It is arguably the most famous equation in all of science (if equations can be considered famous, of course). You likely had this equation memorized well before you ever set foot in a physics classroom.

E = mc^{2}. But what exactly does this equation mean? How was it developed? And how can you use it in your everyday life?

On September 27th, 1905, Albert Einstein submitted the fourth and final of his annus mirabilis papers (latin for “miracle year” due to the monumental scientific advancements he made in 1905). This fourth paper, titled “Does the Inertia of a Body Depend Upon Its Energy Content?”, built upon his third paper which developed the theory of special relativity. In his final work of 1905, Einstein proposed the idea that the mass and the energy of an object are related. This theory, now known as the mass-energy equivalence, is best described by the now famous equation, E = mc^{2}.

So what exactly do we mean when we discuss the mass and the energy of an object? The mass of an object, like an atom, a cat, or a skyscraper, is a measure of the amount of matter in the object. In the case of an atom, it is the measure of the protons, neutrons, and electrons that make up the atom. Einstein theorized that objects, including atoms, had energy, even when they weren’t moving, interacting with other objects, or possessing an electric charge. This energy, called rest energy, is an inherent quantity associated with atoms and it is related to the mass of the atom.

Einstein’s famous equation relates the rest energy (E) of an object to the object’s mass (m) through a constant value (c). This constant value is equal to the speed of light. Light is thought to be the fastest thing in the universe, traveling at a mind boggling 671 million miles per hour. Because light is massless, any object with mass (including atoms, cats, and skyscrapers) will travel slower than light.

The speed of light is a very large number that only gets bigger when it is squared. So the right side of Einstein’s equation (mc2) becomes incredibly large, even for extremely tiny objects. Because equations must balance, the left side of the equation (E) also grows to the same incredibly large value. In other words, a teeny tiny atom with a very small mass still possesses an enormous amount of rest energy.

Just like a tiny atom with a tremendous amount of energy, Einstein’s short and simple equation packs a real punch. Once scientists realized that atoms possessed rest energy, attention quickly turned to harnessing this power and putting it to use. On April 14th, 1932, physicists John Cockcroft and Ernest Walton became the first to split the nucleus of an atom, leading to the development of the atomic bomb through nuclear fission.

So what does Einstein’s work actually mean for our everyday lives? On the surface, not much. Unless you are a nuclear engineer, you probably don’t spend your days converting between mass and energy. But Einstein’s famous equation does have some important implications for our existence here on Earth. Deep in the center of stars, nuclear fusion converts hydrogen atoms into helium atoms. This process leaves behind a small amount of mass which is converted into energy, powering the Sun and providing heat and light to us down here on Earth. So the next time you step outside and feel the warmth of the bright Sun, be sure to think of Einstein and his famous equation. On this day 118 years ago, history was made.

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