Shayne Wissler
Imagine a world where we figured out the right direction to push, and then we pushed in that right direction…

Newton’s Bucket

January 28 2023

This article is a followup to thoughts I had regarding Newton’s Bucket way back in 2002. Originally these were in an email thread between friends[1].

I first became aware of the bucket argument from an article by David Harriman titled “Cracks in the Foundation” (published in “The Intellectual Activist” ca. 2002). This article struck me as obviously wrong and I said so to a physicist friend. While he didn’t agree with Harriman, he didn’t agree with me either – we each had distinct interpretations of the same experiment. So immediately then there are no less than four distinct interpretations of this one simple experiment: Newton’s interpretation (as alleged by Harriman, though there’s reason to suspect that it was a straw man; see below), Harriman’s, my friend’s, and mine.

I find this to be fascinating. How can such a simple experiment cause such a diverse and irreconcilable set of differences? I would have loved to be able to get to the bottom of it, but my friend and I couldn’t come to terms on the issue[2].

To summarize our respective positions: (1) Harriman alleged that Newton thought the experiment demonstrated that space must be “absolute” – that the underlying space is in some sense a real physical reference frame with respect to which something can physically be considered at absolute rest (i.e. as not moving relative to this underlying “absolute space”); (2) Harriman maintained that remote stars determined the physical reference point which physically determines rotational forces, mediated by some property of the underlying space (arguably this view is the same as Bishop Berkeley’s and Ernst Mach’s, but Harriman didn’t cite them); (3) my friend’s view made too little sense to me for me to articulate, but I think his ultimate aim was to argue for Harriman’s view minus the remote stars (“luminiferous aether”).

What follows is my own interpretation. While I thought of it myself I don’t know that it’s novel[3]. It seems to at least be related to a common view among physicists; as Wikipedia puts it: “Newton’s arguments do not settle this [metaphysical] issue; his arguments may be viewed, however, as establishing centrifugal force as a basis for an operational definition of what we actually mean by absolute rotation.”

Note that the following assumes a general understanding of Newton’s Bucket thought experiment and of Newton’s Rotating Spheres thought experiment[4].

The general question is: what metaphysical[5] conclusions may we draw given the behavior of the bucket (or spheres)? Does it say something new about the nature and identity of the underlying “space”? Note that while many have imputed the metaphysical claim to Newton that he thinks his experiment demonstrates that “absolute space” is real, that interpretation of Newton is debatable.

I think that Newton’s Bucket argument (when interpreted metaphysically, as Harriman does) is a classic red-herring: it purports to illustrate something new that earlier and simpler experience had not shown, and yet when scrutinized carefully it does no such thing. It’s an entirely superfluous thought experiment regarding revealing anything metaphysically special. (It’s obviously not superfluous regarding the specific mathematical analysis of the shape the water surface takes in accordance to the speed of rotation nor is it superfluous in terms of illustrating what we mean by “rotation.”)

Inertia is itself a metaphysical property, it is something intrinsic to the basic nature of physical objects, one which we all experience from the time we are born. The concept “mass” and “momentum” are different perspectives on this basic property; these terms entail and imply one another. The metaphysical interpretation of Newton’s Bucket asks: Is there something else beyond these that are entailed and implied? For example, gravity is a distinct metaphysical property, one which is implied by our dropping or weighing things. Does Newton’s Bucket imply some additional metaphysical property as well, namely “absolute space” or “the ether” or some such?

No. The only thing we may infer from the bucket experiment is what we’d already observed regarding inertia: to change an object’s momentum requires force. If that observation did not inform us about the nature of space, then the bucket experiment can’t either, because that is all it comprises: objects continuously exchanging momentum via force. Indeed, this is precisely how you perform the aforementioned calculation of the shape of the water surface.

