theory of special relativity, proposed by Albert Einstein in 1905. According to this theory, the passage of time is not absolute but depends on the relative motion between observers.
One of the key predictions of special relativity is time dilation, which states that as an object approaches the speed of light, time appears to slow down for that object relative to a stationary observer. This effect has been confirmed by numerous experiments and is an essential part of modern physics.
The most famous experimental evidence supporting time dilation comes from particle accelerators. In particle accelerators, high-speed particles are accelerated to velocities close to the speed of light. These accelerated particles have been observed to have longer lifetimes than their counterparts at rest. In other words, their internal clocks tick more slowly compared to stationary clocks.
Additionally, other experimental evidence supporting time dilation comes from high-precision clocks on fast-moving objects such as satellites. Global Positioning System (GPS) satellites, for example, are orbiting the Earth at high speeds relative to observers on the ground. Scientists need to take into account the effects of time dilation to ensure accurate GPS navigation because the clocks on the satellites run slightly slower than the clocks on the Earth's surface.
So, when we say that time slows down through speed, it means that an object moving at high velocities relative to another object will experience time passing more slowly compared to the stationary object. This phenomenon has been supported by various experiments and is a fundamental concept of modern physics.