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How does Newton define motion? What is the background for his

definition, and what arguments does he use to support it?

In this essay I will be looking at what motion means for Isaac Newton. I

will go about this firstly by defining what he means by the term motion.

This section will take in what Newton means by absolute and relative

space and time which provide the necessary grounding for understanding

what he means by motion which he distinguishes between the absolute

and relative varieties of. Next I will be looking at the background to this

definition. In this section I will be looking at what Newton is reacting to

for this informs the way in which he speaks about motion. This section

seeks to elucidate the motivation behind his explanations of motion and

by looking at this motivation I am confident that a greater understanding

of Newton’s conception of motion will come to the fore. Finally I will be

looking at how Newton supports this idea of motion. This section will get

into the arguments which Newton uses to justify his conception of motion

and it will be seen that this argumentation can only be fully understood

along with the background to his conception as explored in the second

section of this essay. The primary source I will be relying on for Newton’s

views is the Scholium section of the Principia. I will also be taking in

elements of De Gravitatione in the second section of this essay. Now then

let us proceed to the definition of motion.

Newton’s definition of motion distinguishes two types of motion:

absolute and relative motion. His definition of these is simply that:

‘Absolute motion is the translation of a body from one absolute place into

another; and relative motion, the translation from one relative place into

another’ (Rynasiewicx 2012b). This difference between absolute and

relative motions requires some further points to fully elucidate its

meaning. To fully understand what Newton means by motion it is

necessary for us to understand the context of these different types of

motions and with this in mind we must look at what he understands by

Absolute and Relative space and Absolute and Relative Time. By showing

what Newton means by these my aim is to give a fuller understanding of

what he understands by motion.

Let us first take what he means by space. Newton distinguishes in his

work between absolute space and relative space. As we shall see in the

second section of this essay this is a critical distinction and very

important in understanding the intention of Newton’s Principia in

general and the Scholium in particular. So what is relative space and

what is absolute space? Relative space is the space we observe and

interact with. Absolute space is independent of matter. It can be thought

of as the container of matter. (Rynasiewicx 2012b).

Now let us turn to the difference between relative time and absolute

time. Relative time is the time we interact with in our lives. It is the time

we measure by observation of the world around us. Relative time is what

we are measuring when we look at the sun or the rotation of the earth or

the rotation of the stars. By measuring the rate of change of these

elements we make a convention of time: a relative system by which we

can measure the passing of time. Absolute time on the other hand is time

itself separate from all body and matter. Absolute time is the continuous

stream of time that progresses at the same rate irrelevant of any change

in matter or observers. So then, relative time is the time we interact with

by observation whereas absolute time is the passing of time aside from

any change or event. Absolute time is not accessible to us. We can only

access time in the form of the change and motion we observe in the

universe (Rynasiewicx 2012b).

In light of these concepts what is the fuller picture of motion for

Newton? Relative motions are the motions we observe and we use these

to form our concept of time which is of course relative. They are

determined by looking at how a motion relates to other motions so for

example I am at relative rest with relation to the Earth whereas I am in

relative motion with reference to the sun and the moon. Relative motion,

then, is based on relation to other bodies. Absolute motion on the other

hand occurs with reference to absolute space. It cannot be observed for

to do so we would have to know how we relate to absolute space, a piece

of knowledge that we lack (Rynasiewicx 2012b). One more feature of

absolute motion is that encapsulated in the law of inertia: unless

interfered with a body in absolute motion will continue in this motion ad

infinitum (Rynasiewicx 2012a).

Having given Newton’s definition of motion I would like, in the

proceeding section, to turn to the background of this understanding of

motion. This background will look at two men and their work and how

they affected Newton for better or worse. These are, of course, Galileo

and Descartes.

Firstly let us look at the role played by Galileo in the background of

Newton’s thought. His role was, in general, a positive one. His big

contribution which we are here concerned with is, to use anachronistic

terminology, his principle of relativity (Barbour 2001). Galileo proposed a

set of experiments to be carried out on a ship: the first when it is

stationary and the second when it is in uniform motion. He informs us

that the results are the same in both cases. There are a couple of

poignant points which come of this. The first is the discovery of a

dynamic symmetry: the experiments could be carried out under different

conditions, in this case varying motions, but the results remain the same.

