Planck to Horizon

Sixty-two steps of ten

From the smallest length physics can talk about to the largest thing we can see, sizes span about 62 steps of ten. One step, an order of magnitude, means ten times bigger. Two steps, a hundred times. Ten steps, ten billion times. A normal ruler cannot hold this. Draw the universe across your screen and a human would be three trillion times smaller than a proton on it. So this page uses a logarithmic scale, a ruler where each step of ten gets the same space instead of each metre. Moving one notch always means "ten times".

One more trap: width is not the whole story. A thing ten times wider has a hundred times the area and a thousand times the volume.

Where you stand

Where is the middle of all sizes? Not in metres: the universe would swallow everything. In steps of ten, the middle is the geometric mean: the size that is as many times bigger than the Planck length as it is smaller than the universe. Before you read on, drag the pin to where you think it is.

The answer is about 0.12 millimetres: a human egg cell, the one cell you can almost see, about the width of a thick hair. You stand 35 steps above the smallest length and 27 below the largest, 57 % of the way up. Big enough to build telescopes, small enough to be made of cells. Every adult population's average height, from shortest to tallest country, fits in 0.14 % of the ruler.

The sticky small world

Shrink below a few millimetres and the world turns sticky. Surface tension, the skin-like pull of water's surface, beats gravity below the capillary length, 2.7 mm for water, so drops stay round and insects walk on ponds. Shrink further and viscosity, the thickness of a fluid, takes over from inertia below about 0.3–1 mm. For a bacterium, water feels like honey: stop swimming and it stops within a fraction of an atom's width.

Then light itself gives up. A microscope cannot sharpen details finer than about half the wavelength of light, about 200 nanometres (the diffraction limit). Viruses and molecules lie below that line. We see them with electrons and X-rays instead.

Inside the atom

The picture of an atom as a little solar system is a century old, and it is wrong. Electrons do not orbit like planets. Quantum physics, the rulebook for very small things, says an electron has no exact path: it is a cloud of chance, thick where you are likely to find it. That cloud is the atom's size, about a tenth of a nanometre. At the centre sits the nucleus, 63 000 times narrower, holding almost all the mass.

People say atoms are mostly empty. Better: they are mostly cloud. That cloud is what pushes back when you press on a table. The atom is 137 times the electron's own quantum length because the electric force is weak, and that one number, α ≈ 1/137, sets the size of everything made of atoms.

The edge of the knowable small

Our best collider, the LHC, smashes protons hard enough to resolve details near 10⁻¹⁹ m, a ten-billionth of a billionth of a metre. Below that we have no data at all. The map then runs blank for 16 more steps of ten, about a quarter of the whole ruler, down to the Planck length, the length at which gravity and quantum physics must both matter and neither works alone.

The Planck length is often called the pixel size of space. Nobody knows that. It is where our current ideas break, the way old maps once said "unknown lands". It is drawn on this page as a measured span, never as a dot or a grid.

When gravity takes over

Gravity is by far the weakest force: between two protons, the electric push is 10³⁶ times stronger. A fridge magnet lifts a paperclip against the whole Earth. But gravity never cancels, so in big things it adds up. On a mountain it sets the height limit, about 10 km on Earth (Everest is 8.8 km; on Mars, with weaker gravity, Olympus Mons reaches 22 km). On a body a few hundred kilometres across, the potato radius, it crushes the whole thing into a ball.

Mass and size: the forbidden corners

Plot every object by mass and by size and a pattern appears. Almost everything solid lies near one line: the density of water and rock, because ordinary matter is atoms touching, and atoms are all about the same size. Two other lines fence the map. Below the first, anything would be so dense that it is a black hole: a place light cannot leave. Below the second, a mass is too small to be held in so small a space: quantum fuzz spreads it out (its Compton wavelength). These two lines lean towards each other and cross at the Planck scale. That crossing, not a pixel, is why the Planck length matters. The smallest possible black hole would be as fuzzy as it is heavy.

The largest things and the horizon

Stars gather into galaxies. Galaxies gather into clusters, and clusters into a web of threads around huge empty voids. Zoom out past a few hundred million light-years and the web evens out: every large patch looks about the same. Then there is a limit. Light has had about 13.8 billion years to travel since the Big Bang, and space has stretched meanwhile, so the farthest light we can see comes from about 46 billion light-years away. That makes a sphere about 88 billion light-years wide: the observable universe. It is our horizon, like the edge of the sea from a ship. More ocean lies beyond.

How we know

No single tool measures everything. Rulers and tapes work from millimetres to kilometres. Microscopes go down to cells, electron microscopes to atoms, and scattering experiments, which fire particles and watch them bounce, into the nucleus. Upward, radar times echoes off planets, parallax uses the shift of nearby stars as Earth circles the Sun, and stars and exploding stars of known brightness work as distance markers. Each method hands over to the next like rungs on a ladder, and errors pile up as you climb. That is why each size on this page carries a flag: measured, derived, a range, a convention or a limit.