The Physical Worldornament
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The Restless universe
Introduction to The restless Universe

1 The lawful Universe

2 The clockwork Universe

3 The irreversible Universe

4 The intangible Universe

5 The uncertain Universe

6 Closing items


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

Answer and comments

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Question 1.2
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.

This question is unusually open-ended, with no single correct answer. In preparing our answer we have taken the opportunity to expand the discussion slightly, but would not expect you to include all the points listed below. There are several reasons why it would be impossible, in practice, to follow through the Newtonian programme of predicting the entire future of the Universe.

(i) We would need to know the positions and velocities of all the particles in the Universe at a given instant. Nowadays we know that the Universe contains an immense number of fundamental particles. The visible Universe contains about 1080 protons and the same number of electrons. Measuring the positions and velocities of such a large number of particles is an unimaginable task. (Indeed, there may be some regions of the Universe that are so remote that we cannot yet know of their existence because the Universe is too young for light from them to have reached us!)

(ii) In order to predict the exact future of the Universe, we would need to know the exact initial positions and velocities of all the particles. Small errors in measurement may, at first, produce only small errors in prediction, but the errors are cumulative and will eventually become serious. (Nowadays we know that some simple systems are extremely sensitive to the initial conditions. In some cases, it is impossible to measure the initial conditions accurately enough to make anything more than a very short-term prediction. Such systems are said to be chaotic. They will be discussed more fully in Predicting motion, book 3.)

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(iii) We need to know all the forces acting between particles. Newton only produced an explicit formula for gravitational forces. His work was later extended to cover electromagnetic forces, but our understanding of the interactions between particles remains partial and a complete understanding elusive.

(iv) Even if we had all the information necessary, the calculations would be far too difficult to carry out. No computer could ever attempt an exact solution. And even if the calculations could be done, there would be nowhere to store all the results. Answers and comments For all these reasons, we cannot hope to predict the exact future of the Universe. That would be too much to expect. The great successes of physics emerge when we ask specific questions about systems that are simple, or can be thought of as being simple, so that the mathematical analysis remains feasible for humans and their computers.

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