Einstein's little equation

In 1905, long before Albert Einstein was a household name, the young man spent his days assessing inventions as a patent clerk. I suppose that made physics his hobby. Yet that year he reasoned his way to a whopping four papers, plus a doctoral thesis. These weren’t minor papers making incremental advancements in an esoteric area of knowledge. These were game changers. Among them, Einstein changed the way scientists perceive light, and unified time and space.

Einstein’s iconic equation didn’t appear until the last of his papers that year. It was a short paper, almost an addendum to his earlier work on special relativity, a short paper in which Einstein reached "a very interesting conclusion”: that mass and energy are two forms of the same thing.

E=mc2. Energy is equal to mass multiplied by the speed of light squared. Since the speed of light multiplied by itself is a very large number, a little bit of mass is equivalent to a huge amount of energy.

Energy and mass are intuitively completely different - energy is heat and motion while mass just sits there - but the universe runs on physics, and Einstein's equation shows that, to physics, energy and mass are essentially the same, connected by light. Einstein admitted this was “a somewhat unfamiliar conception for the average man”, but when we accept it, otherwise inexplicable things suddenly make sense.

Take the sun. If the sun burned as wood does, it would have burned itself out within about 6000 years. Einstein’s equation provides the clue as to how it has been going strong for four-and-a-half billion years, and will continue to do so for billions more. Burning wood involves a chemical reaction, rearranging atoms within molecules that are held together relatively weakly. Since mass and energy are interchangeable, you could say that not much mass is tied up within the bonds, so while the energy released when the bonds are broken is enough to heat a room with just a couple of logs, it is modest compared with the sun's mode of energy production.

The sun produces energy via nuclear reactions, which involve the dense central nucleus of the atom. Almost the entire mass of the atom resides in the nucleus, yet if an atom were the size of the room you are sitting in, the nucleus would be that speck of dust floating in front of your screen. Dense. Rearranging the particles that make up the nucleus can therefore lead to a much greater loss of mass than rearranging the atoms within molecules.

In the sun's core, hydrogen nuclei are squeezed together to form heavier helium nuclei. Those helium nuclei have a slightly lower mass than the sum of the hydrogen nuclei they came from. Multiply that little bit of mass by the 600 tonnes of hydrogen fused every second, multiply that by the speed of light squared, and you have enough energy to warm all the planets of our solar system.

Nuclear power and nuclear bombs likewise involve reactions of the atomic nucleus itself, this time splitting a large nucleus into smaller ones, and in the process releasing a small amount of mass as a whole lot of energy.

Back in 1905, the nucleus not yet discovered, it was some time before the consequences of Einstein's equation became apparent. He was just starting out on his career. Ahead of him lay the general theory of relativity and a celebrity status rarely lavished upon theoretical physicists. Both that "A-list" status and his work outlive him. Today, more than 60 years after his death, his name is used interchangeably with “genius”, and his little equation is almost as famous as the man himself.


Further reading:

Einstein 1905: The Standard of Greatness by John S. Rigden, 2005, Harvard University Press

Ten top physicists describe Einstein's equation, NOVA

The legacy of E=mc2, NOVA

The Forgotten Life of Einstein's First Wife, Scientific American