Spacetime and the cosmos

1905

E = mc²

Albert Einstein

How can a tiny bit of matter power a city?

A few months after relativity, Einstein added a short note: if a body gives off energy, its mass goes down. Mass and energy are the same thing in different forms, and c² is a very big number.

How they figured it out

In September 1905, Einstein sent a three-page follow-up to his relativity paper, asking whether a body’s inertia depends on the energy it contains. He imagined a body giving off two flashes of light in opposite directions and looked at it from two different moving viewpoints.

The only way the accounts agreed was if the body lost mass equal to the energy carried away divided by the speed of light squared. He didn’t even write “E = mc²”; he used L for energy. He suggested radium might one day test it.

The equation

E=mc2E = mc^2

A small amount of mass is a huge amount of energy.

Everyday echoThe Sun turns about 4 million tonnes of mass into light every second.

See it in real life

Your charged phone is heavier

A fully charged phone battery stores about 50,000 joules. By m=E/c2m = E/c^2, that makes it about half a nanogram heavier than when it is flat: far too little to weigh, but real. A large nuclear power station turns only a few grams of mass a day into the energy that lights a city.

Where engineers use it

  • Nuclear power

    Reactors release energy from a tiny loss of mass in splitting nuclei.

  • PET scans

    Hospitals detect the light from matter and antimatter annihilating: mass turning entirely into energy.

Worked example: One gram

  1. E=0.001×(3×108)2=9×1013E = 0.001 \times (3\times10^8)^2 = 9 \times 10^{13} J
  2. About 21 kilotonnes of TNT.

Where it came from