In reality, we do experience time dilation, but the effects are usually negligible in our everyday lives. The reason why we don't perceive time dilation in our daily experiences is that the effects become significant only at speeds close to the speed of light or in extremely strong gravitational fields.
According to special relativity, time dilation occurs when an object or observer is in relative motion with respect to another or when they experience different gravitational potentials. However, the magnitude of time dilation is directly proportional to the velocity or gravitational potential difference involved. For typical velocities and gravitational fields encountered in our daily lives, the time dilation effects are incredibly small and difficult to detect without extremely precise measurements.
For example, at everyday velocities, such as those experienced in cars, planes, or even Earth's rotation, the time dilation effects are far too minuscule to be perceptible. It is only when objects approach speeds close to the speed of light or in the vicinity of extremely massive objects like black holes that time dilation becomes more noticeable and measurable.
To give you an idea of the magnitude of the effect, a clock moving at 99% of the speed of light relative to an observer would experience a time dilation effect of about 7 times slower. However, such high speeds are not encountered in our everyday experiences.
In practical terms, the differences in time dilation for everyday scenarios are so small that they are practically unnoticeable to us. Our perception of time remains consistent with our local frame of reference, and we do not observe significant time dilation effects in our daily lives.
Nonetheless, time dilation has been experimentally confirmed in various high-precision experiments involving particle accelerators, space travel, and satellite navigation systems. These experiments provide empirical evidence for the validity of special relativity and the existence of time dilation, even if we do not directly perceive its effects in our everyday experiences.