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Galileo and the Birth of Experimental Physics
From: Cambridge University Press
| By:
Prabhakar Gondhalekar |
EDITOR'S INTRODUCTION |
 Most people know of Galileo as the Renaissance astronomer who encountered the wrath of the Vatican for making credible the idea that the earth moves around the sun, and not vice versa. However, Galileo's greatest contribution to humankind was the establishment of mechanics as a science; it was he who first clearly grasped the notion of force as a mechanical agent, maintains physicist Prabhakar Gondhalekar. In this extract from his book The Grip of Gravity (available through Fathom), Gondhalekar outlines Galileo's discoveries, and points to their effects which remain with us to this day. |
 alileo Galilei (1564-1642 AD) created the modern idea of experiment. He was also the first man to realise that mathematics and physics, previously kept in separate compartments, should join forces. He, more than any other natural philosopher of the seventeenth century, was responsible for replacing Aristotle's logico-speculative approach with mathematical rationalism; he emphasised this in his insistence that the "Book of Nature... is written in mathematical characters". His long life was blessed by unparalleled intellectual activity and blighted by ignorance and intolerance. Galileo was born in Pisa on 15 February 1564. His early education was at a monastery near Florence, where his family had moved. In 1581 AD, at the age of 17, young Galileo went to the University of Pisa to study medicine, but he soon tired of the doctrinal texts of Aristotle and other Greek works. During his stay at Pisa he overheard a lecture on geometry being given to the pages of the Tuscan court, which so fired his interest in mathematics and physics that he started taking lessons in these subjects. While praying at the cathedral in Pisa he is supposed to have noticed the swinging chandelier and noted that the lamp always required the same amount of time to complete an oscillation, no matter how large the range of the swing. Later in life he was to conduct experiments which established that the period of oscillation of a pendulum of a fixed length is independent of the amplitude, the weight and the nature of the suspended body. This suggested to him that the pendulum could be applied to regulate clocks. |
Poverty and talent
In 1585 Galileo left the University of Pisa without taking a degree because his family could no longer afford the university fee. He left with a reputation for extraordinary talent in mathematics and also a reputation for being both an independent spirit and an iconoclast. Galileo returned to Florence to teach at the Florentine Academy. There his thesis on the hydrostatic balance, published a year later, made his name known throughout Italy. Around this time he also began to reflect on the nature of measurement and its vital role in science. Galileo regarded demonstration unsupported by experience to be 'the world on paper' while actual measurements were 'the real world'. An essay on the centre of gravity of solids, published in 1589, won for him the honourable but not so remunerative post of lecturer in mathematics at the University of Pisa. Here he started investigation of accelerated motion. He was to show through experiments that a number of Aristotle's conclusions, which for 2000 years had been held to be authoritative, were actually false. He conducted experiments with balls rolled down an inclined plane, effectively 'slowing down the free fall of bodies' so that the fall could be timed. Through his experiments he arrived at a clear understanding of acceleration as well as of the concept of inertia. At Pisa, Galileo laid the foundation of the science of kinematics (a branch of mechanics that deals with the description of motion of bodies). He (and others) attempted to formulate an explanation of the cause of motion (the science of dynamics) but this was not successful; the task was to be left to Newton. Tradition has it that he disproved the Aristotelian doctrine of motion, that the speed of falling bodies is proportional to their weight, by dropping two different objects simultaneously from the Leaning Tower of Pisa. Sadly, there is no evidence that this experiment was actually performed. Galileo has not mentioned it in his well-kept notes and there is no record of this experiment in the archives of the University. This 'Tower of Pisa experiment' was, however, performed in 1993 by members of a European collaboration considering a satellite experiment to test the theory of free fall. At Pisa Galileo wrote a thesis, De motu, which was an improvement on the contemporary discussion of motion. Using more mathematics than was customary in dealing with motion, he refuted many 'received' opinions. He refuted the Aristotelian notion that the medium collaborated in the motion of a body moving through it. He also asserted that the vertical motion of a body, up or down, could be described by weight alone. However, he retained the concepts of 'lightness', 'heaviness' and the proximate cause. Because the conclusions reached in De motu had not been established by experiments, Galileo felt that the arguments advanced were not sufficiently convincing to be published. But by contradicting Aristotle he had managed to offend professors of philosophy and it was unlikely that his contract at the University would have been extended. |
In 1592 Galileo was appointed Professor of Mathematics at the prestigious University of Padua. Galileo was 28 and he was to spend the next 18 years at Padua completing the bulk of his work on mechanics. Here he proved theoretically (around 1604) that falling bodies obey the law of uniformly accelerated motion (that is, motion in which the speed of a body increases or decreases uniformly in time). He also formulated the law of parabolic fall. He was to write later, in his Dialogues Concerning Two New Sciences ( 1638):
It has been observed that missiles and projectiles describe a curved path of some sort; however, no one has pointed out the fact that this path is a parabola.
