Motion Mountain - The Adventure of Physics

Can motion be described in a manner common to all observers?. – " Πλεῖν ἀνάγκε, ζῆν οὐκ ἀνάγκη.* Pompeius " A over the Earth – even in Australia – people observe that stones fall 'down'. is ncient observation led to the discovery of the universal 'law' of gravity. To nd it, ll that was necessary was to look for a description of gravity that was valid globally. e only additional observation that needs to be recognized in order to deduce the result a = GMr is the variation of gravity with height. In short, thinking globally helps us to make our description of motion more precise. How can we describe motion as globally as possible? It turns out that there are six approaches to this question, each of which will be helpful on our way to the top of Motion Mountain. We will start with an overview, and then explore the details of each approach. — e rst global approach to motion arises from a limitation of what we have learned so far. When we predict the motion of a particle from its current acceleration, we are using the most local description of motion possible. For example, whenever we use an evolution equation we use the acceleration of a particle at a certain place and time to determine its position and motion just aer that moment and in the immediate neighbourhood of that place. Evolution equations thus have a mental 'horizon' of radius zero. e opposite approach is illustrated in the famous problem of Figure. e challenge is to nd the path that allows the fastest possible gliding motion from a high point to a distant low point. To solve this we need to consider the motion as a whole, Challenge 343 d for all times and positions. e global approach required by questions such as this one will lead us to a description of motion which is simple, precise and fascinating: the so-called principle of cosmic laziness, also known as the principle of least action. — e second global approach to motion emerges when we compare the various descriptions of the same system produced by dierent observers. For example, the observations by somebody falling from a cli, a passenger in a roller coaster, and an observer * Navigare necesse, vivere non necesse. 'To navigate is necessary, to live is not. ' Gnaeus Pompeius Magnus (–), as cited by Plutarchus …