You know it, your friends know it, heck even your parents and grandparents know it, but how many of you actually know what E=mc^{2} really means? If you do not know don’t feel bad about it. Because the reality is that most people are unable to explain this equation properly. E=mc^{2} is the most famous mathematical equation on Earth. Discovered by none other than one of the greatest scientist to ever live, Albert Einstein. This equation has been elegantly described as Shakespearean like, or mathematical poetry. It is so simple and elegantly described that its profoundly powerful importance is easily and understandably overlooked or misunderstood. So let’s break it down:

- E = Energy
- m = Mass
- c
^{2}= The speed of light squared.

So to encapsulate the equation it states that:

“energy equals mass times the speed of light squared. On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing. Under the right conditions, energy can become mass, and vice versa. We humans don’t see them that way—how can a beam of light and a walnut, say, be different forms of the same thing?—but Nature does.” [source: PBS]

The reason we square the speed of light has to do with how “energy” or in the case of the equation kinetic energy works:

“Kinetic energy, to take a brief primer, is the energy of an object in motion, and the more mass or velocity a moving object has, the greater its kinetic energy released. Today, many electric cars take advantage of kinetic energy to operate more efficiently, using the car’s kinetic energy to charge its batteries. Kinetic energy is distinct from another kind of energy — potential energy, stored by an object. You may think of batteries, such as those in the electric car, as stored, potential energy, but in fact, all sorts of objects contain potential energy, objects you might not even expect. For instance, by placing a ball at the top of a hill, you’re effectively storing the energy that it took to move the ball up the hill in the ball itself. The higher the hill and the heavier the ball, the more energy is required to move the ball up the hill (and, accordingly, the more potential energy is contained in the ball). Even a rubber band, when pulled back as far as it can go, contains potential energy in that stretched position.” [source: http://curiosity.discovery.com/question/why-speed-of-light-squared]

100 Greatest Discoveries E=mc^{2}

When (m) Mass is converted into energy the resulting energy by definition is moving at the speed of light. The result of this means that if a Mass (m) is moving at a Speed (c) that is four times faster than something else, it doesn’t have 4 times the energy, but rather 16 times the energy – or in other words that figure is squared. [source: http://curiosity.discovery.com/question/why-speed-of-light-squared]

That leads us to the Speed of Light (c^{2}) squared, and since we know that Mass (m) converts to energy at the speed of light we end up with 448,900,000,000,000,000 in units of mph. Or 449 quadrillion miles per hour. With this equation E=mc^{2} it is easy to see how the smallest amount of mass can store massive amounts of energy. For those who have already guessed, we have now famously or infamously ended at a very scary and real world application. The proof that this equation works? That’s right; Atomic Bombs.

But don’t fear because E=mc^{2} isn’t just a formula for destruction, but rather it is one of the greatest forces of creation in the universe as well. The beginning of the universe or E=mc^{2} is the only acceptable explanation of what was going on seconds after the Big Bang occurred. Massive amounts of energy and matter went back and forth indiscriminately in exact accordance with the equation. [source: PBS]

The stars, those distant specks of light are a visual representation of E-mc^{2}. Our very existence and the warmth we feel everyday from our Sun is a direct result of this equation occurring at the very core of the Sun.

“The carbon, oxygen, nitrogen, and hydrogen that make up living organisms were baked in the innards of a star,” Rigden says. “In terms of what goes on in stars, we owe our existence to

E = mc^{2}“. [source: PBS]

Some everyday applications of this equation can be seen in both the medical and space community. You may perhaps have been a direct beneficiary of the equation if you have ever had a PET Scan.

We take advantage of that realization today in many technologies. PET scans and similar diagnostics used in hospitals, for example, make use of

E = mc. “Whenever you use a radioactive substance to illuminate processes in the human body, you’re paying direct homage to Einstein’s insight,” says Sylvester James Gates, a physicist at the University of Maryland. [source: PBS]^{2}

Other applications where E=mc^{2} is used but not limited to include:

- Smoke Detectors
- Exit Signs
- Radio Carbon Dating Process
- Power for Telecommunication Satellites
- Heat for the Mars Rovers
- Nuclear Power

So where does this leave us? Hopefully with a new appreciation and understanding of the worlds most famous equation. But hopefully you walk away with a new appreciation for what Albert Einstein’s discovery has done for man kind. It’s destructive force was first harnessed and used to help end World War II and force Japan into surrender. But since this time the formulas profoundly important principle that, Mass and Energy are two different forms of the same thing, has a far greater capacity for creation than destruction. This is the power Einstein realized, and the greatest discoveries and accomplishments man will achieve will be a direct result of his famous equation.

Until Einstein’s time, scientists typically would observe things, record them, then find a piece of mathematics that explained the results, he says. “Einstein exactly reverses that process. He starts off with a beautiful piece of mathematics that’s based on some very deep insights into the way the universe works and then, from that, makes predictions about what ought to happen in the world. It’s a stunning reversal to the usual ordering in which science is done. So that’s one of the legacies—that we’ve learned the power of human creativity in the sciences. Or, as Einstein himself might have said, ‘to know the mind of God.’ [source: PBS]

Launch this interactive demo of everyday objects applied to E=mc^{2}.

For those who always wondered what has Physics done for me. Take a look at the below video.