- Education and Science
Newtons Laws of Motion; Space and Time.
How does Newton define motion and what arguments does he use to support it?
Newton's theory of space, time and motion is founded primarily in his text Philosophae Naturalis Principia Mathematica. In common life, space, time, and motion are understood in terms of relative bodies yet Newton believed there to be a true and mathematical state of these beyond their relativity contraty to what Descartes had argued in some of his work. Within much of Newton's work he attempts to criticise the Cartesian views of kinetics and dynamics which he believed to be the main contending opinion. At the time of Newton there came to fruituion many changes which had been gradually developing. The contending of Aristotelian views and the use of experierimental evidence to support theories meant that a lot of perviously held beliefs were being brought into question. Newton was working in a time in which there were more open contending opinons than there had been before and in which evidence was beginning to suggest that those beliefs held perviously were incorrect and unreliable. There seemed to be a call for a formulation of a theory which encapsulated both new findings and to some degree intuition. New theories needed in particular to appease the church’s understandings of the universe and so God had to fit into any theories of the time.
Central to Newtons theory of kinematic and dynamics are absolute space and absolute time which are distinct from relative space and relative time. Our means of measuring space and time though are unreliable as we are only able to observe and measure the relative while absolute space and time remain unobservable though constant. Absolute Space is distinct from body and exists whether there are bodies or not, others such as Leibniz and Descartes would claim that Space does not exists without bodies. For Newton though absolute space is similar and immoveable while relative space is the relation of bodies with one another and is therefore most likely in motion. Absolute time, Newton would claim, passes uniformally without regard to any happenings in the external, physical universe. Any measure of time is therefore unreliable as it uses relational information observable through changes in the universe, this though is not a representation of absolute, true time. Both absolute space and absolute time, although not genuine substances, are real entities with their own manner of existence which is necessitated by God's existence (omnipresence and eternality).
It is with these definition of absolute space and time that Newton forms his notion of true motion which he defines as a body's motion through absolute space. Place is defined as the space occupied by a body and can be absolute or relative based on whether the space is absolute or relative. These parts of absolute space do not change in relation to one another as the parts of space are their own places and so for a place to be moved out of itself is surely an absured impossibility. Absolute motion uses this definition of place as absolute motion is the movement of a body between absolute places while relative motion is the movement of a body between relative places. According to Newton, there is a true fact as to whether a given body is in motion and which its true qauntity of motion is; the true motion of a body does not require the motion of relational bodies in order to define it. Newtons notion of true motion requires only reference to absolute place and absolute space, nothing relational. It is Newtons aim to make the existence to absolute space the most feasible theory. Those who rejected absolute space believed that true motion could be analyised by their relative motions and the causes of these relative motions. This though is difficult because when taken in a relational sense it is difficult to tell which bodies are in motion and which are not or if perhaps all other bodies are in sequential motion thus making them seem at rest relative to the body in question etc. The most well known aspect of Newtons theory today are his three laws of motion:
If a body is not compelled by forces to change its state of motion it will persist in a state of uniform motion
If a force acts on a body then this body is accelerated in the same direction as the force and the magnitude of the acceleration is given by F= ma where m is the mass of the body which is an invariable quantity
If a body A exerts a force on body B, then B exerts a force on body A in the opposite direction and the same magnitue.
Newton's first law of motion is the same as Descartes law of inertia and was greatly influenced by Galileo's notion of inertia. The main essence of these laws is that of force and how it quantifies the way bodies deviate from their uniform rectilinear motion determining their acceleration. Newton also offers laws of force, particularly that of gravitation. Gravity according to Newton acts instantaneously at a distance and it is through the theory of gravitation that Newton was able to produce quantitive details of planetary motions as well as the means to describe falling objects and other such terrestrial phenomena. From the first two laws of motion follows Kepler's second law of planetry motions which has empirical content. With both the laws of motion and the laws of force it is theoretically possible to calculate all motions given the initial conditions. If Newton's laws are to be taken as true then it would be impossible to distinguish absolute uniform motion in a straight line, or one absolute position from another, or one absolute direction from another, or one absolute time from another.
