What Does Curved Spacetime Mean Here?

How can paths and clocks change without imagining gravity as an invisible rope?

You defined curvature through geometry, identified geodesics as straightest-possible paths, connected them to lensing and clocks, and marked the limits of the rubber-sheet analogy.

A light ray and a freely falling probe follow curved global paths past a compact black hole while distant starlight is gravitationally lensed. — Vastward artistic reconstruction. The light and probe paths visualize straightest-possible motion in curved spacetime; this generated image is not an observed trajectory or a literal fabric bending in another dimension.

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