Newton's Bucket and Relationalism

← Back to Philosophy Essays

Newton's bucket is one of the most famous experiments in the history of philosophy of physics, and for good reason: it takes an everyday observation and turns it into a metaphysical claim about the nature of space itself. The set-up is deceptively simple. A bucket full of water is suspended on a rope, twisted, and then released. At first, the bucket spins but the water lags behind, its surface staying flat. As the water gradually catches up and begins to spin uniformly with the bucket, the surface curves upward, concave at the edges. Newton highlights the striking fact that the concavity remains even when the water and the bucket rotate together, so there is no relative motion between the two. From this he draws a larger inference: if the effect cannot be explained by relations between the water and the bucket, and if it would still occur even if there were no other bodies in the universe, then it must be explained by the water's relation to absolute space. The curved surface, in other words, is meant to reveal the reality of space as something substantive and independent, and thereby to show that relationalism is false.

At first, this argument has a powerful intuitive appeal. Watching the water curve, it is tempting to say that the water is "really rotating," even if there is no relative change with nearby objects. This sense of "real rotation" suggests there must be something beyond relations that anchors the motion. For Newton, that something is absolute space, an invisible backdrop against which true motion is measured. He distinguishes this "true motion," which is defined relative to space itself, from "apparent motion," which is merely relative to other bodies. The bucket experiment, in his view, forces us to admit that apparent motion is not enough: concavity is evidence of true motion, which only makes sense if absolute space exists.

But Newton's inference depends on a controversial assumption. As Dasgupta (2015) explains, Newton introduces what we might call "absolute structure"—entities or frameworks posited to exist over and above the facts about bodies and their relations. Absolute space is one such structure. The question is whether it is really needed. If relational facts are sufficient to explain phenomena, then absolute space risks being an unnecessary surplus. Dasgupta argues that metaphysics should avoid such redundancy: our ontology should not include structures that add no explanatory value. The bucket argument, then, becomes a test case. Does the concavity of the water's surface force us to posit absolute space, or can it be accounted for by relational facts alone?

A relationalist reply begins by pointing out that Newton's experiment only shows that rotation cannot be defined relative to the bucket alone, not that it cannot be defined relationally at all. Later thinkers such as Mach argued that acceleration and rotation can be understood as relations to the mass distribution of the universe. On this view, the water curves not because it spins relative to an invisible container but because it spins relative to the "fixed stars," the distant bodies that constitute the cosmic frame. Far from being irrelevant, these distant bodies play an essential role in grounding the distinction between rest and motion. If the water were not rotating relative to them, there would be no centrifugal force. The bucket's concavity therefore does not compel substantivalism; it simply highlights that relationalism must look beyond local comparisons.

This first reply shows that relationalism can make sense of acceleration, but Newton anticipates it with his thought experiment: suppose the stars themselves were annihilated, leaving only the bucket and the water. Would the water still curve when spun? Newton says yes, and takes this to mean that motion must be defined relative to absolute space. But the relationalist can press back: the very idea of rotation in an otherwise empty universe is incoherent if motion is relational. Without other bodies to compare to, there is no fact of the matter about whether the bucket is rotating. Newton's counterfactual presupposes that rotation must still make sense in isolation, which is precisely the substantivalist view at stake. Rather than proving relationalism false, the empty-universe scenario simply begs the question against it.

Another strand of the relationalist reply draws on Dasgupta's anti-redundancy principle. Absolute space is not an observable entity, nor does it exert causal influence. Its sole role is to anchor a definition of motion. But if relational facts can fulfill this role, absolute space adds nothing of substance. To posit it is to multiply entities beyond necessity. Dasgupta argues that when metaphysical explanations introduce surplus structures, they should be eliminated in favor of leaner accounts. Newton's bucket therefore fails to establish substantivalism: it dramatizes the reality of acceleration but does not justify the metaphysical cost of absolute space.

To appreciate the strength of this reply, it helps to compare the debate to other cases in metaphysics where absolute structures were once assumed but later discarded. Consider time. Newton himself believed in absolute time, flowing uniformly regardless of events. But modern physics shows that time is relationally linked to motion and gravity. The shift from absolute to relational conceptions of time illustrates how explanatory parsimony can overturn seemingly obvious metaphysical assumptions. The same may hold for space: what looks like evidence for an independent container may instead reflect our limited conceptual tools.