Newtons work was set in a time when Aristotelian beliefs were still common. The Aristotelian view of the universe was that it is finite and bounded by the outermost fixed stars. For Aristotle, time itself was merely a measurement of motion and qualitative change and so uniform time could be defined by the uniform rate of the motion of the fixed stars. Motion itself was concieved by Aristotle to be the actualisation of potentialiality but this idea was thought be to meaningless by the 17th Century when Newton was theorising. The idea of motion was simple and had few problems within the Aristotelian geocentric universe in which elementary substances move towards or away from the centre. The universe itself consists of celestial spheres made of aether which is disposed to circular motion around the earth (centre of the universe). These celestial spheres must move uniformally if they are to be taken as the measurement of time. However, by the time Newton began his work on space/time/motion it was clear that the simplicity of Aristotelian ideas were not accurate enough as the motion of celestial spheres was not so uniformal or simplicitic as they had previously been understood to be. This was perhaps due to the lack of evidencial testing around the time of Aristotle and so his views of space, time and motion were purely conceptions which lacked evidence.
Aristotle's idea's that motion in the universe was simplistic to describe and that the stars could be used to define and determine time and position had been held for around 2000 years. However, by the 17th century evidence and discoveries were being made which contended Aristotle and thus made an updated theory of the nature of the universe a primary concern among many. There were many discoveries and new idea's founded in the 16th and 17th Century such as Copernicus' helio-static system, and Galileo's telescopic observations. Such things raised doubts about the long standing beilefs held regarding time, space and motion. Copernisus' system led to a feasible understanding of the universe without the earth at the centre and thus raised doubts about Aristotelian terrestrial physics, though not the rest of his framework as Copernicus worked within Aritstotelian notion of the universe. Galileo's observations of the surface of the moon and the moons orbiting around Jupiter meant the defined distinction between terrestrial and celestial became unclear. And the ability to see more stars further out made the idea of an infinite universe with no outermost boundary of fixed stars more plausible. Galileo's improvements upon the telescope also did much to undermine the Ptolemanic, geo-centric universe and instead seemed to favour the Copernican helio-centric system. Thus, Copernicus' theory was endowed with evidence in its favour. Galileo's interest in kinematics also led to the discovery that in natural free-fall objects accelerate towards the earth at an equal and constant rate; natural accelerated motion. It was Newton who stated the quantititve laws of motion, mechanics and gravitation which were influenced by Galileo's discoveries. Galileo's inertia was also improved up by Newton, Descartes and Huygens.
The concept of inertial motion was an issue of the time of the 17th century. There was a gradual evolution from Aristotlelian notion that each body had its own state of natural motion through to Newton's new definition of natural motion in which the universal motion of bodies was uniform straight line or rest. Thus, the 16th and 17th centuries seem to have been a time of change in the understanding of the movement of the universe. Galieo's discoveries were of particular importance as he was first in discovering the importance of the natural persistence of motion. Galileo used the idea that ones state of uniform motion is undetectible in principle in order to argue against Aristotelian opponents who maintained that if the earth moved we would notice. He attempted to prove this by his discussion of motion on a ship. If one were to jump forward while on a stationary ship and were to jump the same while on a moving ship we would expect them to land in a different place and to have travelled a different distance on the ships floor while jumping in each case. However, this does not happen. It seems the person jumping within the ship is subject to the relational movement of the ship rather than to the movement of the land/earth, or any other 'stationary' body/force. Thus it seems that uniform motion is undetectable: the principle of relativity. This is our first example of a dynamical symmetry in which the laws of physics cannot tell between the two different situations.
