According to Einstein's theory of general relativity, mass and energy cause spacetime to curve. This curvature of spacetime has significant implications for how we experience time. The presence of mass or energy can create a gravitational field, and the strength of this field determines the curvature of spacetime in its vicinity.
In regions of stronger gravitational fields, where spacetime is more curved, time passes more slowly compared to regions of weaker gravitational fields. This phenomenon is known as gravitational time dilation. It means that clocks closer to a massive object, such as a planet or a black hole, will tick more slowly relative to clocks further away from it.
A classic example to illustrate this effect is the thought experiment of having two synchronized clocks, one placed on the surface of a massive object and another located far away in space. Due to the gravitational time dilation, the clock closer to the massive object will tick slower than the remote clock. As a result, an observer near the massive object will experience time passing more slowly compared to someone far away.
This concept has been experimentally confirmed, albeit in very subtle ways. For instance, atomic clocks on Earth, which are closer to the planet's center of gravity, run slightly slower than identical clocks placed on satellites in space. The Global Positioning System (GPS), which relies on precise timekeeping, actually needs to account for this time dilation effect to maintain accurate measurements.
So, in summary, spacetime curvature caused by mass and energy influences the way we experience time by introducing gravitational time dilation. The stronger the gravitational field, the greater the curvature of spacetime, and the slower time passes in that region.