The idea that spacetime might be discrete at the Planck scale is based on various speculative theories, such as loop quantum gravity and some versions of string theory. However, it's important to note that these ideas are still under active research and are not yet fully supported by empirical evidence.
In loop quantum gravity, for example, the theory suggests that spacetime is fundamentally granular or quantized at extremely small scales, on the order of the Planck length (approximately 1.6 x 10^-35 meters). This discrete nature of spacetime implies that it is not infinitely divisible but consists of discrete units or "atoms" of space.
Similarly, certain formulations of string theory propose that spacetime emerges from underlying one-dimensional objects called strings. At the smallest scales, the strings vibrate in multiple dimensions, giving rise to the familiar three spatial dimensions and one time dimension of our macroscopic experience.
As for gravity, the question of its discrete or continuous nature is closely related to the search for a theory of quantum gravity. General relativity describes gravity as a continuous curvature of spacetime, but it does not incorporate quantum mechanics. Quantum gravity seeks to reconcile gravity with quantum mechanics, and it is within this framework that the idea of discrete spacetime arises.
However, the search for a complete theory of quantum gravity is an ongoing challenge in theoretical physics, and there is currently no definitive experimental evidence to confirm or refute the discreteness of spacetime at the Planck scale. It remains an active area of research and speculation, and further advances in theoretical physics and experimental techniques may shed more light on this topic in the future.