Yes, time dilation at relativistic speeds is indeed evident when we compare observations made from different reference frames. If two observers are moving relative to each other at significant speeds, they will perceive time to be passing at different rates.
For example, let's consider a scenario where one observer is stationary (rest frame) and another observer is moving at a high velocity relative to the stationary observer. From the perspective of the stationary observer, they would measure time to be passing normally. However, the moving observer would perceive time to be passing slower compared to the stationary observer.
This effect has been experimentally verified in numerous ways, such as with high-precision atomic clocks. For instance, experiments have been conducted with atomic clocks mounted on fast-moving airplanes or satellites. These experiments consistently show that the moving clocks experience time dilation, and when compared to stationary clocks, they register slightly slower time.
The observations of time dilation have practical consequences as well. For instance, the Global Positioning System (GPS) satellites, which are in motion relative to observers on the Earth's surface, experience time dilation. The satellite clocks are adjusted to compensate for this effect, ensuring accurate GPS positioning calculations.
So, while time dilation may not be immediately apparent in our everyday experiences at low speeds, it becomes more pronounced as objects approach relativistic velocities. By comparing observations between different reference frames, the effects of time dilation become evident, providing empirical evidence for the predictions of special relativity.