2 The clockwork Universe

2.1 Mechanics and determinism 1/4

2.1 Mechanics and determinism 2/4

2.1 Mechanics and determinism 3/4

» 2.1 Mechanics and determinism 4/4

2.2 Energy and conservation 1/2

2.2 Energy and conservation 2/2

3 The irreversible Universe

4 The intangible Universe

5 The uncertain Universe

6 Closing items

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Other titles in the Physical World series

Describing motion

Predicting motion

Classical physics of matter

Static fields and potentials

Dynamic fields and waves

Quantum physics: an introduction

Quantum physics of matter

2.1 Mechanics and determinism

Part 1 of 4 | Part 2 | Part 3 | Part 4

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In keeping with his grand vision, Newton proposed just one law for gravity - a law that worked for every scrap of matter in the Universe, for moons and planets as well as for apples and the Earth. By combining this law with his general laws of motion, Newton was able to demonstrate mathematically that a single planet would move around the Sun in an elliptical orbit, just as Kepler claimed each of the planets did. Moreover, thanks to the understanding that gravity was the cause of planetary motion, Newtonian physics was able to predict that gravitational attractions between the planets would cause small departures from the purely elliptical motion that Kepler had described. In this way, Newton was able to explain Kepler's results and to go beyond them.

In the hands of Newton's successors, notably the French scientist Pierre Simon Laplace (1749-1827), Newtonís discoveries became the basis for a detailed and comprehensive study of mechanics (the study of force and motion). The upshot of all this was a mechanical world-view that regarded the Universe as something that unfolded according to mathematical laws with all the precision and inevitability of a well-made clock. The detailed character of the Newtonian laws was such that once this majestic clockwork had been set in motion, its future development was, in principle, entirely predictable. This property of Newtonian mechanics is called determinism. It had an enormously important implication. Given an accurate description of the character, position and velocity of every particle in the Universe at some particular moment (i.e. the initial condition of the Universe), and an understanding of the forces that operated between those particles, the subsequent development of the Universe could be predicted with as much accuracy as desired.

Figure 1.10 An orrery (a mechanical model of the Solar System) can be taken as a metaphor for the clockwork Universe of Newtonian mechanics. Click here for larger image (12.84kb)

Needless to say, obtaining a completely detailed description of the entire Universe at any one time was not a realistic undertaking, nor was solving all the equations required to predict its future course. But that wasn't the point. It was enough that the future was ordained. If you accepted the proposition that humans were entirely physical systems, composed of particles of matter obeying physical laws of motion,

then in principle, every future human action would be already determined by the past. For some this was the ultimate indication of God: where there was a design there must be a Designer, where there was a clock there must have been a Clockmaker. For others it was just the opposite, a denial of the doctrine of free will which asserts that human beings are free to determine their own actions. Even for those without religious convictions, the notion that our every thought and action was pre-determined in principle, even if unpredictable in practice, made the Newtonian Universe seem strangely discordant with our everyday experience of the vagaries of human life.

Question 1.2 Answer
In principle, according to Newtonian mechanics, it is possible to predict the entire future behaviour of the Universe provided the initial positions and velocities of all the particles in it are known, and the laws describing their interactions are known. List at least two reasons why this goal is, in practice, beyond our reach.
Continue on to 2.2 Energy and conservation, part 1 of 2

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