In other words, solely by knowing that objects will persist in a certain line of motion unless some force causes its speed or direction to change (i.e. the principle of inertia, or Newton’s First Law), we can know that rotation is a state in which objects continuously exchange momentum, and ergo are under a constant state of force. In particular, if two objects not under the influence of outside forces have equal and opposite momentum from one another and are moving towards each other along parallel lines, then if when they reach the point at which they are closest a rigid line were to instantaneously connect them, we can logically deduce that they would begin to rotate: their respective momentums would be continuously exchanged across that line of connection. In other words, we can fully derive and understand the prospect of rotation solely from our understanding of momentum in a given line. In other words, the bucket experiment brings no new information about the underlying nature of the universe into play.

Why does this thought experiment confuse so many people? It seems to be that they tacitly assume that they need to derive these physical properties in terms of relative motion to other objects. If we imagine Newton’s Bucket rotating in empty space, then the only reference point is the bucket itself, but from the bucket’s point of view there is no motion at all, and therefore (allegedly) nothing to distinguish a rotating bucket from a still bucket. The thought experiment illustrates no relative motion and yet real force, ergo it seems to some to suggest some “absolute” space the rotation must be with respect to – a new metaphysical object.

But we do not need to be able to derive the properties of rotation from apparent motion; we can fully derive them from a different and real and measurable property: momentum exchange. The bucket experiment arranges the fact that the various parts of the bucket are continuously exchanging momentum while maintaining constant relative position. If we imagine an extremely tiny scientist moving to each part of the bucket, he would observe no motion but would be able to measure that the force pulling him toward the bucket’s edge would be zero at the center and maximal at the edge. His prior familiarity with Newton’s Laws would permit him to infer: the force he experiences is from a continuous change in momentum at each point; the bucket is rotating.

What the tiny scientist would be able to infer could be more directly seen by his release of a tracer object at arbitrary points in time and position: the tracer object would define “straight line” and illustrate the momentum that exists at that point in time and place. From this any tiny layman would also be able to witness more directly “we are rotating.”

Again, the point here is that all the metaphysical information contained in the experiment was already contained in Newton’s Laws; nothing new is revealed by the bucket experiment.

The question that could coherently be asked is whether the principle of inertia itself implies anything new and interesting about the nature of the underlying space an object moves through that we didn’t already know before we recognized such law, something akin to “absolute space” or at least some identity we can associate with the underlying space (“ether”). I won’t engage that question here.


The following addresses issues raised by others, though not necessarily literally expressed in the way they originally expressed it, and I will often extend and embellish their point in order to strengthen their objection and deal with anticipated followup objections that they themselves did not voice. In the interest of privacy I won’t publicly reveal the names of those who made such objection unless they request it.

  1. The rotating and non-rotating cases have something different about them: the internal forces. And yet there is no relative motion. So what physical thing accounts for the difference?

    I have seen this type of response a lot and I can so far only interpret it (so far) as confusion about whether momentum is ultimately understood as being a real property of a real object as opposed to understanding the system in terms of formulas written on a page.

    Note that the question at issue is: does the bucket argument successfully argue for a special new metaphysical object as in “absolute space” or “ether” or Mach’s “principle”? The question is not about whether Newton’s laws apply in all reference frames or how to accurately represent what’s going on with coordinate systems and formulas.

    Given that question, I have license to refer to reality as it really is, I don’t need to stay within the bounds of mere formulas about reality or arbitrary stipulations that I not refer to some property that really exists in the rotating object (internal force due to momentum exchange). In particular, the relative motion of these objects is zero, so the formulas will say the relative momentum is zero. But the real fact is that the relative momentum is non-zero.

    So to your question “What physical thing accounts for the difference?”, the fact is that I did mention it many times – the real difference in relative momentum.

    Yes, yes, I of course know there is a real difference in relative momentum, I’m not stupid. The question is: Why?

    I think this question boils down to asking “Why does momentum as such exist?” That’s a really good question, for which the bucket experiment can’t give us any answer. But once you accept Newton’s Laws, then you accept the idea that free objects moving in a straight line have momentum, objects moving along antiparallel lines defining a plane, and then upon their connection rotating with respect to such plane and experiencing a real force according to Newton’s Laws and whose motion is specifically defined according to such rotation.

