Many conclusions can be derived from this experiment. Two favourable to Newton are:

• The metaphysical conclusion - the concavity shown by the water even in the absence of relative motion is due to the water moving relative to absolute space.
• The epistemological conclusion- if we are in a rotating reference frame, or have no means of constructing a reference frame, we can detect a motion of the bucket by identifying concavity in the water. This is supported by Newton’s rotating spheres experiment. Here, we can identify the movement of the spheres by reference to the tension in the string that connects them, even though they may appear at rest.

Absolute space?

The metaphysical conclusion seems suspect. The relativist will decry the existence of Newton’s postulated ‘absolute’ rotation leads to the existence of absolute space. It is clearly problematic to describe the rotation of the bucket without reference to anything else, if it is relative to the existence of other bodies then it cannot prove the existence of absolute motion, if it is relative to ‘absolute space’ then this is likely to be circular as it relies on the existence of absolution space to prove absolute motion.

It also seems that the bucket could rotate relative to something. Firstly, one can claim that it is rotating relative to the cord. One could distinguish the rotation without positing the existence of absolute space - though one could solve this by postulating a spinning, cordless bucket.

Secondly, one could argue that the water is rotating relative to itself, the outer edges of the water may be relatively at rest relative to the bucket‘s edge but if we imagine the water as to be composed of concentric circles, the inner circles are moving at a much lower speeds relative to the bucket’s edge and the outer circles. The concave effect is caused in part by the velocity differential between the centre of the water’s speed and the edge of the bucket’s speed. One could describe the bucket’s inertial forces purely with reference to its internal motions and without reference to absolute space. The outer concentric circles may be at rest relative to the bucket, but the inner concentric circles are not.

Additionally, even if we accept that the thought experiment demonstrates absolute acceleration, it doesn’t demonstrate absolute rest. It seems Newton could pick out a class of moving inertial frames in which the bucket is contained, but it is not clear that any of these frames entail, or contain an absolute space (Lacey p341). Furthermore, Sklar holds that acceleration is a primitive monadic property, and one does not need to make reference to absolute space to describe it (Dainton p179). Whatever one’s perspective, it seems clear that the BE does not strictly entail absolute space.

Differentiating

I believe that this thought experiment attempts not to necessarily affirm the existence of absolute space or motion but expresses the illustration of a case where absolute ‘rotation’ can be distinguished from merely relative rotation if one holds Newtonian mechanics to be true. In the BE, it is when the water is relatively at rest to the bucket that the concavity at its zenith. It is the inertial effects of the continued accelerations of the bucket that force the water into concavity. The existence of inertial forces in the bucket indicates that it is it that is rotationally accelerating, not the reference frame.

However, what is it that causes these inertial forces? Is it, as Mach holds, that the existence of a framework of other situated objects causes these forces at a distance (Dainton p176)? With this option, we can hold that it is not necessarily any absolute motion that causes the inertial forces it could be instead the action at a distance of other relatively situated objects.

Furthermore, frame dragging phenomena demonstrates that a rotating inertial frame around the bucket is enough to institute concavity in the bucket – it is not necessarily the rotation of the bucket that causes the concavity.

However, if we presuppose Newtonian mechanics the BE shows a case where we can distinguish between absolute and merely relative motion.

I will now move onto a discussion of the TP.

Exposition

The classical TP involves two twins, A & B. A remains on earth, while B accelerates to near the speed of light. At a certain distance away, B stops, then returns to earth at an identical speed. When B returns he is significantly younger than his twin. The paradox exists because the Principle of General Relativity entails that we can describe a reference frame in which twin B is at rest while it is twin A that travels at near c, and it is no more privileged a reference frame than the one in which A is resting (even though the constructed reference frame where A rests may contain pseudo-gravitational fields). The paradox is also caused by the Principle of Special Relativity - from the perspectives of both of the twins, the other twin’s clock seems to be retarded. If these above special and general situations are both valid, why is it the case that B is younger? Surely, both twins should be younger than the other.

Normally the paradox can be solved by explaining that the movements of the twins are asymmetrical and twin B ‘jumps’ an inertial reference frame, upon his return to earth. The reference frame shift could be caused by acceleration or the change of speeds between the outward and return journey – and this is what causes the asymmetrical time dilation.

However, one can postulate the ‘triplets paradox’ (Salmon p6) in which no changes in speed occur. Both paradoxes are solved by the lack of an absolute present in Special Relativity. A present is defined as a set of events that are simultaneous from the point of view of a given observer. The apparent symmetric retardation in the clocks is due to the relativity of simultaneity, the asymmetric time dilation is caused by the relativity of simultaneity of which I will explain more later.

Analogy

Both the TP and the BE seem to posit the existence of a privileged reference frame, or some sort of absolute space. We ask, of both scenarios, if they are strictly relative, what accounts for the water’s concavity and twin B’s (relative) youth? As I’ve mentioned above, the BE could argue that without the existence of an absolute space, one cannot explain the inertial forces within the bucket. Or, at least, there is a means to distinguish and confirm the existence of an absolute acceleration from a relative acceleration by perceiving the inertial forces in the bucket. In the TP, the postulations are similar if one rejects the consequences of Special Relativity. The appearance of the symmetric retardation of clocks and the asymmetric differences in seconds passed lead one to argue for absolute space and motion to attempt to explain why twin B is not as old as twin A (why B has ‘actually’ moved, while A has not), when in fact, the phenomena experienced can be explained by the relativity of simultaneity as entailed in special relativity.

Disanalogy

One disanology is that the BE must affirm Newtonian mechanics to assert the incongruous absolute motion. The TP, on the other hand must deny the entailments of Special Relativity (particularly the relativity of simultaneity) to produce paradoxical conclusions.

A more concrete difference between the two supposed paradoxes is that the solution to the BE is a dynamical one, while the solution to the TP is a kinematical one. If the BE is thought to have a solution, one can be found by postulating that the inertial forces in the bucket are created by the water moving relative to that of absolute space. In the TP, it is a conceptual shift in the lines of simultaneity as represented in Minkowski space time that accounts for the ‘time gap’ and asymmetricity of time dilation (Lucas and Hodgeson p.76). It is not the effect of acceleration, or change in speed but the kinematic shift in perspective upon the ‘return journey’ of twin B that leads us to resolve the paradox.

Conclusion

In this essay I have claimed that the BE demonstrates the experimental conditions under which we could detect absolute acceleration as distinguished from relative acceleration if we accept Newton’s dynamics. I went on to present that the TP urges us to pursue absolute space also, in order to determine that it was ‘actually’ twin B that moved though this is based upon the misunderstanding of Special Relativity. Finally I discussed two disanalogies between the thought experiments. The BE asks us to affirm Newtonian Dynamics in order to create the conditions for distinguishing absolute motion while the TP requires us to reject or misunderstand Special Relativity in order to generate the paradox. Finally I demonstrated that a presentation of the BE requires use of dynamics, while a resolution of the TP requires use of kinematics.

Bibliography

Dainton, B. Time and Space. (Acumen 2001)

Lacey, H. ‘The Scientific Intelligibility of Absolute Space’, Brit. J. Phil. Sci., (1970) pp.317-342

Laymon, R. ‘Newton’s Bucket Experiment’ J. Hist. Phil. 16 (1978) Lucas and Hodgson. Spacetime and Electromagnetism (OUP 1990)

Newton, I. Philosophiae Naturalis Principia Mathematica, Bk. 1 (1689); trans. Andrew Motte (1729), (University of California Press, 1934)

Salmon, W. Space, Time and Motion (University of Michigan Press 1975)