Lectures on Dynamics and Relativity - David Tong

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Classical mechanics is an ambitious theory. Its purpose is to predict the future and reconstruct the past, to determine the history of every particle in the Universe. The theory of classical mechanics was formulated by Newton in 1687, building on earlier insights of Galileo. Starting from a few simple axioms, Newton constructed a mathematical framework which is powerful enough to explain a broad range of phenomena, from the orbits of the planets, to the motion of the tides, to the scattering of elementary particles. Before it can be applied to any specific problem, the framework needs just a single input: a force. With this in place, it is merely a matter of turning a mathematical handle to reveal what happens next. We start this course by exploring the framework of Newtonian mechanics, understanding the axioms and what they have to tell us about the way the Universe works.

We then move on to look at a number of forces that are at play in the world. Nature is kind and the list is surprisingly short. Moreover, many of forces that arise have special properties, from which we will see new concepts emerging such as energy and conservation principles. Finally, for each of these forces, we turn the mathematical handle. We turn this handle many many times. In doing so, we will see how classical mechanics is able to explain large swathes of what we see around us. Despite its wild success, Newtonian mechanics is not the last word in theoretical physics. It struggles in extremes: the realm of the very small, the very heavy or the very fast. We finish these lectures with an introduction to special relativity, the theory which replaces Newtonian mechanics when the speed of particles is comparable to the speed of light. We will see how our common sense ideas of space and time are replaced by something more intricate and more beautiful, with surprising consequences. Time goes slow for those on the move; lengths get smaller; mass is merely another form of energy.

Ultimately, the framework of classical mechanics falls short of its ambitious goal to tell the story of every particle in the Universe. Yet it provides the basis for all that follows. Some of the Newtonian ideas do not survive to later, more sophisticated, theories of physics. Even the seemingly primary idea of force will fall by the wayside. Instead other concepts that we will meet along the way, most notably energy, step to the fore. But all subsequent theories are built on the Newtonian foundation. Moreover, developments in the past 300 years have confirmed what is perhaps the most important legacy of Newton: the laws of Nature are written in the language of mathematics. In this course, we take the first steps towards understanding these laws.