The symmetry evident in Galileo's ship is beneficial for Newton as his theory does not refute the possibility of such symmerty as he does not include the notion of absolute velocity in his laws. The issue of how to accurately measure time was also significant in the 17th century if for no other reason than how it could aid navigation and thus military and economic superiority. Astronomy commonly had to account for the inequalities in standard time which can vary by 20 minutes a year so the difference between absolute and relative time seemed to already be used in practice. Huygens' pendulum clock and the eclipses of the moons of Jupiter based on Kepler's period law where both mentioned by Newton as relatively accurate means of meauring uniform time. An equation for absolute, true time though was thought to be necessary by the like of Newton because motion can be subject to external forces and so can be subject to retardation and acceleration in a way that time cannot. Newton believed that absolute time would be unaffected by these influences and would remain always constant despite external motions.
Charleton and his revival of Atomism seems also to have been a great influence on Newton's work. Charleton claimed time and space are real entities and that time “flows on eternally in the same calm and equal tenor”. Motion though can be subject to “accerleration, retartation, or suspension” thus motion must surely be inadequate for meauring time; time is distinct from any measure of it. Space itself is 'absolutely immovable and the bodies within it share those parts of space which they occupy. Space existed before any bodies within it; God created Space first and is present within it. Motion for Charleton is the movement of a body from one place (part of immovable space) to another place. Newton and Charleton thus share their views on time, yet not on empty space. The terms relative time/space/place are not dealt with by Charleton and so he fails to challenge the differences between absolute motion and relative motion which Newton pays particular attention to. Alongside the influence of Charleton there was the influence of Descartes. The Cartesian theory was of great significance to Newton in that he focused much attention on refuting it's plausibility. Descartes disagreed with atomists as he claimed that bodies have only extension, not quantities, and so body and extension are one and the same. He argued that the universe is infintie and that space is only the relational characteristics of bodies and so it does not exist beyond the bodies within it. Motion for Descartes is 'the translation of one part of matter, or one body, from the vicinity of those bodies, which are immediately contiguous to it and are viewed as it at rest to the vicinity of others'. Thus, each body has its own proper motion as well as the additional relative motions which are caused by surrounding bodies. He also believed that a body in circular motion has an endeavour to recede from the centre of rotation. Together with Descartes idea that a body participates in the motion of a body of which it is a part it seems as though Descartes idea of proper motion does not fit well with his system of the world. When describing motion of a body the rest of the matter within the universe does not remain rigid so a given body can be said to move in several different ways with respect to these other bodies. Descartes in fact introduces the notion of 'true and philosophical' motion which is motion relative to the surface immediately contiguous to that body. The introduction of this idea seems only to aid Descartes in claiming that although the earth moves with respect to the sun it is transported by the immediately surrounding cosmic fluid so that 'truly and philosophically' the Earth does not move. Newton claimed that Descartes doctrine is actually self-refuting and that Descartes had used the idea of space independent of body when it was beneficial for him to do so. One issue with Newtons characterisation of the Cartesian theory as self-refuting is that Descartes theory changed much between publications. This change seems to have been primarily in response to the inquisition of the church made especially evident in the case of Galileo and his persecution. It seems that Descartes feared his initially proposed work would clash with the church's views and so he withdrew from publishing it. The work which he did eventually produce thus failed to coincide with his previous publication and this could be the reason for the self-refuting information in Descartes' work as a whole. Newton had many critics at the time such as Leibniz, Berkly, Descartes, and Huygens. In terms of motion these critics all believed that in order to understand true motion one had to account for the motion relative to other bodies, although it alone was not a sufficient condition. Newtons critics were often percieved as denying the notion of true motion and instead believing all motion to be relational yet it was understood by all, Newton and critics alike, that true motion is distinct from relative motion.
