Observing gravitational time dilation in real life requires extremely precise measurements and sophisticated equipment. However, there are a few ways you can indirectly observe its effects. Here are a couple of examples:
GPS Satellites: One of the practical applications of general relativity is correcting the time measurements of Global Positioning System (GPS) satellites. Due to their high orbital speeds and the gravitational field differences between Earth's surface and space, the satellites experience time dilation. The onboard atomic clocks run slower than those on Earth, and this effect must be taken into account to ensure accurate GPS positioning.
Atomic Clock Experiments: Scientists have conducted experiments with extremely precise atomic clocks to observe gravitational time dilation. In these experiments, clocks are placed at different altitudes or in areas with varying gravitational fields. By comparing the time measured by clocks at different locations, the effects of gravity on time can be observed. Notably, the Gravity Probe A experiment conducted by NASA in 1976 provided experimental confirmation of gravitational time dilation.
It's important to note that directly observing gravitational time dilation on a personal scale is challenging due to the extremely small effects involved. These effects become more pronounced near massive objects or in extreme gravitational conditions, such as near black holes or in the vicinity of neutron stars. However, such observations require advanced scientific instruments and are typically carried out by researchers with specialized knowledge and resources.