"For example, if you added energy to something, like a cup of water, you could think about it speeding up the little water mole­cules in the cup, but not changing the mass of the water.

After all, adding heat didn't change how many H20 molecules there were; it just made them w...

"Then, Einstein stepped in with a clever argument that settled the debate.

"At the time, Einstein had been preoccupied with the idea of rela­tivity, the study of how the laws of physics apply to things that are moving relative to one another.

It was known back t...

This fundamental limitation makes for some really strange effects when you consider how things look to someone standing on Earth and someone going really fast on a rocket ship.

"For example, Einstein considered the case of a rock in space giv­ing off heat. That heat will come o...

"But if you were traveling past Earth on a speeding rocket ship, you would see something different. Einstein used the formulas of relativ­ity to figure out that you would see the photons coming off the rock at a different frequency of light.

This is an effect called the relati...

"On the other hand, we tend to think of energy as something com­pletely different. We associate energy with heat, light, fire, or motion.

It seems like something ephemeral that can flow or be transmitted. It gives you the power to do things and burn things. Like a magical quan...

 Initially, they looked at the electron, which had just been discovered. Physicists noticed that when a charged particle (like the electron) moves, it makes a magnetic field.

This magnetic field then pushes back on the particle, making it harder to get the partic...

The net effect is that you, in the spaceship, would measure the energy of the photons to be different than if you measured it when you're floating next to the rock.

But since it's the same photons, something else must have changed.

"According to Einstein, what a...

This change in mass is the same (if you multiply it by the speed of light squared) as the energy of the photon emitted.

It seems that a little bit of the mass of the rock was transformed into energy, which then went off in the form of a pho­ton (remember that photons don't hav...

"This was a pretty groundbreaking result, to say the least.

It threw out thousands of years of human intuition that told us that mass and energy were totally different things.

Instead, Einstein's equation says that the two things are related to each other and t...

But kinetic energy comes from the mass and the veloc­ity of an object, and since the rock's velocity didn't change when it gave off photons, Einstein concluded that its mass must have changed.

In fact, he found that the mass of the rock changed by an amount equal to the energy...

"But physics formulas are not just math; they're supposed to de­scribe something about the physical universe. And this is another reason why E = mc2 sticks in people's minds.

Here E stands for energy, m means mass, and c is the speed of light in a vacuum, or 299,792,458 meters...

"But what exactly does that mean? How are mass and energy and light actually related to one another? And what does this relationship say about the fundamental nature of ourselves and the universe?

"For most of us, mass is the stuff we're made out of. If something has mass, it g...