It is commonly misunderstood that Newton is attempting to disprove the thesis that all motion is merely relative motion. Carterian and Aristotelian philosophy assumes that bodies have their own unique state of true motion and rest. Newton however questions whether it it possible to take true motion as a special instance of relative motion with respect to other bodies around it. Newton proposes arguments from properties, cause, and effect to make his point that true motion is distinct from relative motion. Argument 1 from properties claims that it is impossible to define a body as truly at rest when it is taken in terms of its position relative to other bodies in the local vicinity. When meaured like this one cannot know if this body is at rest with respect to a fixed body at rest in further space or not, it could be that it merely seems at rest relative to the motions of the relational, surrounding bodies. Knowing the local configurartion of bodies is not enough for a body to be determined to be at absolute rest. Argument 2 from properties claims that true and absolute motion cannot be taken as relative to the immediately surrounding body. If a given body is surrouded by bodies moving (simulataneously, together at the same rate) while it is seemingly not then the given body is at relative rest to the surrouding bodies. Accoring to the Cartesian definition of motion though the true motion of the given body would be in accordance with the surrouding bodies and so if the surrouding bodies were at rest then the surrouded body would be truly at rest which as illogical. The third argument from properties works from the property that if a part of a body maintains a fixed position with respect to the body as a whole, then it participate in the motion of the whole body. Newton concludes that true motion can only be found by relation to a stationary place. A body within a place which is itself in motion must account for the motion of the place and so on until a stationary reference is found. These stationary places must be fixed in position for eternity; these are what Newton called immobile absolute space. The argument from causes states that true motion of a body cannot be defined as any instance of its motion relative to other bodies. The application of net force on a body is not enough to generate motion relative to other bodies; the same net force could have been applied to the relative bodies or a net force could have been applied to all relative bodies but not the body in question and so it appears to be the body put into motion. The argument from effects uses the bucket experiement in order to estabilish the point that true rotational motion cannot be defined as relative rotation with respect to the surrouding bodies. Newton uses the bucket experiment to show that cetrifugal endeavor (force of receding from the axis of rotational motion) is not necessary or sufficient for the existence of relative circular motion with respect to its surroundings. The Bucket Experiment:
Given a bucket filled with water and suspended by rope, if one were to rotate the bucket when these effects would be observed. Initially the water surface would remain flat while the bucket rotated and so the water's motion is relational to the bucket as they are not uniform with one another. As the water begins to acquire the motion of the bucket the surface of the water becomes concave until the motion of the water and the motion of the bucket are not longer relational with one another. Once the bucket stops spinning and the water continues to move and remains concave then the motions are relational again. Thus, the shape of the surface of the water and the waters motion is not determined by the spin of the water relative to the bucket. The centripetal force which is acting upon the water tells us that the water is in absolute motion.
It is wrongly believed, and criticised on the basis of this beleif, that this experiment aimed to prove the existence of absolute space. The rotating bucket experiement though was used only to show that Descartes' idea's of motion were inaccurate. It is designed to show that in order to meaure motion accurately one must make reference to absolute space not merely relative bodies. Newton further used the globes experiment as evidence that although we cannot observe absolute space/time/motion we are able to observe aspects of them indirectly. We are in theory able to infer the quantity of absolute motion from cases similar to the globes experiment. The Globes Experiment:
Given two identical globes rotating about their centre of mass joined together by a cord. The tension in the cord can be used to observe the rate of rotation of the globes. Non-zero tension in the cord indicates rotation of the spheres whether this rotation is observable or not.
Newton does not claim that either of these experiments proves his theory, he only claims that they refute Descartes and so in terms of choosing between his own system and the Cartersian system it is beneficial to him. The experiments only work as support for his own theory when working from the basis of an pre-existent assumption of absolute space. It is through the combination of the laws of motion and the laws of force that Newton was able to claim indirect observation of absolute space and time through motion. One has to rely upon and assume these Newtonian mechanics initally though in order to see the support they offer.
In conclusion, it seems as though Newton's defintion of motion is grounded in a time in which the culminating changes and new evidence were beginning to take effect on the new theories being produced. The achievements of Newton's work led to the adopting of Newtonian physics above Cartersian and Leibnizian, particuarlly in the 19th century. Newton made use of the best prevailing concepts of the time and added his own views of time and motion in order to arive at his 3 fundamental principles which were held in such stature that they were accorded the title of 'laws' of science and became the new basis of time and motion in science. Newtonian ideas have since been again improved upon and supersceded, by Einstein in particular at the moment. However, some of what Newton claimed in terms of motion have remained within Einstein's theories and thus remain today. Newton and his influence within the sciences though remains a great makered point in history.