The second point of note is that when one is in a state of uniform motion

it is imperceptible. The latter point here is the principle of relativity and

its implications are grand (Barbour 2001).

Next we come to Descartes who played a considerable part in the

background of Newton’s thought though his influence was of a generally

negative character. He influenced Newton more by contrast than

complement. Descartes’ historical role in this background is complicated.

His views in The World are much more in line with Newton’s thought

than his views in Principles of Philosophy but it is the latter that he

published and to which Newton reacted. In the intervening time between

The World and Principles Descartes had become concerned about what

Rome would think of his new work given Galileo’s troubles so he

suppressed the book and reworked his views in order to make them

acceptable to the Church (Barbour 2001). The latter work is the

Principles and so it is to the inorganically evolved form of his thought

that Newton reacts to. It seems to me that, in order to understand the

full extent to which Newton reacted to Descartes, a fuller picture of his

thought in the Principles is called for. As some of its main points are

elucidated the contrast with Newton’s thought will be pronounced.

The first important point about Descartes’ conception is that

on his account there is no absolute space (Rynasiewicx 2012a). Rather

his is a universe consisting solely of matter. Absolute space, so key to

Newton’s understanding of motion, is ruled out by Descartes as a logical

impossibility. He says it is impossible for there to be space because there

can be no motion in a vacuum it is as absurd for him as a mountain

without valleys (Barbour 2001). Instead for Descartes there is only

matter. Rather than having space as the container of matter for

Descartes matter is the whole of the story. This universe of matter is

called the plenum. Another point related to this one is Descartes’

contention that the only property of matter is extension (Barbour 2001).

This point is related to the above: the universe is all matter and the

property of matter is extension. With this Descartes replaces the notion

of positions in space with position relative to other matter. Now onto the

crucial part of Descartes’ system: his theory of motion. In this universe of

matter with positions only relative to other matter how does motion

work? In Descartes’ system all motions are relative. He distinguishes,

however, between three types of relative motions (Huggett and Hoefer

2009). The first type he distinguishes is change of place. This is motion

relative to some arbitrary reference body. The second is the common

usage of motion which is that something is itself moving. The third type

he distinguishes is true motion. This he defined as the motion of a body

relative to contiguous matter. Of course in Descartes’ system the

universe is all matter and so all bodies are contiguous to matter. While

this last type of motion is privileged as true motion it is still a type of

relative motion. Descartes takes these points together to make his vortex

theory of planetary motion. In this theory the planets are relatively at

rest with respect to the subtle matter of the celestial vortex of the sun.

Using his definition of true motion, as being with respect to contiguous

bodies, the planets, in this relative rest with respect to the subtle matter

of the plenum, have no true motion. His motives for this may not have

been completely genuine and perhaps have to do with the

aforementioned fear of trouble with Rome. Regardless of this he defends

this view of the rest of the planets. As we shall see in the next section

this is not an altogether coherent conception.

This concludes my overview of the background to Newton’s

understanding of motion. In the proceeding section I will be turning to

the arguments which Newton’s invokes in support of this understanding.

As Rynasiewicx (Rynasiewicx 2012a) notes there has been a culture

of misunderstanding relating to Newton’s intentions in the Scholium. It

has been read as if Newton were trying to prove the existence of absolute

motion but this is a flawed understanding. From Newton’s De

Gravitatione, which contains all the germs of the Scholium, Newton is

seen to be explicitly arguing against Descartes arguments against

absolute space (Rynasiewicx 2012a). Many of the arguments which we

shall look at in this third section of this essay were already to be found in

this work written some decade or so before his Principia. So if we

understand Newton’s intention as arguing for the existence of absolute

space and not absolute motion in the Scholium the context of his

arguments and his intention become much clearer.