    I.e. rotation is “absolute” in the sense that regardless of reference frame, all observers (who take all pertinent facts into account, i.e. they don’t arbitrarily disregard internal forces and solely focus on motion) will give identical answers for how fast the object is rotating. (Leaving aside relativistic effects.)

    According to Newton’s Rules of Reasoning, “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” In terms of the bucket experiment, we only need the causes indicated by Newton’s Laws to explain everything about it. Therefore speculations of the “ether” or of “Mach’s Principle” are one thing beyond what’s necessary, and therefore illegitimate.

  2. You don’t get it.

    I understand perfectly your point that a rotating object can define its own plane of rotation through a procedure of “tracer objects” and so on. Such is referred to as an “operational definition of rotation.” But the point of the thought experiment is that everything other than the rotating object has been removed from the universe. You don’t get to reintroduce them as “tracer objects.” You’re just being silly.

    My argument did not actually depend on “tracer objects” except for the layman. The “tiny scientist” can infer that the object is rotating without having to release tracers.

    The “tiny scientist” breaks the rules too. You only get the two connected balls and that’s it. Given the actual setup of the actual thought experiment, there’s no motion but there is force.

    It’s all so mysterious.

    Just because someone stipulates something for a given thought experiment, that does not mean it’s a reasonable stipulation. Your stipulation is just an arbitrary removal of our ability to measure internal forces (and thus the fixed plane actually defined by the aforementioned tracer objects that are freed from such forces). And then you wonder at how we can tell the difference between the two cases.

    A thought experiment aimed at discovering truth about reality should not consist of arbitrary handicaps; the full arsenal of measurement and thought about the experiment should still be available.

    If that were true then this would be a trivial matter, not a profound one. Yet Newton thought it was a good experiment for demonstrating “absolute space.”

    Yes, it’s trivial. I can only refer you back to those who’ve disputed the notion that Newton was doing anything here other than operationally defining rotation. I’d agree that such an epochal genius as Newton would be very unlikely to make such mistake, ergo I believe that he was probably misinterpreted.

  3. So why indeed does this experiment cause so much disagreement and confusion?

    We live in an era of authoritarianism, gross metaphysical (in the philosophic sense) confusions, and the nearly complete obliteration of meritocracy, so all basic questions in all fields have the same property. Try asking a lawyer what “justice” is, or a psychologist what “mental health” is, and on and on, and you’ll find the same sorts of problems. So it really should be no surprise that the physics community can’t resolve such basic matters.

  4. Newton’s bucket argument is a non-issue for mainstream science, which resolved long ago that it shows only that a rotating reference frame is non-inertial. It does not imply or suggest anything about the nature of space itself.

    I am at least a little sympathetic to the view that this conundrum isn’t really one anymore. However, I don’t know how to determine what the mainstream view is. Posts such as this and this contradict your premise that the mainstream accepts the correct view.

    Furthermore, if you scrutinize it carefully, the very notion that there is such a thing as “mainstream scientific consensus” falls part as only being a sloppy way of dodging contrarian points of view. Consider: at what percentage of agreement would you start using that term about an issue? And note your lack of due diligence in assigning your own views as the “mainstream” ones – you merely assert an opinion that your view is the mainstream view, without any polling data or anything to back that up. Meanwhile, we have posts like the foregoing that demonstrate an ongoing confusion.

    It’s important to stifle misinformation. Only credentialed authorities should be allowed to publicly voice contrarianism on this issue. You lack credentials and you are spouting misinformation; if I had the power to silence you, I most certainly would.[6]

    Yes, I believe you would – incompetence has always dealt with competent criticism in that manner.

    I don’t really know what the landscape of opinions are on this topic at present and I don’t know a good way to easily figure it out. As a timely experiment I asked ChatGPT this question. While the answer is somewhat suggestive given how this AI was trained, I offer it more as entertainment than as a definitive:

    me: Do physicists still think that the bucket experiment reveals anything about the nature of space?

