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.

BibliographyAll references made in this paper came from: Alexander, H.G. The Leibniz-Clarke
Correspondence. Manchester University Press; New York: 1998.