What does E=mc² mean?

The short answer

Einstein's famous equation means energy is equal to mass times the speed of light squared. In short, it means that energy and mass are different forms of the same thing.

The long answer

The equation itself is simple and elegant: E=mc² (or energy = mass x the speed of light squared). But what does it really mean and why does it matter?

What E=mc² means

Here's a breakdown of the equation's components to help you (and me) understand how it works:

What is energy (E)?

Energy, in the most general sense, represents the capacity to do work. In physics, it's talking about the work required to something against a force. There are lots of different forms of energy: kinetic (energy of moving objects), chemical, electrical, nuclear, and thermal, to name a few.

What is mass (m)?

Mass is a measurement of how much stuff is in an object, often measured in grams. Mass can be confused with volume and weight, other physical properties. Let's take a can of soup🥫as an example to explain what mass is and isn't.

If you have two identical cans of soup, but one is empty and the other full, they both have the same volume. This means they take up the same amount of space, but the full one has more mass. Mass is also not weight, since weight is dependent on the amount of gravity applied. The full can of soup has a different weight when weighed on Mars vs. Earth, but it still has the same amount of mass on both planets.

Why do you multiply mass by the speed of light (c)?

Energy travels at a constant speed of 186,000 miles/second – the speed of light.

Why do you have to square the speed of light (c²)?

It has to do with how kinetic energy (or the energy of moving objects) is proportional to mass. When an object moves four times as fast as another object, it has 16 times the energy, not four times the energy.

Okay, so what does E=mc² mean?

To quote Einstein himself, "The mass of an object is a measure of its energy content." Energy and mass were previously seen as entirely different things, but E=mc² demonstrates that mass and energy are interchangeable forms of the same thing.

One of the most mind-blowing things this equation reveals is just how much energy is in matter. You can measure an object by its mass and then plug that into the equation to calculate its energy. And since we're multiplying an object's mass by the speed of light squared, the amount of energy in even a small amount of matter is outrageous. For example, the amount of energy in a penny could theoretically provide enough energy to power the New York City metropolitan area for at least two years.

Why E=mc² matters

Okay now that we have a pretty good understanding of the components of the equation, let's move into why it matters.

What can you do with E=mc²?

In practical terms, this equation opened the doors to nuclear energy. Why? Because E=mc² states that a change in mass requires a change in energy. So if you were to split apart an atom into two parts (nuclear fission) or fuse two atoms together (nuclear fusion), the change in mass would release an enormous amount of energy.

How does E=mc² change the way we view the universe?

E=mc² is kind of hard to wrap your head around because we tend to think of mass as tangible and energy as intangible. But what this famous equation shows us is that mass is the most condensed form of energy, and energy has mass (i.e. it's tangible). It's not that you can convert mass into energy, but that they are two sides of the same coin.

Bonus brain points

Accordingly to E=mc², a hot cup of coffee weighs more than a cold cup. This has been measured using incredibly precise scales.

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Sources

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