General Relativity & Curved Spacetime Explained! | Space Time | PBS Digital Studios

General relativity resolves the “gravity illusion” paradox by replacing Newton’s global inertial frames with a geometry where inertial behavior only holds locally. In Newton’s picture, a freely falling apple accelerates because gravity acts like a real force, while Earth’s frame is treated as inertial and deep space as the standard of non-acceleration. Einstein flips the bookkeeping: the apple’s frame is inertial, and Earth’s frame is effectively accelerating, so the “downward force” is an artifact of using the wrong reference frame. The trouble is that if inertial frames are supposed to define non-acceleration, it seems inconsistent to call both Earth’s and the apple’s frames inertial.

The fix comes from curved spacetime. Instead of treating straightness as a global property, Einstein’s framework limits inertial frames to tiny spacetime patches. The transcript uses a 2D ant-on-a-sphere analogy: a small region of a sphere can look flat enough that great circles appear straight, but a larger “grid” drawn on the sphere inevitably distorts what counts as straight. Likewise, axes and clocks—what defines an inertial frame—work reliably only over small regions if spacetime is curved. Observers in deep space can still define local inertial frames, but those frames must be “reset” from patch to patch. In this view, the apple’s world line is a geodesic—its path requires no gravitational force—while the Earth surface is not on a geodesic because forces (and the non-inertial nature of the frame) are present.

Curvature also explains why two apples in a falling box converge. Newton attributes the closing gap to their trajectories being “radial” rather than “down.” Einstein attributes it to the fact that two initially parallel geodesics in curved spacetime can cross, just as geodesics on a sphere can meet. Meanwhile, points on Earth’s surface are not geodesics because they experience net forces, so their motion reflects acceleration rather than free-fall geometry.

The transcript then moves from consistency to experiment with a geometric argument attributed to Alfred Schild. Fire a laser pulse from the ground to a detector on the roof, repeat after five seconds, and compare arrival times. In flat spacetime, the photons’ world lines and the stationary clocks at ground and roof should line up so the second arrival matches the first by exactly five seconds. But the measured discrepancy—small, under a second—implies gravitational time dilation: clocks at different heights run at different rates. That breaks the geometric possibility of flat spacetime, forcing the conclusion that spacetime must be curved.

Finally, the “why” is given at a high level: spacetime curvature is determined by energy content through the Einstein equations. Plug in the sun’s energy distribution and the resulting geodesics translate into the familiar orbital behavior and trajectories that Newton would describe as being driven by gravity. The closing question—why physicists still say “gravity” if it isn’t a force—gets a human answer: “gravity” is a convenient shorthand for the curvature effects most people can’t directly visualize in four dimensions.