    ChatGPT: Modern physicists generally do not interpret Newton’s bucket experiment as revealing anything about the nature of space itself. Instead, the experiment is more commonly viewed as a demonstration of the principle of inertia, which states that an object in motion will remain in motion unless acted upon by an external force. Newton’s bucket experiment shows that a rotating object, such as a bucket of water, experiences a force away from the center of rotation, which is due to the object’s inertia and not any inherent property of space. In the context of modern physics, the experiment is typically used as an illustration of the principle of inertia, rather than as a statement about the nature of space.

    me: About what fraction of physicists still cling to the notion that the bucket experiment reveals something interesting about the nature of space itself? Such as indicating that there must be an ether medium or “absolute space” or remote stars as physical references of rotation?

    ChatGPT: A very small minority of physicists might still believe that the bucket experiment reveals something interesting about the nature of space itself, but the vast majority of physicists reject the idea that the experiment provides evidence for the existence of an ether medium or “absolute space.” This view is not widely held among contemporary physicists, as it has been discredited by a large body of scientific evidence, including the famous Michelson-Morley experiment of 1887.

    Most physicists today accept that the bucket experiment is simply a demonstration of the principle of inertia and has no direct bearing on the nature of space itself. The idea of an ether medium as a reference frame for rotation has been replaced by the more widely accepted concept of a curved spacetime, as described by Einstein’s theory of general relativity. Thus, the notion that the bucket experiment reveals anything about the nature of space itself is not widely accepted in contemporary physics.

    me: How do you know this?

    ChatGPT: I know this through the training data I was provided by OpenAI. The training data includes a large corpus of text written by experts in various fields, including physics. The information in this text reflects the current understanding and consensus among physicists on the subject of the bucket experiment and its relevance to the nature of space. This information is regularly updated as new scientific discoveries and advancements are made, allowing me to provide accurate and up-to-date information to users. Additionally, my training also includes a deep understanding of scientific concepts and theories, which allows me to provide context and explanation for the information I present.

    me: Can you provide any references, so I can see for myself what the scientific consensus is?

    ChatGPT: Certainly! Here are a few references that you can use to learn more about the current understanding of Newton’s bucket experiment in physics:

    “Classical Mechanics” by Herbert Goldstein: This is a classic textbook on mechanics that provides a detailed explanation of the principles underlying Newton’s laws of motion, including the bucket experiment.

    “University Physics” by Francis Sears and Mark Zemansky: This widely used textbook provides a clear and concise explanation of the bucket experiment and its relationship to the principle of inertia.

    “Introduction to Electrodynamics” by David J. Griffiths: This popular textbook provides a comprehensive treatment of classical mechanics, including a discussion of the bucket experiment and its relationship to the principle of inertia.

    These are just a few examples of the many resources available that can help you understand the current scientific consensus on the bucket experiment. By studying these resources and consulting with experts in the field, you can gain a deeper understanding of the current state of knowledge on this topic.

    If the mainstream only knows to reject the bucket argument’s metaphysics due to being “discredited by a large body of scientific evidence, including the famous Michelson-Morley experiment of 1887,” then it’s fundamentally wrong.

  5. Momentum is mass times velocity. The relative velocity of the rotating spheres is zero, therefore so too is the relative momentum.

    Momentum is a real but relational physical property, not merely a calculation. Whereas that formula for momentum is only valid in an inertial frame.

    An object’s relative momentum may be directly observed by freeing it from all forces, such as in measuring the velocity of the tracer particle, as mentioned above.

    But then what are the spheres spinning with respect to?

    Thinking about rotation fundamentally in terms of relative motion is misleading, unless you define an inertial plane through the foregoing operational procedure.

    But the experiment is asking about an empty universe. Your procedure is introducing new things (“tracer objects”) and therefore invalidates the premise of the experiment.

    Again, see my remarks against arbitrary stipulation above. No valid thought experiment can arbitrarily ban a legitimate scientific apparatus.

    If this is true, then the thought experiment is technically invalid and your arguments are moot.

    I’d accept that interpretation.

    So then is there such a thing as “absolute momentum,” such as with respect to an ether medium?

    This experiment only indicates that the relative momentums of the rotating spheres are opposite from one another, as measured from their center of mass at any given point in time.

    You’re saying then that momentum is “real,” but not “absolute?” This makes no sense.

