See Question 1.2 with its relevant text

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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.)