Newton’s arguments for his understanding of motion can be

divided into two categories: metaphysical and epistemological

(Rynasiewicx 2012a). The metaphysical arguments consist in five

arguments from properties, causes and effects. He uses these arguments

to support his case that absolute space exists and not, as has commonly

been assumed, to give empirical grounds of absolute motion. The

epistemological argument speaks about the possibility of knowing true

motion using the two globes example (Rynasiewicx 2012a).

The first three of the five metaphysical arguments are arguments

from properties of motion and rest (Rynasiewicx 2012b). The first of

these properties is that for bodies to be truly at rest they must be at rest

relative to each other. In this argument he looks at the possibility of

judging a body to be at rest with respect to a far off body based on bodies

in its vicinity. He concludes that true rest cannot be determined by

comparing position with bodies in the vicinity. The second of these

arguments deals with the property that if a part of a body is in a fixed

relation to the body and the body moves then the part of the body

partakes in this movement. This argument states that if a group of bodies

are all moved by the same force then though they stay in relative rest to

each other they have still partaken in motion since all of them can be

seen as parts of one body. The conclusion Newton draws from this

arguments is that, contra Descartes, true motion cannot be conceived as

motion relative to bodies in the immediate vicinity since in a case such as

this it would deny the occurrence of movement. The third argument from

properties argues that if something is in a moving place it moves along

with that place and as it moves relatively away from that place it

partakes in movement of that place. For Newton this means that if a

place is moving relative to another place then the movement of that other

place must be added and if that other place is also in motion relative to

yet another place then that place’s motion too must also be added. This

regress continues onto infinity or else it ends with motion relative to a

stationary place. The conclusion Newton draws from this property is that

the absolute motion of a body cannot be determined except with respect

to a body at rest. These then are the three arguments from properties

(Rynasiewicx 2012b).

Next is Newton’s argument from causes. This argument distinguishes

between the causes of relative and absolute motion. By distinguishing

between the cause of these Newton argues implicitly against Descartes

contention that true or absolute motion is a special case of relative

motion. The argument here comes in two parts. The preamble to these

points is the law of inertia, shared by both Newton and Descartes, that if

a body is in absolute motion then it will continue in this motion ad

infinitum unless a force acts upon it. To disrupt an absolute motion a

force must act on that body. The first point he makes can be illustrated

by taking a body which is at absolute rest with no forces acting upon it.

Now if we take other bodies to which we relate this body and we apply a

force to these bodies so that they are at rest relative to each other but

they are in motion relative to our original body. Now the original body

which is in absolute rest is simultaneously in relative motion because the

bodies which it is being compared with are in motion relative to it. So

here we see that relative motion does not require a force to act upon it

but only on the bodies to which it is being compared. So a force need not

act on a body to set it in relative motion. The second point in this case is

to take a set of bodies and apply the same force to all of them. The bodies

in this case, though they have had a force acted upon them, are at

relative rest with respect to each other. Thus, even though a force has

been applied, there is no relative motion (Rynasiewicx 2012b).

The final of the five arguments is the argument from effects. Here

Newton is speaking about the forces of centrifugal endeavour which

distinguish relative from absolute motion. In this argument Newton

introduces the rotating bucket experiment. The set up for this

experiment involves taking a bucket and attaching it to a length of cord.

Next the bucket is filled up with water. Then the bucket is twisted and

twisted until the cord is strongly twisted and then the bucket is released.

What one observes is that, at first, as the bucket turns with the uncoiling

of the cord, the water inside the bucket stays flat as it was. At this stage

of the experiment a number of remarks can be made. The first is that

when the bucket first starts turning it is in swift relative motion to the

observer. On the other the water which stays flat in the bucket is

relatively at rest with respect to the observer and thus also in relative

motion with respect to the bucket. What we can take from these remarks

is that the existence of centrifugal endeavour in the parts of a body, in

this case the water, is not necessary for the body, in this case the

bucket, to be in relative rotational motion (Rynasiewicx 2012b).

