Gravity and acceleration can cause time dilation as predicted by Einstein's theory of general relativity. To understand the mechanism behind it, let's start with the concept of spacetime.
According to general relativity, gravity is not a force in the traditional sense but rather the curvature of spacetime caused by massive objects. Objects with mass or energy deform the fabric of spacetime, creating a gravitational field. The presence of this gravitational field affects the motion of objects and the passage of time.
Time dilation occurs because the curvature of spacetime near massive objects affects the flow of time. The key idea is that the fabric of spacetime is not flat and uniform, but rather it can be stretched or compressed in the presence of gravity.
When an object is in a strong gravitational field or experiencing acceleration, it is essentially moving through a region of curved spacetime. As a result, the flow of time is altered compared to a region with weaker gravity or no acceleration.
To explain this phenomenon more quantitatively, let's consider two observers: one near a massive object or in an accelerated frame and another in a region of weaker gravity or in an inertial frame. Each observer has their own local measurement of time.
According to general relativity, the rate at which time passes for an observer depends on the strength of the gravitational field or the acceleration they experience. In regions with stronger gravity or higher acceleration, time flows slower compared to regions with weaker gravity or lower acceleration. This effect is known as time dilation.
The reason behind this time dilation is that the curvature of spacetime affects the geometry of the observer's worldline—the path they follow through spacetime. The curvature causes the worldline to be "bent" or "stretched," leading to a slower passage of time.
To summarize, gravity and acceleration cause time dilation because they affect the curvature of spacetime. The stronger the gravitational field or acceleration, the greater the curvature and the slower the passage of time for an observer in that region. This effect has been experimentally confirmed, most notably in the famous experiments involving atomic clocks on Earth and in orbit.