Philosophy of Modern Physics

8/7/2019 Philosophy of Modern Physics

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200-353-705

What do you think Newtons bucket thought experiment shows? Discuss the

analogies and disanalogies with the twin paradox in special relativity.

In this essay I will exposit Newtons bucket experiment (BE), describe two perspectives on

the things it shows, and then examine one analogy and two disanologies to the twin/clocks

paradox (TP) (Newton p10).

Exposition

In the Principia, Newton describes a bucket, suspended by a cord. The cord is twisted while

the bucket is held stationary; the vessel is then filled with water. The bucket is then released.

As the cord untwists the surface of the water will at first be even, then as the vessel begins to

revolve the water will, after a short delay, form itself into a concave figure. When the water

and the bucket are at rest relative to each other, the water remains concave (Newton, p10).

Forces

I will now discuss what Newtons BE shows. Firstly, it does not attempt to demonstrate a

circular velocity, instead in shows an absolute acceleration. The idea of a circular velocity is

fictitious instead it consists of a series of directional accelerations. The concavity is formed

by a series of restrictions on the movement of water by the bucket. The particles in a fluid

have a natural tendency to move at a tangent to the curvilinear path they are following, and

when they are restricted they produce the characteristic concave shape (Dainton, p174).


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Two options

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 Newtons 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

Newtons 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 buckets edge but if we imagine the water

as to be composed of concentric circles, the inner circles are moving at a much lower speeds


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relative to the buckets edge and the outer circles . The concave effect is caused in part by the

velocity differential between the centre of the waters speed and the edge of the buckets

speed. One could describe the buckets inertial forcespurely 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 doesnt 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 ones 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 ifone 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 itthat 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


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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, Bstops, 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 nearc, 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

twins 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


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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 waters concavity and twin Bs (relative) youth? As Ive 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.


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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 Newtons 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.


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