Yes, it is possible to observe gravitational time dilation with current technology. Gravitational time dilation is a phenomenon predicted by Albert Einstein's general theory of relativity, which states that time runs slower in the presence of a strong gravitational field.
One of the most famous demonstrations of gravitational time dilation is the Pound-Rebka experiment conducted in 1959. In this experiment, gamma rays were emitted from the top of a tower and detected at the bottom. Due to the difference in gravitational potential between the top and bottom of the tower, the gamma rays experienced a change in frequency as they traveled, which was measured and confirmed the prediction of time dilation.
Today, more advanced technologies such as atomic clocks are used to observe gravitational time dilation with even greater precision. Atomic clocks are extremely accurate timekeeping devices that rely on the vibrations of atoms to measure time. By comparing clocks located at different gravitational potentials, scientists can detect the minuscule differences in the passage of time due to gravity.
For example, in the famous Hafele-Keating experiment conducted in 1971, atomic clocks were placed on airplanes flying in opposite directions around the Earth. The clocks on the airplanes experienced slightly different gravitational fields due to their different altitudes and velocities, leading to measurable differences in the passage of time.
These experiments demonstrate that gravitational time dilation is a real and observable phenomenon. While the effects of time dilation are generally small unless extreme gravitational fields are involved (such as those near black holes), modern technology allows us to detect and measure these effects with high precision.