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in that a single number will suffice to specify it. But what is “energy”? How do we define it? What is it measuring? Momentum was easy in that regard: An arrow points in the direction of motion and is of a length equal to the product of the mass and the speed. Energy is less easy to pin down, because it can come in many different guises, but the bottom line is clear enough: Whatever happens, the sum total of all the energy in any process should remain unchanged regardless of how things might be changing. Again, Noether gave us the deep explanation. The conservation of energy arises because the laws of physics remain unchanged with time. That statement does not mean that things do not happen, which would obviously be silly. Instead it means that if Maxwell’s equations hold true today, then they ought also to hold true tomorrow. You can replace “Maxwell’s equations” with any fundamental law of physics—Einstein’s postulates, for example.

That said, and as with the conservation of momentum, the conservation of energy was first discovered experimentally. The story of its discovery is a meander though the history of the Industrial Revolution. It sprang from the work of many a practical experimenter who came across an immense variety of mechanical and chemical phenomena in pursuit of industrial Jerusalem. Men like the unfortunate Count Rumford of Bavaria (born Benjamin Thompson in Massachusetts in 1753), whose job it was to bore cannon for the Duke of Bavaria. While boring away, he noticed that the metal of the cannon and the drill bit got hot, and correctly surmised that the rotational motion of the drill was being converted into heat by friction. This is the opposite of what happens in a steam engine, in which heat gets converted into the rotary motion of the wheels of a train. It seemed natural to associate some common quantity with heat and rotational motion, since these seemingly different things appear interchangeable. This quantity is energy. Rumford has been termed unfortunate because he married the widow of another great scientist, Antoine Lavoisier, after Lavoisier lost his head to the guillotine in the French Revolution, in the mistaken belief that she would do for him as she had for Lavoisier and dutifully take notes and obey him as a good eighteenth-century wife should. It turned out that she had been submissive only under the duress of Lavoisier’s iron will, and in his rather wonderful book The Quest for Absolute Zero, Kurt Mendelssohn described her as leading him “a hell of a life” (the book was written in 1966, hence the quaint turn of phrase). The key point is that energy is always conserved, and it is because it is conserved that it is interesting.

Ask someone on the street to explain what energy is and you’ll get either a sensible answer or a pile of steaming New Age nonsense. There is such a wide spectrum of meanings in popular culture because “energy” is a word that is widely used. For the record, energy has a very precise definition indeed and it cannot be used to explain ley lines,5 crystal healing, life after death, or reincarnation. A more sensible person might answer that energy can be stored away, inside a battery waiting in suspension until someone “completes the circuit”; it could be a measure of the amount of motion, with faster objects having more energy than slower ones. Energy stored in the sea or in the wind provide particular examples of that. Or perhaps you would be told that hotter things contain more energy than colder ones. A giant flywheel inside a power station can store up energy, to be released onto the national electrical grid to meet the demands of an energy-hungry population, and energy can be liberated from inside an atomic nucleus to generate nuclear power. These are just some of the ways we might encounter energy in everyday life, and they can all be quantified by physicists and used to balance the books when it comes to making sure that the net effect of any process is such that the total energy remains unchanged.

To see energy conservation in action in a simple system,