He had deduced that the motion of a projectile was the consequence of simultaneous and independent inertial motion in the horizontal direction and falling motion in the vertical direction. |
Aristotle and motion
Galileo gives a full exposition of his experimental and theoretic work on motion in the Two New Sciences, completed in 1634. He wrote that 'there is, in nature, perhaps nothing older than motion' about which 'books written by philosophers are neither few nor small'. But most of these writings were qualitative and even speculative. In the Two New Sciences Galileo proposes that any science of motion should be mathematical and experimental. Galileo was to write that he had 'discovered by experiment some properties...'. The book is divided into four parts or days, the first two days dealing with the strength of materials and nature and properties of fluids, the third dealing with motion and the fourth with projectiles. The third day is divided into two parts; the first part deals with uniform motion and the second with naturally accelerated motion. Galileo retained the rather handy distinction, made by Aristotle, between natural and forced motion. Natural motion was motion in a vertical line near the surface of the Earth, that is free fall. This distinction has now been eliminated by reducing natural motion to motion under 'the force of gravity'. In the Two New Sciences Galileo defines uniform motion as follows:
By steady or uniform motion, I mean one in which the distances traversed by a moving body during any equal interval of time, are themselves equal.
(Quoted from Great Experiments in Physics, ed. M. H. Shamos, 1959.)
Galileo is being very precise by inserting the word 'any'--the distances must be equal for all equal intervals of time and not equal in an average sense over the total distance. From this definition Galileo derives a number of axioms before defining velocity as v = s/t (in modern notation), where s is the distance traversed in time t. Galileo then proceeds to investigate motion of accelerated bodies. He defines uniformly accelerated motion as when
A body acquires equal increments of speed during any equal intervals of time
(quoted from Great Experiments in Physics, ed. M. H. Shamos, 1959.)
This is equivalent to  , a formula taught in the introductory course in physics. It is worth noting that this was an intuitive leap by Galileo: he had defined uniformly accelerated motion without any experimental evidence. He then proceeded to 'prove' this definition deducing mathematically the consequences of such motion. He showed that for uniformly accelerated motion the distance traversed increases as the square of the elapsed time ( ), and the velocity acquired in free fall from different heights is proportional to the square root of the height ( ). He goes on to give logical arguments to prove continuity of motion, which was not at all obvious at the time. |
He applied his formulae to motion down an inclined plane and showed that in the absence of all resistance or opposition the speed acquired by any body moving down planes of different inclination is equal when the height of these planes is equal. That is, a heavy (to reduce the resistance of air) and perfectly round ball descending along the lines AB, AC, and AD (Figure 1) would reach the terminal points B, C and D with equal speed. He also asserts that a body descending a plane will acquire 'momentum' (this should really be energy) sufficient to carry the body back to the same height. That is, a ball descending from point A along the line AD will be carried to the point A' that is at the same height as A. Galileo is careful to point out that there is a discontinuity at the point where the planes meet (i.e. D) and that this will present an obstacle to the descending ball. But he proves his assertion by a pendulum experiment, as shown in Figure 2. If the bob is pulled to position C and released it will descend along the arc CB to reach the lowest point B and then continue along the arc BA to reach point A where the vertical distance CB will equal AB. Galileo was careful to stress the difference between motion along a curved path and motion along a straight path. The principle of conservation of energy (kinetic plus potential) is implicit in these experiments, but it was some time before this was realised. |
Starting with this simple experiment Galileo made the great intellectual leap and proposed the concept of inertia. He argued that if the height of the point A' (Figure 1) was reduced then a ball rolling down the inclined plane AD would travel further and further as the height of the second plane is reduced. When the plane was horizontal the ball would continue to roll indefinitely unless stopped by any other means like friction or an opposing force. (But Galileo got it slightly wrong: he thought that the indefinite motion would be circular, round the Earth. This was because a circle is a perfect Platonic figure. Galileo's inertia was circular. Fortunately the difference between a straight line and a curve was too small in Galileo's experiments to affect his analysis. Galileo's classical education clearly had influenced his thinking.) The principle of inertia is encapsulated here--a body will continue in its state of rest or motion in the absence of application of an altering force. |
Conclusion
Galileo thus showed that force was not necessary for motion, but only necessary to bring about a change in motion. Galileo had also demonstrated that no proximate cause was necessary for motion. At a stroke he had demolished the Aristotelian notions of motion and causes of motion. Aristotelian doctrine maintained that a body would move as long as an agent moved it. Galileo insisted that motion is preserved and requires no agent. A body set in motion on a perfectly smooth horizontal surface will continue to move forever if the surface has no limit. In the Two New Sciences Galileo created the new science of mechanics, in which the concept of motion is radically different from the concept that had prevailed for the previous 20 centuries. The new concept of motion that he proposed is substantially our current conception. |
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