Newton's bucket

Newton's bucket

the rotating vessel

The four stages. The water is flat at II, where the bucket turns fastest against it, and curved at III, where it turns with the water and there is no relative motion at all. The argument is the comparison of those two, and nothing else on the plate is needed for it.

Devised by	Isaac Newton
Published	1687, in the Scholium to the Definitions[1]
Apparatus	A bucket, a cord, and water
Position in the argument	Fifth of five, and cumulative
Concludes	That rotation is absolute
Now cited to show	That it is not
Performed?	Disputed; simple enough
Mach's counter-trial	Not performed

Newton's bucket is a demonstration set out by Isaac Newton in the Scholium to the Definitions of the Principia (1687), in which a vessel of water is suspended by a cord, wound, and released.^[1] The shape the water's surface takes at each stage is offered as evidence that rotation is not a relation between the water and its immediate surroundings, but a fact about the water alone.

It is the last of five arguments Newton advances in that Scholium, and they are cumulative: no one of them was intended to carry the case by itself.^[2] The bucket is the only one still regularly quoted, and it is now most often produced in support of the view that reference frames are interchangeable, which is the position the five arguments were written against.

The experiment

The bucket is filled, hung from a twisted cord, and let go. What follows has four stages, and the whole of the argument is in the comparison of the second with the third.

At stage II the water and the vessel are in the greatest relative motion the experiment affords, and the surface is flat. At stage III there is no relative motion between them whatever, and the surface is curved. The effect is therefore not produced by the water's motion with respect to the bucket, and is if anything the reverse of it.

Nor will the room serve, or the walls, or the observer. The water climbs by the same amount wherever the bucket is hung and however the surroundings are arranged. Having removed each local candidate in turn, Newton concluded that the rotation is a rotation with respect to space itself.

The other four

The bucket is the fifth, and it appeals to the effects of motion. The four before it run from the eighth paragraph of the Scholium to the twelfth, grouped by Newton under the properties of motion and then its causes, and they narrow the field by stages: that true motion belongs to a body rather than to the bodies about it; that a thing at rest within a moving whole is carried along by it; that motion must therefore be referred to places which do not themselves move; and that forces impressed produce true motion and not merely apparent.^[2]

Newton adds, after the bucket, a second and stranger case: two globes joined by a cord in an otherwise empty universe. The tension in the cord would reveal whether they turned, though there were nothing else in existence to turn with respect to.^[3]

None of the five was offered as sufficient alone. The bucket is quoted alone.

Mach's objection

Ernst Mach, in 1883, accepted every stage and refused the conclusion.^[4] The experiment shows only that rotation relative to the sides of that particular vessel produces no centrifugal force, he held, which is unsurprising, the sides being thin. The forces are produced by rotation relative to the Earth and the other celestial bodies, and the experiment as performed cannot distinguish the two accounts, because the bucket is not massive enough to matter either way.

He declined to say what a heavier vessel would do, observing that no one is competent to say how the experiment would turn out if the sides were increased in thickness until they were several leagues thick. And he named the trial that would settle it: fix the bucket, turn the heaven of fixed stars about it, and show the forces absent.

That trial has not been carried out. Neither, on the evidence, has the objection been answered.

Whether it was performed

Newton describes the stages as a man describes something he has seen, and the apparatus is a bucket, a cord and some water, so that any reader may check it in an afternoon. Whether he checked it himself is not settled: the Scholium presents the case as argument rather than as report, and scholarship is divided on how much of it Newton actually spun.^[5]

The position is therefore this. The most cited experiment in the dispute may not have been performed by the man who published it, and the counter-experiment proposed to settle the dispute has certainly not been performed by anyone. Both parties have been arguing for three centuries about a bucket that neither of them turned.

The inversion

In the modern literature of frames the bucket appears more often than any other item, and appears there as a demonstration that motion is relative and the choice of frame is free.^[6]

It is not. It is the argument that motion is not relative, offered by a man who thought the point required five arguments and gave five. The route by which it changed sides runs through Mach, who used the bucket to argue that inertia is fixed by the distant masses, and thence to a modern claim that a rotating universe and a rotating Earth are interchangeable. The middle step is a real position, seriously held and never refuted. The last is a conclusion Mach did not draw and Newton wrote against.

The same distinction is measured optically by the Sagnac effect, which detects rotation and, in the same apparatus, declines to detect uniform motion.

The experiment continues to work. Water in a turning bucket climbs the sides, whatever is said about it in the room next door, and does not consult the literature first.

See also

• Isaac Newton – who devised it, and gave four other arguments with it
• Ernst Mach – who accepted the stages and refused the conclusion
• Kinematic and dynamic equivalence – the use lately made of it
• Albert Einstein – who named Mach's principle and later set it aside
• Geocentrism – where the inversion is put to work
• Michelson–Morley experiment – another null result assigned the opposite of its finding
• Curved visual space – a real result enlisted past its range
• The Sagnac effect – the optical version of the same distinction
• Foucault's pendulum – the same fact demonstrated on a wire
• General relativity – which changed the answer to the question and not the question

References

1. ^ Newton, Philosophiæ Naturalis Principia Mathematica (1687), Scholium to the Definitions. The bucket appears near the end of the Scholium, after the arguments from properties, causes and effects.
2. ^ Newton's own grouping is by the properties, causes and effects of motion, across paragraphs eight to twelve of the Scholium; the four summaries above are a paraphrase and not his wording. The five are cumulative by construction, each removing a candidate for what true motion might be a relation to, and the bucket removing the last. Quoted singly, it is asked to do the work of five.
3. ^ The two-globes case is the more interesting of the pair and the less quoted, being harder to perform in an afternoon.
4. ^ Mach, Die Mechanik in ihrer Entwicklung (1883). The leagues-thick vessel and the proposal to turn the heavens are both his.
5. ^ See the scholarly literature on whether the Scholium reports an experiment or constructs one. The question is live, and the answer does not affect the argument, which was never evidential in the first place.
6. ^ Counted across the material surveyed for this encyclopedia, the bucket is named more often than parallax, aberration and the microwave background together, none of which is a thought experiment.

External links

• Newton's Views on Space, Time, and Motion – Stanford Encyclopedia of Philosophy – the Scholium and its five arguments
• Newton's bucket – MacTutor History of Mathematics
• Absolute and Relational Space and Motion: Post-Newtonian Theories – Stanford Encyclopedia of Philosophy – Mach's objection and what became of it