# Bucket argument

Newton's rotating bucket argument is aimed at showing that there is a meaningful difference between what he calls 'true motion' and 'relative motion'. Motion under the influence of a force is true motion, motion without the presence of a force is relative motion.

(It must be kept in mind though, that this article is based on a translation of Newton's writing from Latin to 17th century English (by A. Motte), and later translation of this text to modern English (by F. Cajori). It is possible that the particular understanding of the translators has introduced a bias in the translation. See the External links.)

By necessity, whenever a velocity is given as a number, it is velocity relative to some chosen zero point of place. Any point can be chosen as zero point (usually, choosing the common center of mass of the set of objects under consideration is most convenient).

What Newton calls 'relative motion' is what in modern terminology is called 'uniform motion', motion with a constant velocity in a constant direction. When a group of objects is co-moving in uniform motion the distances and the directions of the distances between them don't change. When two objects are co-moving in uniform motion, and one of them is being deflected by a force, then the motion of the second object relative to the first object changes too, but that, Newtons argues, has nothing to do with true motion, for there was no force on the second object.

Then Newton discusses a bucket filled with water. Many versions of this story put this bucket in otherwise empty space, but that is not the setting in which Newton discusses it. In Newton's version it is a bucket with water in the universe as he knew it, and the bucket is on Earth. If both the bucket and the water inside are in uniform motion, then the surface of the water is flat. If a force starts a rapid spinning motion of the bucket, then the water, not immediately assuming the spinning rate of the bucket, retains a flat surface. Finally, as the water is co-rotating with the bucket the surface of the water is concave, in accordance with the rotation. The relative angular velocity of bucket and water are inconsequential, argues Newton. Something other than relative angular velocity determines whether the surface of the water should assume a concave shape.

Further on Newton discusses the following situation: what if an observer sees only two globes, floating in space, connected by a cord that is under tension, with no other clues to assess the situation. Measuring the amount of tension in the cord alone, argues Newton, suffices to know how fast the two objects are revolving around the common center of mass. (Here Newton tacitly assumes the weight of the globes is known.) Also, writes Newton, much information can be gathered by changing the revolution rate of the system; there will be just a single revolution rate with zero tension in the cord, providing an intrinsic, unambiguous zero rate of revolution. So even in a universe that is otherwise a complete vacuum, argues Newton, it would still be possible to establish the true revolution rate of two cord-connected objects in it.

This shows, argues Newton, that although we have no way of measuring the absolute velocity of the common center of mass of the solar system in absolute space, we do know with certainty that the planets are moving around the Sun. That part at least of the true motion with respect to absolute space is knowable.

From a modern point of view, Newton is discussing the significance of inertia.
Uniform motion will continue indefinitely. But to maintain circular motion a constant force is required. In general, maintaining any form of accelerated motion requires a continued force. This distinguishes relative motion from true motion (as Newton meant it). Any true motion is composed of some uniform motion, that is unknowable, and accelerated motion (orbiting around the Sun), that is observable.

There are tacit assumptions in Newton's reasoning. He assumes that absolute space is telling matter whether it is moving in uniform motion or being accelerated. Uniform motion continues indefinitely, but acceleration is being opposed, acceleration requires continued exertion of a force. In modern terminology: to be consistent, any theory assuming absolute space must assume that this absolute space is acting on objects, if absolute space is assumed then interaction of matter with this absolute space must be the causal agent of inertia.

Philosophy of space and time see section on Absolutism vs. Relationalism

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