Yes, several experiments have been conducted to provide evidence for time dilation due to gravity, which is a prediction of general relativity. General relativity describes the gravitational effects on spacetime and predicts that time runs slower in stronger gravitational fields.
One of the most famous experiments that confirmed this prediction was the Pound-Rebka experiment, conducted in 1959. In this experiment, Robert Pound and Glen Rebka measured the change in frequency of gamma-ray photons emitted from a source at the bottom of a tower compared to those detected at the top. The source and detector were connected by a vertical height difference, and the photons had to climb against Earth's gravitational field.
According to general relativity, the photons traveling against gravity would experience a gravitational redshift, causing their frequency to decrease. Pound and Rebka successfully measured this frequency shift, providing experimental evidence for time dilation due to gravity.
Since then, numerous experiments have further confirmed this phenomenon. For instance, high-precision atomic clocks have been used to test time dilation due to gravity. Clocks placed at different heights experience slightly different gravitational potentials, leading to measurable differences in their rates. Comparisons of clocks on Earth's surface with clocks at higher altitudes, such as on GPS satellites, have consistently confirmed the predicted time dilation effects.
Additionally, gravitational time dilation has been observed indirectly through astronomical observations. For instance, the effects of gravitational time dilation can be observed in binary star systems where one star is much more massive than the other. Precise measurements of the timing of their orbital motion reveal small deviations consistent with general relativity's predictions.
Overall, these experimental results provide strong evidence for the existence of time dilation due to gravity, supporting the predictions of general relativity.