Albert Einstein’s theory of special relativity resulted in perhaps the most famous equation every created, and changed the world of science forever. The Equivalence of Mass and Energy. Special Relativity and E = mc²

Einstein originally released his theory of Special Relativity in the form of a relatively short (no pun intended) paper in the German science journal, *Annalen Der Physik* in the year of 1905 – which has been called by some his “Miracle Year,” as it was during these twelve months that he published four of his most groundbreaking theories; one on the nature of atoms, one on the physics of electromagnetism (light), and two on Special Relativity. The first, entitled, *On the Electrodynamics of Moving Bodies*, was the paper which gave the world the basics of time and space dilation, along with the accompanying mathematics. The second, entitled *Does the Inertia of a Body Depend Upon its Energy Content*, appeared as a sort of “footnote” to the special relativity paper. It was only a couple pages long, but was perhaps just as revolutionary as its predecessor.

In this, his fourth and final paper of 1905, Einstein took his readers through the thought process which led him to that all-too-famous equation, E = mc².

While Einstein had already shown, via his equations for time and space dilation, both the flexibility and the interconnectedness of space and time, he soon realized that his theory showed something very crucial about two other universal “concepts,” as well – mass and energy.

## What are Mass and Energy?

Mass, of course, is often associated with weight. This may be a good way to begin thinking about it, but these two things are not equivalent. Where weight is the measure of the effect of gravity on a certain object, *mass* is a measurement of exactly how much stuff there is in the first place, with or without gravity. Mass is also a measure of inertia – the more mass an object has, the harder it is to move it, and once it’s moving, the harder it is to stop it.

Energy, on the other hand, seems to be about as far removed from the concept of mass as something can be. Where mass seems to be something real, physical and perfectly tangible, energy is more of an idea. It is often defined as “the ability to do work,” and while this may leave things a bit vague, it really is rather accurate.

## How Do Mass and Energy Relate to One Another?

How are mass and energy connected to one another? In quite a few ways, actually. First off, they both have been known for some time to obey conservation principles, meaning that they can be neither created nor destroyed. While they can be converted into different forms (mass can turn from solid to liquid to gas, and can be cut up or turned to dust, while kinetic energy can be transferred to potential energy or sound energy or heat energy), there will always remain the same amount in our universe.

They are also related, Einstein found, in another, much more fundamental way.

Einstein began, it is said, by looking at the equation for finding an object’s kinetic energy:

E = 1/2mv²

Clearly, this equation, which had been around for some time, showed that there was some relationship between mass and energy – the two were subtly related, and their relationship was defined by the velocity of an object.

Einstein, having a particularly clever year, was able to take this equation, combine it with other known equations, do a little bit of math, and come up with the following (which looks more like the familiar equation, but not quite):

E = mc²/√(1 – v²/c²)

This, in essence, is the equation Einstein published in his paper. The equation most people are familiar with, E = mc², can be obtained by assuming that the “object” in question has a speed of zero. If an object is perfectly still, the entire right half of the equation cancels out, and we are only left with the familiar equation.

## But What Does it Mean?

In essence, this equation (which is called the equation of Mass-Energy Equivalence) shows that Mass and Energy are not just similar – they are the same thing, but in different forms, with the ability to be converted into one another. Mass can be turned into energy, and energy can be turned into mass. Further, this equation shows us that a tiny bit of mass can be turned into a *lot* of energy (the equivalent of the amount of mass *times the speed of light squared!*), while a lot of energy can only be turned into a little bit of mass.

The equation truly was a revolutionary one, though no one knew just how much so until it was realized that it would be possible, using radioactive elements, to actually use the principles of this equation – to turn regular matter into pure, intense energy. The result, as you may have guessed, was the atomic bomb, and later atomic energy.

It is Einstein’s equation which helped scientists predict just what would happen when that first nuclear explosion was triggered, and it is what tells particle physicists what will happen when they smash two beams of particles together in an accelerator. In essence, it is still E = mc² which drives much of experimental and theoretical physics to this very day.

It’s fame, therefore, is substantiated.