Newton’s Absolute Space1 When Newton proposed his axioms describing fundamental laws of physics, he insisted on the necessity of absolute space to a completed theory of mechanics. Absolute space can be best described as not-relationally-dependent space. Newton purports that there is something more to space than just being a vessel to conceptualize positional differences between specific bodies; he claims that there is some objective truth to space — that spatial differences are not dependent upon the matter contained within space. In his Principia, he states that the difference of relational and absolute space becomes manifest in the consideration of place, velocity, and acceleration. These considerations serve to metaphysically establish absolute space in themselves.
However, Newton attempts to support the existence experimentally in his famous ‘bucket experiment’. Through an explication of his reasoning and an analysis of his motivation, I intend to show that Newton’s notion of space is, at best, incomplete. Newton describes the difference between absolute and relative space in the scholium to definition eight in the Principia: Absolute space..without relation to anything external, remains similar and immovable. Relative space is some movable dimension or measure of the absolute spaces (152). His first relevant explication in the scholium is of place.
Place is that which a body occupies in space. Absolute place differs from relative place in that it requires no relationship to any other body to be determined; it is determined by the construct of absolute space itself. Absolute motion, then, is the translation of a body from one absolute position to another. In the same trend, absolute velocity is constant absolute motion in time, and absolute acceleration is a change in absolute velocity in time. With that clearly laid out, Newton has explicitly shown how absolute space is conceptually applied to mechanics.
The validity of absolute space in itself still remains in question. These definitions of absolute mechanics are, in fact, used retroactively to validate the existence of absolute space. In using discussions of absolute place, velocity, and acceleration, Newton’s proponents hope to show that there is a difference between these and their relational counterparts. There is an inherent flaw, though, in arguing for an independent, self-evident difference between absolute and relational in considering place or velocity. However, acceleration, as considered in the bucket experiment, shows promise.
The difference in absolute versus relational place is mere semantics; instead of being defined by making reference to another body, absolute place is determined by making reference to the unsubstantiated concept of absolute space. The question can be asked: What if the universe were to be moved four inches that way? Such a shift would be entirely undetectable, because there would be no shift from any point of reference, save a place in a presupposed absolute space. Only after accepting absolute space does absolute position make sense. Claiming theoretical superiority would be entirely based upon preconceived bias. Absolute velocity is equally indiscernible from relational velocity.
Velocity of a body can only be determined in reference to something. In common perception, I determine the velocity of a body by reference to another. In absolute space though, that velocity, considered in the absolute sense, might have a different magnitude. Newton’s example of a passenger on a ship roughly runs: A man standing still on a ship moving at a constant velocity can be said to be in absolute motion, though he is in relative rest to the ship. An observer not on the ship is able to see that the man is in motion.
Theoretically, it would be an observer, aware of absolute space in itself, that would be able to determine the man’s true motion (as it is known by Newton). However, there is no such observer, save maybe God, with such an awareness, and thus absolute velocity is indiscernible. It requires a pre-established absolute point of reference to be determined. True motion is a technical term that Newton employs. The existence of true motion, he thinks, directly lends to the existence of absolute space. Newton distinguishes absolute and relative motions by the forces impressed upon bodies to generate motion (156).
True motion of a body is motion that occurs as a result of a force imparted directly on that body; relative motion can occur as a result of peripheral forces causing motion in the referential bodies. This means that true motion of a body can only be determined in the right inertial frame. An inertial frame describes the total spacio-temporal system that a surveyor considers when assessing the mechanics of a body. By considering all relevant effectors on a body, an accurate portrayal of the active forces can be determined, rather than just relative accelerations to surrounding bodies. Newton assumes that the ‘right’ inertial frame to consider all ‘relevant’ forces is universal for every body, because there must be an underlying absolute truth to the motion of bodies that is objectively determinable. This ultimate inertial frame is implicit in absolute space.
The concept of inertial frame is important, because it is integral to an attempt at rationalizing the existence of absolute acceleration, Newton’s final hope in proving the existence of absolute space. A proper inertial frame allows an observer to view the action of real forces, and real forces produce real and not merely relative accelerations (xxxvii). From this, it follows that absolute acceleration is discernible. However, depending upon the understanding of force to describe acceleration is circular, because force is defined to be equal to the product of a body’s mass and acceleration. Therefore, the observable effects of an acting force are otherwise undetectable except for it’s effects on acceleration.
Then, by viewing a body’s real acceleration, we can determine it’s real acceleration. This is fruitless. Because of the theoretical impossible of separating force from acceleration, we can no longer determine the force’s magnitude. We lose the notion of ‘real’, and we are forced to resign ourselves to the language of relations. Rotational motion saves the consideration of acceleration from the circularity of purely linear considerations.
This is shown in the bucket experiment. The experiment consists of a bucket, filled with water, hanging from a rope. The bucket is rotated manually, building tension in the rope. The bucket is then released and allowed to spin. The focus of this experiment is on the action of the water: The water begins initially at rest. As the bucket spins, there is a transfer of momentum from the bucket to the water, causing the water the swirl in the bucket.
The water continues to angularly accelerate until its angular velocity equals that of the bucket. An interesting phenomenon occurs in the water: as it accelerates, it ascends up the sides of the bucket; it’s surface becoming vaguely funnel-shaped. This ascension is due to centripetal acceleration. There is a force that occurs orthogonal to the path of any body in rotational motion, which is equal to the product of the body’s mass and the square of its tangential velocity divided by the radius of its path. The importance of this lies in the fact that the water is in relative rest to the bucket, because their velocities are equal.
An observer on the surface of the water would assume that he is at rest, because his reference body is the bucket. However, the ascension of the water is indicative of motion, so the same observer could be lead to believe, with knowledge of physics, that he is not at rest. Since there is a logical inconsistency in considering merely relational references, Newton concludes that he has found proof for absolute space in the need of physics for absolute reference points. His experiment falls short of his lofty hopes, because all Newton has really accomplished is proving the existence of true motion. More specifically, he has shown that every inertial frame will not necessarily capture all imposing factors on a system. The inertial frame has to be carefully chosen, so all relevant action is considered.
If the observer is immersed in the observed system as an element being acted upon, then the inertial frame is ‘too small’. An observer on the surface of the water might not be able to tell that he is in motion, but an observer looking down at the bucket can see the water and bucket moving together. The second observer has a ‘wide’ enough inertial frame so that the questioned action is put into perspective. Newton wants True perspective though. He believes that the only truly correct inertial frame is the one that encompasses everything.
He suggests that no relational perspective can completely account for the relevant forces affecting a body. Though to figure out that the water in the bucket experiment was moving, I don’t need to take the seat of God. It simply requires me walking up to the bucket, as a man, and then looking down. Newton knows that the distinction of absolute space isn’t of practical importance in physics. In our everydayness instead of absolute places and motions, we use relative ones. It is only in philosophical disquisitions we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them (155).
The reason why Newton insists on universal truth is to buttress his Faith in God. In fact, the idea of absolute space is completely manufactured around the presupposition that there is an observer who has ultimate knowledge of the truth of space. God has ultimate knowledge of everything, including spatial relations, thus what he knows is absolute space. The idea of absolute space is reactionary, rather than empirical. I don’t think that it was necessarily intentional. However, it is easy to see how religion motivated an otherwise unfounded claim. He simply declares true motion requires absolute space, because there isn’t adequate empirical rationale.
Perhaps, he never looked for such a connection, because he just assumed it was there the entire time. Bibliography All references made in this paper came from: Alexander, H.G. The Leibniz-Clarke Correspondence. Manchester University Press; New York: 1998.