curved spacetime

Curved spacetime is the central idea of general relativity. In special relativity, space and time form a flat four-dimensional arena, like an endless sheet of perfectly flat paper. General relativity says that mass and energy warp this arena, giving it hills and valleys. Where there is matter, the geometry is no longer flat, and that altered geometry is gravity.

A common picture is a heavy ball resting on a stretched rubber sheet, dimpling it so that nearby marbles roll inward. The picture is helpful but imperfect, because it shows only space sagging, while the deeper truth is that time is curved too, and in fact the warping of time is what produces most of the gravity you feel standing on Earth. Clocks run slightly slower lower down, and objects naturally drift toward where time runs slow.

Objects in free fall do not feel any force; they simply follow the straightest possible paths through the curved geometry. The Earth orbits the Sun not because a rope pulls it, but because the Sun has curved the surrounding spacetime and the Earth is coasting along the straightest route available. We can detect this curvature directly: light bends as it passes a massive body, and clocks at different heights tick at different rates.