No, seeing objects being distorted by caustics underwater and seeing objects in time dilation are not similar phenomena. They involve different physical principles and have distinct causes.
Caustics underwater refer to the patterns of light that are created by the refraction and reflection of light rays as they pass through water. When light passes through a medium with varying refractive index, such as water, it can create complex patterns of light and dark areas on surfaces underwater. These patterns can distort the appearance of objects and create shimmering or wavy effects.
On the other hand, time dilation is a consequence of the theory of relativity, specifically the concept that time can be affected by gravity or high relative velocities. In a gravitational field or when moving at high speeds, time can appear to run differently for observers in different reference frames. This effect has been confirmed through various experiments and observations, such as the famous experiments involving atomic clocks on fast-moving airplanes or near massive objects like black holes.
While both phenomena involve distortions in perception, they arise from different physical mechanisms. Caustics underwater are a result of light interacting with the medium it passes through, while time dilation is a consequence of the fundamental nature of spacetime and the theory of relativity.