# An equals sign states a balance

In physics an equals sign usually states that two quantities are the same, like the two sides of a balanced account. It does not say which side to work out first.

Written for this edition, not translated from Einstein. Editorial review pending.

## Is an equals sign an instruction to calculate, or a statement?

In school, 7 + 5 = asks for an answer. In physics the equals sign more often states a fact: two ways of counting the same thing agree.

Here is an account in made-up units. A body starts with 100 units of energy, sends 30 away as light and keeps 70. Energy before equals energy after plus energy sent out: 100 = 70 + 30. The line is a balance to check, not a sum to do, and it is just as true written 100 − 70 = 30.

The mass-energy paper writes the same kind of balance: E₀ − E₁ = L. The body's energy before, minus its energy after, equals the energy L that the light carries away. It is a statement about the two accounts. Nothing in it says to work out E₀ first.

Because an equation states a balance, it can be read from either side and rearranged without changing what it says. E₁ = E₀ − L tells the same story.

## Worked example: Rearranging a balance without changing it

1. Start from 100 = 70 + 30, in made-up units.
2. Take 70 from both sides: 100 − 70 = 30. Still true, and still the same account.
3. Put the paper's letters in place of the numbers: E₀ = E₁ + L, or E₀ − E₁ = L.
4. Whichever form is written, it states one fact: what the body lost is what the light carried away.

## Where this lesson stops

An equals sign states that two quantities are the same. Which quantities, measured how, is what the paper around it has to say.