    I’m saying that Newton’s Laws identify real properties of objects. Such laws inherently concern relative changes between real bodies. The rotating spheres experiment illustrates a constant and real momentum exchange in exactly that sense.

  1. Special thanks to James Ellias for prompting me to finally write this article.
  2. The confusion over this topic is commonplace, e.g. and and “Empedocles, Newton, the Centrifugal Force and Their Bucket Experiments”; Apeiron, Volume 20, Hors série 3, August 2017
  3. On 2/4/2023 as I was revising this article for objections, I finally found what appears to be an intellectual doppelganger on this issue in this post by AnssiH on 10/30/2006, and in his followup posts. For example:

    Regarding this water bucket thought experiment, I’ve always been amazed about how Newton could have been so confused about something he postulated himself. His first law of motion says: …object in uniform motion tends to stay in uniform motion unless acted upon by a net external force…

    It is also plain to see that any rotating object is a case of all of its elements attempting to continue in a straight line but since they are constrained to each others, they are forced to accelerate all the time. The rotational speed does not accelerate, but the elements feel inertial acceleration because they really are changing direction all the time.

    Maybe this is just a common misconception about what Newton thought, I don’t know. In any case, after having established his first law of motion: “An object in motion will remain in motion unless acted upon by a net force”, it should be quite clear that the water in the bucket is also a case of something “trying to remain in motion”, regardless of the existence of absolute space or not. And likewise it should become clear that “rotating frame of reference” is just a mental concept and not something that objects create (i.e. not something the bucket creates for the water). What he can arrive to from the first law of motion directly is that “straight lines” exists, and still he could not have told if the straight lines are properties of “space” or defined by matter… Should not have been too complicated to him, seems to me…

    Yes, I’m quite sure that the curvature of the water is tautologous to Newton’s own first law of motion. Certainly doesn’t seem like too hard to figure that out.

    As to why so many clever people have missed the obvious, well, we come to think about reality with certain concepts, they are hard to let go, and some concepts can mislead you to wrong paths.

    I.e., if someone thinks about this experiment in terms of rotating frames, as many people intuitively do, they will have to conclude there exists one special rotation frame where things are at rest.

    The error there was assume that the mental concept/definition of “rotation” has got some meaning to reality. No one forced you to ever invoke the idea of rotation at all. You could choose to comprehend reality - and that bucket - in terms of tiny sphere-symmetrical elements in linear motion/acceleration.

    Curvature of the water is in any case tautologous to Newton’s first law of motion. Oops.

    Well, it’s a logical consequence of Newton’s first law of motion. If you hold the first law as valid, you must also expect your hands to rise. Otherwise your worldview is not self-coherent.

    We are juggling with mental concepts that somehow correspond to the behaviour of reality, and it’s one thing to hold mental concepts that yield correct predictions, and another to actually understand what reality is like ontologically.

  4. Regarding the cited Wikipedia article on the Rotating Spheres experiment, note Max Born’s description of Mach’s objection to Newton:

    “Mach took some issue with the argument, pointing out that the rotating sphere experiment could never be done in an empty universe, where possibly Newton’s laws do not apply, so the experiment really only shows what happens when the spheres rotate in our universe, and therefore, for example, may indicate only rotation relative to the entire mass of the universe.”

    This objection is invalid. Newton was reasoning on the basis of what was actually known at the time, and it is of course perfectly legitimate to reason in terms of what is known. Mach imagines unknown, unproved properties (“may indicate only”) which might contradict inferences from the basis of what is known; such imaginings are not a legitimate basis on which to reject what is rationally inferred from what is known.

    So sure, it “may,” hypothetically, be true that “if further information along certain lines comes to light, then Newton will be shown to be wrong.” But until such time actually comes to pass, Newton should be regarded as being right. We reason in terms of what is known, not what might one day turn out to be known. This policy is otherwise known of as Newton’s Rule of Reasoning IV.

  5. In this article use the term “metaphysical” in a different sense than when I use the term philosophically.
  6. This is based on a real interaction but is of course not a literal quote.