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Take, for example, an ordinary pail. Fill it to the brim with plain tap water. Suspend the bucket from a rope, attached to the limb of a tree. If the bucket is still, the water should appear completely level.

Not the stuff of Nobel prizes, so far, but here’s where things get strange. Spin the bucket. Twirl it around gently but resolutely. As the bucket turns, you notice several things. First, the water remains in the pail. Thanks to inertial tendencies, it pushes against the walls of the bucket but doesn’t spill out.

Yet something does change about the fluid. Its surface begins to hollow out, as if sculpted by a potter. In short order, the once-level top has become as curved as a soup bowl.

The principle of inertia can explain this concavity, but only if you adopt the right perspective. From your point of view, the reason is simple: The water is building up against the sides because, despite the spinning of its container, it wants to travel in a straight line. This lowers the central part of the fluid, hollowing it out.

Consider, however, the perspective of a tiny observer (a savvy ant, perhaps) perched on the side of the pail. If he ignores the world beyond the bucket, he might well believe that the bucket isn’t spinning at all. For him, therefore, inertia should keep everything inside the bucket at rest. Then, imagine his surprise if he looks down at the water and sees it change shape. What bizarre supernatural effect, he might wonder, could deliver such a targeted punch?

Newton used his bucket argument to make the point that, while the principle of inertia does not depend on the relative velocity of two reference frames, it clearly does depend on the relative acceleration of the frames. In physics, acceleration refers not just to alterations in speed but also to changes in direction. Therefore, a spinning bucket is accelerating because the motion of any point within it keeps changing direction. But indeed that is true about Earth itself—rotating about its own axis as it revolves around the Sun. Therefore, given all these gyrating vantage points, how can we uniquely define inertia’s unmistakable action? Where in this whirling cosmic carnival can we find solid ground?

The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001