##### E=mc²

E=mc². Quite possibly the most popular equation in the world, the equation discovered by Albert Einstein describes the energy of a motionless object with mass. However, this equation does not tell the whole story. Really, the whole equation which Albert Einstein derived is E²=(mc²)²+(pc)², where E is an object’s energy, m is its mass, c is the speed of light, and p is its momentum. To visualize, one can use the Pythagorean theorem to visualize the relationship between all three of these variables where E is the hypotenuse, mc² is the height, and pc is the base.

Now, referring back to the equation E=mc², the Pythagorean theorem shows us that the full equation changes to the more popular equation when momentum is 0 or when the object is not moving, removing pc from the equation. Similarly, the equation E=pc is when an object has no mass and emulates the energy that a light particle exudes. This equation demonstrates that E is equal to momentum (up to a factor of light), and the closer they are to each other, the less mass there is, thus the closer the particle is to behaving like light.

Fun fact: Velocity can never reach the speed of light.

Why?

Well, for starters, Velocity is equal to C pcE and, referencing back to our previous point, as pc and E get closer and closer to one another, the velocity gets closer to the speed of light. However, a triangle’s hypotenuse will always be the longest length. This means that energy will always slightly be larger than pc, meaning that velocity can never completely be equal to the speed of light -- only very closely.

Sources:

Minutephysics, director. E=mc² Is Incomplete. YouTube, YouTube, 28 Oct. 2012, www.youtube.com/watch?v=NnMIhxWRGNw.

Minutephysics, director. Einstein's Proof of E=mc². YouTube, YouTube, 29 Mar. 2012, www.youtube.com/watch?v=hW7DW9NIO9M.