From atoms to the universe

When you zoom into a map on your phone, you jump from your street to your city to the whole planet. Physics does exactly that with all of reality: it zooms from the tiny atom all the way out to the galaxies. To keep track along the way, there is a brilliant trick: powers of ten.

Powers of ten as zoom levels

A power of ten like 10³ means 10 · 10 · 10 = 1000. Each step in the exponent means: times ten. Every power of ten is one zoom level. The power of ten that a length comes closest to is called its order of magnitude. An adult human is about 1.7 m tall, so their order of magnitude is 10⁰ m, because 10⁰ is 1. A kilometre is 10³ m, and the Earth's diameter is a good 10⁷ m. It works downwards too: 10⁻³ m is a millimetre, and an atom measures only about 10⁻¹⁰ m.

You compare two zoom levels by subtracting one exponent from the other. Between 10³ m and 10⁷ m there are 7 − 3 = 4 steps of ten. Converting units works the same way: one kilometre is 10³ m, so 10⁶ m is exactly 10⁶ : 10³ = 10³ km, that is 1000 km.

Why physics needs models

Between the atom (10⁻¹⁰ m) and the Milky Way (10²¹ m) lie 31 steps of ten. No one can see an atom with the naked eye, and no one can pace out the Milky Way. That's why physics builds models: simplified pictures like the ball model of the atom or the map of the solar system. A model doesn't have to be perfect, it has to make the right zoom level understandable.

Light years

For the largest zoom levels, kilometres are no longer enough. That's why we measure in light years: a light year is the distance light travels in one year, about 9.5 · 10¹² km. The nearest star after the sun is a good 4 light years away, and the Milky Way spans about 100,000 light years.