Why can the same atoms be a rock, then sand, then a rock again?

Because rock is never finished. It just keeps changing form. Geologists call this the rock cycle. Three rock families, sedimentary, metamorphic and igneous, keep turning into one another. Each one changes as soon as it is pushed out of the conditions it formed in. A basalt can dissolve when rain and air attack it at the surface. Or it can melt all over again if it is dragged under a continent.

It often starts with breaking down. Wind, rain and rivers chip rock into smaller and smaller pieces and carry them away. Bury enough of those grains, squeeze them, and they fuse into sedimentary rock. A single grain of sand inside is still, technically, the rock it came from. Push rock deep, where heat and pressure are intense, and it turns metamorphic without melting. Push it deeper still and it melts into magma. When magma cools, it hardens into igneous rock. Cooled slowly underground, it makes coarse-grained granite.

The twist is that any rock can become any other. Sedimentary and metamorphic rock can melt into magma too. Plate tectonics and water keep the whole loop turning. New basalt crust is born at mid-ocean ridges. Much later, it sinks back down at subduction zones. When continents collide, erosion attacks the new mountains right away. Their debris piles up as the sediment for the next round.

The Scottish naturalist James Hutton read this story in the rocks long before plate tectonics. In 1788, at a seaside cliff called Siccar Point, he and his friends found tilted, worn-down old layers lying under flat, younger ones. To Hutton, that meant cycle after cycle of burial, uplift and erosion, over enormous stretches of time. His friend John Playfair wrote that the mind seemed to grow giddy looking so far into the abyss of time. Hutton's verdict: no vestige of a beginning, no prospect of an end.