eli5, E = mc squared


Tried watching a few videos and reading articles, dumbed down even for me, still can’t get my head around it.

Let’s assume it is a 1 kg lead weight in the vacuum of space floating at 1mph.

if its floating through space then apart from kinetic energy which sent it there, and the gravitational energy which made it, what energy is there in that object which makes it applicable to the equation. “A small amount of mass is equal to a large amount of energy” but how?

Also, why is it the speed of light squared? Surely it’d just be the speed of light. If squared that’d be a massive speed so why is it used here?

Finally how come it’s so important? Why is it still important today? Don’t want to sound reductionist but this really makes no sense to me to why it’s so famous.

There are plenty of explanations, none of which make this equation make sense. So assume I am actually 5 years old and somehow figured out how to make a reddit post, how would you explain it?

In: 0

The chair you’re sitting in is made of molecules of different things – wood, plastic, leather, whatever.

Those molecules are made of atoms.

Those atoms are made of smaller subatomic particles.

Energy – electricity, light, etc – is also made of subatomic particles.

So: at a very basic level, energy and matter are made from the same basic building blocks.

When you set a log on fire – or detonate a nuclear bomb – you are converting matter into energy. E=mc^2 is the conversion factor for how much energy you could possibly get from a certain amount of mass – or how much matter you could turn a certain amount of energy into – if you could do it at 100% maximum efficiency. Think Star Trek-style transporters and replicators.

Matter and energy are actually the same thing at a fundamental level. You can think of matter kind of like crystallized or ‘frozen’ energy. It takes a ridiculous amount of energy to fuse particles like protons and neutrons together in order to form matter. So, if you break those bonds apart, you will have that energy released.

Matter and energy can never be created or destroyed, only converted.

The formula is just giving us a mathematical framework of exactly one relates to the other. How much energy you can find per unit of mass or vice versa. It doesn’t really have anything to do with actually traveling at the speed of light. (Which should instead be called the speed of causality, but I digress…)

We can’t say “the lead weight is floating at 1mph”. Floating relative to what? Maybe the lead weight is stationary at the center of the universe and everything else is moving.

OK, what if the lead block happens to crash into another lead block made out of anti-matter? Kablooey. All mass is converted into energy at once. The formula tells how much energy you get. The squared term is needed so the units come out correctly.

E=mc^2 is what you get if you convert mass directly to energy. Take hydrogen fusion in the sun. It takes 4 H to make 1 He. If you compare the mass of 4H versus 1 He, you’d see that there is a difference of ~0.7%. That is where the sun’s energy (or nuclear fission) come from.

In conventional physics, you do not change the mass. You can change the amount of kinetic or potential energy in an object. You can remove or add mass, but the mass still exist. For example, if you burn a piece of wood in a closed system, there would be no change in mass before and after. Some of the carbon is converted into CO2, but the actual mass of all the atoms is the same. The energy you get is purely from the potential energy in the chemical bonds.

E=mc^2 is actually taking the mass and converting it to energy (or vice versa). For almost all applications, you will be able to convert 0% of mass to energy, so this term is irrelevant. It’s only when you are dealing with fission or fusion does it start to matter.

If you have the time there was a great NoVA special narrated by John Lithgow about Einstein and the history of his most famous equation. It’s called Einstein’s Big Idea. You can find on YouTube