Yes, time dilation has been experimentally proven and is a well-established concept in physics. It arises from the theory of relativity, which includes both special relativity and general relativity.
In special relativity, time dilation occurs due to relative motion between two observers. According to the theory, as an object moves closer to the speed of light relative to another object, time appears to slow down for the moving object as observed by the stationary object. This means that an observer moving at a high velocity relative to another observer will perceive time as passing more slowly compared to the stationary observer.
General relativity extends the concept of time dilation to include gravitational effects. In the presence of a strong gravitational field, such as near a massive object like a black hole, time also appears to slow down. This effect is known as gravitational time dilation.
Regarding the perception of time, it's important to understand that there is no absolute or preferred frame of reference in relativity. Observers in different states of motion or gravitational fields will experience time differently relative to each other. From their own perspectives, they would perceive their own local time as passing normally.
For example, if you were in a spacecraft traveling at a high velocity relative to a stationary observer on Earth, you would perceive time passing normally from your perspective. However, the observer on Earth would perceive your time as passing more slowly compared to their own. So, both observers would have a different perception of time.
In summary, time dilation has been experimentally confirmed and is a real phenomenon predicted by the theory of relativity. The perception of time depends on the relative motion and gravitational fields between observers, and each observer would experience their own local time as passing normally.