How does the curvature of spacetime create gravity?

In 1919, Arthur Eddington led an expedition to observe a total solar eclipse, confirming that light passing near the Sun is deflected due to its gravity. This observation supported Einstein's theory of general relativity, which differs from Newton's laws by predicting that massive objects warp spacetime, affecting the path of light.

Einstein resolved a paradox wherein photons traveling different distances (AB vs. CD) near a massive object like the Sun reach their destination simultaneously. According to special relativity, light's speed is constant, so photons traveling a shorter path (CD) should take less time. However, in general relativity, the presence of a massive object causes time to slow down, an effect called gravitational time dilation.

To visualize this, imagine spacetime as a cylinder that, when influenced by a massive object, flares into a cone. Clocks lower in the gravitational field (closer to the cone's wide base) tick slower than those higher up, explaining why time passes differently at different altitudes. This effect has been experimentally confirmed, such as with atomic clocks on airplanes running faster than those on the ground.

Gravitational time dilation can be visualized by imagining two ants, one higher (A) and one lower (B) on the cone. Both move through spacetime at the same speed, but B's clock ticks slower due to the cone's shape. Thus, B ages slower than A.

This curvature of spacetime not only affects the flow of time but also creates gravity. Objects naturally follow the curved paths in spacetime, leading them to fall towards massive bodies. A stationary object's path in curved spacetime slopes toward the massive body, causing it to fall, illustrating that gravity is the manifestation of curved spacetime geometry. This explains why an object falls faster as it moves closer to a massive body and why, hypothetically, an object falling infinitely would reach the speed of light due to the extreme curvature of spacetime.