Time dilation does not require superluminal (faster-than-light) speeds. In fact, according to Einstein's theory of special relativity, time dilation occurs even at sub-light speeds when there is relative motion between two observers. The effect becomes more pronounced as the speed approaches the speed of light but is still present at any speed above zero.
The fundamental principle behind time dilation is that the passage of time is not absolute but depends on the relative motion between observers. When two observers are in relative motion, they will measure time intervals differently. The moving observer will perceive time passing slower compared to the stationary observer.
This phenomenon has been experimentally confirmed by numerous high-precision experiments, including measurements with atomic clocks. For example, if you were to travel in a high-speed spacecraft while someone on Earth remained stationary, you would experience time passing slower than the person on Earth. However, the effect would be minuscule and not noticeable in everyday life unless you were traveling at a significant fraction of the speed of light.
Acceleration, on its own, does not directly cause time dilation. However, when an object undergoes acceleration, it can lead to changes in relative velocity, which in turn can result in time dilation effects. In scenarios involving acceleration, the concept of general relativity becomes relevant, which describes the effects of gravity and acceleration on the curvature of spacetime.
In summary, time dilation occurs at any speed above zero and is not limited to superluminal speeds. While acceleration alone does not directly cause time dilation, it can contribute to changes in relative velocity, which in turn affects time dilation.