By Jennifer Coopersmith
Energy is the go of things, the driver of engines, devices and all physical processes. It can come in various forms (electrical, chemical, rest mass, curvature of spacetime, light, heat and so on) and change between these forms, but the total is always conserved. Newton missed energy and it was Leibniz who discovered kinetic energy (he called it vis viva). The idea was promoted on the continent, chiefly by one family, the Swiss family of feuding mathematicians, the Bernoullis, in the first half of the 18th century. The more subtle concept, potential energy, slipped in over a hundred years, uninvited, like the 13th fairy at the party.
In Feynman’s profound allegory (‘Dennis the Menace’ playing with blocks), energy is defined by its property of being conserved. But, this doesn’t answer to all our intuitions about energy. Why does it change smoothly between its various forms? For example, when a child swings on a swing, her kinetic energy decreases as the swing climbs (and gains gravitational potential energy) and then, as the swing descends, she goes faster and faster.
A different approach holds the answer. Consider the walk to the shops. You could take the shortest route or you could optimize other aspects, e.g. take a longer route but less hilly, or more shady or with the least number of road-crossings. Nature also works in this optimizing way: it tries to minimize the total ‘action’ between a starting place and a final destination. ‘Action’ is defined as ‘energy’ times ‘time’, and, in order to minimize action, the energy must be able to change in a prescribed way, smoothly and continuously, between its two forms, kinetic and potential energy, (The Principle of Least Action was discovered by an eccentric Frenchman, Pierre-Louis Moreau de Maupertuis, while head of the Berlin Academy of Science, in the mid 18th century.)
What are kinetic and potential energy? Kinetic energy is the energy of motion of an individual body whereas potential energy is the energy of interaction of parts within a system. Potential energy must be specified for each new scenario, but kinetic energy comes in one essential form and is more fundamental in this sense. However, as potential energy relates to internal aspects (of a system), it doesn’t usually change for differently moving ‘observers’. For example, the game of billiards in the lounge of the ocean liner continues unaffected, whether that liner is coasting smoothly at 30 kph or whether it’s moored to a buoy. The kinetic energy of the liner is vastly different in the two cases.
But sometimes potential energy and even mass do change from one ‘reference frame’ to another. The more fundamental quantity is the ‘least action’, as this stays the same, whatever the (valid) ‘observer’.
Heat energy is the sum of the individual microscopic kinetic energies. But the heat energy and the kinetic energy of an everyday object are very different (e.g. the kinetic energy of a kicked football and the heat energy of a football left to warm in the sun). In fact, for the early 19th century natural philosophers, considering heat as a form of energy was like committing a category error. The slow bridging of this error by people like Daniel Bernoulli, Count Rumford, Robert Julius Mayer and James Joule makes a very interesting tale.
With regards to the looming energy crisis and global warming, here are the things we must remember:
1. Nature always counts the true cost, even if we don’t
2. There is no such thing as safe energy – it is energetic, after all
3. As the sink of all our activities becomes warmer, so all our ‘engines’, cars and humans etc, will run less efficiently
4. We must consider not only energy but also ‘least action’ – and take action.
Jennifer Coopersmith is the author of Energy, the Subtle Concept: The discovery of Feynman’s blocks from Leibniz to Einstein. She is Honorary Research Associate in the Department of Civil Engineering and Physical Sciences at La Trobe University, Australia. You can read her previous OUPblog post here.