The relationalist can also strengthen the case by highlighting how Newton's reliance on common sense can mislead. He assumes it is meaningful to say "the bucket rotates" even without any reference frame. But relationalists argue that such statements are only intelligible within a system of relations. Once we accept that our intuitions about motion may be shaped by everyday contexts rather than metaphysical truths, the appeal to common sense loses its force. Indeed, many features of modern physics—such as relativity's denial of absolute simultaneity—contradict common sense. Why should the bucket be any different?

One might object that relationalism remains vague. What does it mean, exactly, to say the water rotates relative to the universe? What if the stars move? Which frame counts? These worries are legitimate, but they are not decisive. Relationalists can refine their account, for example by defining acceleration relative to the average rest frame of all matter. General relativity provides a rigorous framework: inertial frames are determined by the distribution of matter and energy through the spacetime field. In this context, Newton's bucket becomes an early, if incomplete, gesture toward a problem later solved in relational terms. The very vagueness of relationalism in Newton's time reflects the limits of seventeenth-century physics, not the bankruptcy of the view.

Another objection is that the bucket shows intrinsic effects of motion. The water curves even when there is no apparent relational change, so relationalism supposedly fails. But this claim confuses two levels of description. Locally, the water and bucket may rotate together. Globally, however, the water's state can still be relationally distinguished in terms of its acceleration relative to the universe. The fact that local comparisons are held fixed does not mean all relational comparisons are. This is why Mach's proposal is powerful: it relocates the explanation of concavity from local to cosmic relations. Once this is recognized, the bucket no longer threatens relationalism.

A more subtle objection is that relationalism seems to strip motion of reality. If motion is only relative, is there any fact of the matter about whether something moves? But this objection overlooks that relationalism does not deny motion's reality; it redefines it. To say the bucket rotates relative to the stars is not to say it "merely appears" to rotate. It is to ground motion in relations that are no less real than the bodies themselves. Absolute space is not required to make motion real; relations suffice.

Beyond these direct replies, the relationalist can point to the trajectory of science as indirect support. Modern physics has largely abandoned Newton's substantivalism. In general relativity, spacetime is not an inert container but a dynamic field interacting with matter and energy. The relationalist can argue that Newton's bucket was a snapshot of a conceptual problem later resolved without absolute space. Far from disproving relationalism, the bucket highlighted a puzzle that relationalism was eventually better equipped to solve.

This matters because Newton frames the bucket as a decisive refutation of relationalism. If the water curves even when there is no relative motion to the bucket, relationalism must fail. But what the experiment really shows is that local relational accounts are insufficient. It does not follow that relationalism as such is false. Once we expand the scope of relational comparisons to include distant bodies or the universe as a whole, the bucket's concavity can be explained without absolute space. The inference from "local relations are insufficient" to "absolute space exists" is a non sequitur.

From a metaphysical perspective, this debate illustrates the importance of resisting overreach. The bucket gives us an observable effect—curvature caused by rotation. The question is what explains it. Newton jumps to absolute space. The relationalist insists that we first exhaust relational explanations. Dasgupta's framework supports the relationalist: absolute structure should only be posited if it does explanatory work that nothing else can. Since relational facts can account for acceleration, absolute space is redundant.

The bucket also reminds us of the danger of conflating physics with metaphysics. Newton's physics was revolutionary, but his metaphysical conclusions were shaped by the assumptions of his time. Later developments showed that those assumptions were not inevitable. Relationalism, once dismissed, gained new life as physics advanced. This suggests that metaphysical humility is warranted: we should be cautious about inferring ontological truths from limited experiments.

In conclusion, Newton's bucket is a vivid and enduring thought experiment, but it does not refute relationalism. It shows that motion cannot be explained solely in terms of local relations, but it does not prove that motion must be defined relative to absolute space. Relationalists can explain the concavity of the water's surface by appealing to relations with the universe as a whole, can challenge the coherence of Newton's empty-universe scenario, and can invoke the principle of parsimony to reject unnecessary absolute structures. Dasgupta's insights underscore the point: metaphysics should avoid redundant posits. Newton's bucket, then, dramatizes the problem of rotation, but it does not settle the debate. Far from disproving relationalism, it invites us to refine it, showing that motion and acceleration are real but relational, grounded not in an invisible container but in the network of bodies that constitute the world.

References

Dasgupta, S. (2015). Substantivalism vs. Relationalism about Space in Classical Physics. Philosophy Compass, 10(9), 601–624.

Newton, I. (1687/1999). Philosophiæ Naturalis Principia Mathematica. Trans. I. B. Cohen & A. Whitman. Berkeley: University of California Press.

Mach, E. (1883/1960). The Science of Mechanics. LaSalle, Ill.: Open Court.