Light passes through six millimetres of solid glass as if it weren't there. It won't cross a sheet of paper a tenth as thick — and the glass is the denser of the two.

Not a matter of gaps

The intuitive picture is that light slips through glass — threading the gaps between atoms, finding a clear channel the way water finds a sieve. But glass is a packed solid, heavier per cubic inch than paper, with no more open passages than a brick. A photon is also enormous next to the spacing between atoms, far too big to squeeze "between" them. Whatever makes glass clear, it is not holes.

Nor is it the old tale that glass is secretly a slow liquid — that medieval windows are thicker at the bottom because the glass crept downward over the centuries. It didn't. Glass is a true solid; those old panes were simply poured unevenly. Transparency has nothing to do with flowing.

Light asks for a rung, and glass hasn't got one

Here is the real reason, and it is pure quantum mechanics. When light meets any material, each atom's electrons are offered the photon's energy — but they can accept it only if there is an allowed empty level exactly that far above where they already sit. Electron energies come in fixed rungs, not a smooth ramp, and if no rung matches the photon, the offer is refused and the light sails on untouched. Physicists call that match a resonance; glass simply offers none in the visible range.

In glass, the climb to the next available rung is large — larger than the energy any particle of visible light carries. Red, green, blue: none can pay the fare. The electrons can't absorb them, so the photons pass straight through. It's the same currency Einstein cashed in the photoelectric effect: a photon's energy is fixed by its colour and spent all-or-nothing.

You can catch glass being choosy. Ultraviolet light carries more energy per photon — enough, at last, to clear the gap. So glass really does absorb UV, which is why you won't get a sunburn sitting behind a closed window. The same pane is invisible to your eye and a solid wall to the ultraviolet, at once.

Glass isn't clear because light gets through the gaps. It's clear because visible light has nothing it's allowed to spend its energy on — no electron can take the offer, so the light is never stopped to begin with.

Why paper isn't glass

Two more things must go right, and paper fails both. First, no absorbing pigment — no dye or metal whose electrons do have a matching rung for visible light, which is precisely how everything around you gets its colour. Second, nothing inside to scatter the light off course. Glass is smooth and uniform down to the scale of a wavelength; paper is a riot of fibres, every surface flinging light a different way until none comes through straight. It's why a clear ice cube and white snow are the same substance — snow is only a heap of tiny crystals, scattering at every face.

Even the light that gets through doesn't get off free. Passing in, it is slightly delayed and bent — the small toll that sorts a plain sunbeam into a rainbow.