As the experiment progresses, the bucket continues to turn the

water begins to recede from the axis of rotation and to climb the walls of

the bucket. As well as this the surface of the water becomes concave in

the centre. The water then stops climbing the bucket and remains at the

same level against the side of the bucket. The water has now fully

acquired the rotation of the bucket. The first remark to be made here is

that the water is now at rest with reference to the bucket and in

rotational motion with reference to the observer. The fact that the water

has stopped climbing the walls though the bucket continues to spin

indicates it has reached the maximum of its centrifugal endeavour. From

these we can say that just because of the presence of centrifugal

endeavour in a part of a body it does not mean that the body is in relative

circular motion with reference to its surroundings. This then is the

bucket experiment in detail but I will now be looking at its greater

consequences, in combination with the foregoing arguments from

properties and causes, for Newton (Rynasiewicx 2012b).

Following these arguments in the Scholium Newton consolidates

these points into what can be read as a counterargument to the Cartesian

conception of space and motion. Specifically he can be read as attacking

the vortex theory of planetary motion as outlined above. Descartes claims

that all the planets are relatively at rest but this is observably not the

case. From the first of the arguments we have it that since the planets

are in motion relative to each other then they cannot be at rest for to be

at rest they must be at rest with respect to each other. Taking the second

argument from properties we have it that the planets must partake in the

circular motion of the solar vortex. Finally taking the argument from

effects, the rotating bucket experiment, we have it that because they

partake in the circular motion of the solar vortex they should have an

endeavour to recede from the axis of rotation. Thus Descartes is wrong in

asserting that the Earth is at rest and thus his theory of true motion is

false (Rynasiewicx 2012a).

Next Newton turns to the epistemological element of his theory. The

question here is what can we know about absolute motions given that we

cannot directly observe them as we are not in absolute rest and so are

unable to judge the absoluteness of the motions we observe? For starters

we can observe relative motions which are the differences between

absolute motions. We also have evidence of forces which are the causes

and effects of absolute motions. It is on this point that Newton invokes

his famous two globes experiment. In this experiment he entreats us to

imagine two globes in a remote area of space with nothing else to serve

as a reference point. These two globes are connected by a cord and they

are engaged in circular rotation. Even without reference points we can

determine the quantity of the rotation by the tension in the cord created

by the centrifugal endeavours of the respective globes. Also, by applying

a force to this side or that side of the globe, we are able to determine

whether the globes are rotating clockwise or counter clockwise by the

presence of increased or decreased tension in the cords. Building on this

example, Newton asks us to imagine a further two bodies being added to

the equation. These bodies are remote from the globes as the stars are

from us. Now we have the problem of determining which of the systems

of bodies is rotating. We can determine this, Newton tells us, by the

tension in the cord. Then knowing that it is the globes that are in motion

we are able to determine in another manner whether the globes are

rotating clockwise or counter clockwise. This is the two globes

experiment (Rynasiewicx 2012b).

These then are the arguments which Newton invokes in favour of his

understanding of motion. As I have shown these arguments are best

understood as a reaction to the Cartesian background. We also see that

he has incorporated the relativity principle of Galileo into his

understanding. What I’ve tried to show in the course of this essay is what

exactly Newton is talking about when he is dealing with motion. We have

also looked at the background to this understanding and how this

background informed Newton’s understanding. Finally we have seen

what arguments Newton used to support his understanding.

In conclusion Newton’s definition of motion is best understood in

contrast to Descartes. He was not a random occurrence in history but his

work was built on the shoulders of the tradition of natural philosophy.

Bibliography

Barbour, J.B. 2001. The Discovery of Dynamics (Oxford University

Press, 2001), sections 8.5, 8.6, 8.7, 8.8, 11.3 and 12.5

Huggett, N. and Hoefer, C. 2009. ‘Absolute and Relational Theories

of Space and Motion’, The Stanford Encyclopedia of

Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL =

<http://plato.stanford.edu/archives/fall2009/entries/spacetime-

theories/>.

Rynasiewicx, R. 2012a. 'Newton's Views on Space, Time and

Motion', The Stanford Encyclopedia of Philosophy,

<http://plato.stanford.edu/entries/newton-stm/>

Rynasiewicx, R. 2012b. 'Newton's Views on Space, Time and

Motion', The Stanford Encyclopedia of Philosophy, <including the

text of the Scholium,

http://plato.stanford.edu/entries/newton-stm/scholium.html>