How to Understand E=mc2

Two Parts:Understanding the Equation Applying the Equation in the Real World Community Q&A

In one of Albert Einstein’s revolutionary scientific papers published in 1905, E=mc² was introduced; where E is energy, m is mass, and c is the speed of light in a vacuum.^[1] Since then, E=mc² has become one of the most famous equations in the world. Even people with no background in physics have at least heard of the equation and are aware of its prodigious influence on the world we live in. However, most people do not exactly know what the equation means. In simple terms, the equation represents the correlation of energy to matter: essentially, energy and matter are interchangeable.^[2] This relatively simple equation has altered the way we think about energy and provided us with numerous technological advances.

Part 1
Understanding the Equation

1
Understand where usable energy comes from. Most of our consumable energy comes from the burning of coal and natural gas. Burning these substances takes advantage of their valence electrons (unpaired electrons in the outermost shell of an atom) and the bonds they make with other elements. When heat is added, these bonds break and the energy released is used to power our communities.
- Obtaining energy this way is not very efficient and is costly to the environment.
2
Apply Einstein’s equation to make energy conversion more efficient. E=mc² tells us that there is much more energy stored inside the nucleus of an atom than in its valence electrons.^[7] The energy released from splitting an atom is much higher than that of breaking electron bonds.
- Nuclear power is based on this principle. Nuclear reactors cause fission (the splitting of atoms) to occur and capture the massive amount of energy released.
3
Discover the technologies made possible by E=mc². E=mc² has enabled the creation of many new and exciting technologies, some of which, we can’t imagine living without:^[8]
- PET scans use radioactivity to see inside the body.
- The equation allowed for the development of telecommunications with satellites and rovers.
- Radiocarbon dating uses radioactive decay based on the equation to determine the age of ancient objects.
- Nuclear energy provides cleaner and more efficient energy sources to our society.
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Community Q&A

Answered Questions

How does nuclear fission release so much more energy than the break in electrons from burning fossil fuels?
- Almost all of the mass in an atom is located in the nucleus, where protons and neutrons are bound together very tightly. Nuclear fission breaks apart these tight bonds and converts some of the nucleus mass into energy.
Helpful? 12 2
You use a melting ice cube as an example of an object changing forms without losing mass. But surely the melted water will occupy less volume than the ice cube?
- Mass and volume are not the same. You can stretch or compact an object to change its volume, but the amount of matter inside it will stay the same. In the ice cube example, the molecules in liquid water are closer together, but they're still the same molecules that were in the ice.
Helpful? 13 3
How is gravity impacted by e=mc2?
- F=ma and E=mc2 are both encompassed, surpassed, and related by this most fundamental law/truth in all of physics: Inertial resistance is proportional to gravitational force/energy. (Gravity has energy.) This law applies to the Sun and to photons, and it applies to black holes. Balancing gravity and inertia is what is most fundamental and important here. So, force/energy, acceleration, photons/light, gravity and inertia, and larger and smaller space are central considerations for what is impacted by this equation.
Helpful? 10 2
Why can't an object with mass travel at the speed of light?
- Special relativity explains that accelerating an object with mass takes more and more energy as the speed increases. When you're near the speed of light, this effect is so noticeable that you can only edge closer and closer to light speed, no matter how much energy you put in.
Helpful? 9 2
I've heard that special relativity is related to time travel. How does that work?
- There's no such thing as absolute time. Two people moving at different relative speeds can disagree on how much time has passed between two events. However, if you could send a signal faster than light, things get weirder: the two people could disagree over which event came first. This leads to "time travel" paradoxes, such as sending a message to yourself in the past. Most physicists think faster than light signals are impossible, partly for this reason.
Helpful? 10 4
You use a melting ice cube as an example of an object changing forms without losing mass. But surely the melted water will occupy less volume than the ice cube?
- Mass is nothing but the ratio of volume and area. The area of water is more than that of the ice cube and the volume has also changed. As a result, the mass will stay constant.
Helpful? 3 1
Is there a spiritual aspect to this equation, treating energy as the soul and mass as the body?
- Physics terms refer to precisely defined, physical phenomena. Burning wood transforms matter into energy, but most religions would not call the result a soul. Einstein himself and many people since have interpreted his theories from a religious perspective, but that's outside the scope of the equations themselves.
Helpful? 3 2
Why can't we consume the 100% energy of a matter?
- To consume 100% energy of a matter would be to destroy it completely. Matter can only change form, not be completely destroyed. If you could destroy matter 100% then, in theory you could destroy energy 100%. That doesn't sound like a good idea.
Helpful? 1 2
Could you simplify this even more, for teaching kids 13 or 14 years old?
- I would focus on the idea that energy (for instance light and sound) and mass (and physical object) can be converted to each other. The "c squared" part is more difficult to explain, but you could talk about how Einstein figured out that c (the speed of light) is the "speed limit" in the universe.
Helpful? 1 3