Gravity does indeed affect time according to the theory of general relativity. The presence of a gravitational field can cause time to pass at different rates in different regions of space. Specifically, time runs slower in stronger gravitational fields compared to weaker fields.
This phenomenon is known as gravitational time dilation. It occurs because gravity warps the fabric of spacetime, and the rate at which time passes is influenced by the curvature of spacetime caused by massive objects.
To understand the effect of gravity on time, let's consider two scenarios: one where gravity is negligible (far from any massive objects) and one where gravity is significant (near a massive object like Earth).
In a scenario with negligible gravity, time dilation is negligible, and time runs at a nearly uniform rate. However, as we approach a massive object, such as Earth, where gravity is stronger, time dilation becomes noticeable.
The factor by which time is dilated due to gravity can be described using the gravitational time dilation formula:
Δt' = Δt √(1 - (2GM / rc^2))
In this formula, Δt' represents the time interval experienced by an observer in a strong gravitational field, Δt represents the time interval experienced by an observer far from any massive objects, G is the gravitational constant, M is the mass of the massive object, r is the distance from the center of the massive object, and c is the speed of light.
For example, on the surface of Earth, where gravity is significant, time is slightly dilated compared to a scenario far away from any massive objects. However, the effect is extremely small. The time dilation due to Earth's gravity is approximately 1.000000000034 times the time interval far from Earth. In other words, the difference is extremely minute and not noticeable in our everyday experiences.
To observe more significant gravitational time dilation effects, one would need to be in an extremely strong gravitational field, such as near a black hole. In such cases, the time dilation becomes more pronounced, and significant differences in the passage of time can occur.
In summary, while gravity does affect the passage of time, the difference in time dilation between being subject to Earth's gravity and being far away from any massive objects is incredibly small. It would not have a noticeable impact on one's lifetime or daily experiences here on Earth.