What is interference, and why does everything depend on it?

Drop two stones in a pond. Where a crest from one meets a crest from the other, the water rises twice as high. Where a crest meets a trough, they cancel and the water stays flat. That's interference: two waves combining, adding in some places and cancelling in others.

You use it more than you think. Noise-cancelling headphones play a sound wave that's the exact opposite of the noise, so the two cancel. The anti-glare coating on glasses lenses uses a thin film that makes reflected light cancel itself. The colours on a soap bubble come from light reflecting off its two surfaces and adding for some colours and cancelling for others.

Around 1801 to 1803, the English doctor and scientist Thomas Young split a thin beam of light in two. On the wall behind he saw bright and dark stripes, not two simple bright patches. Light from the two halves was adding and cancelling. Young concluded that light is a wave. Optional page 4c tells his story, which includes helping to decode the Rosetta Stone.

Here's where it gets interesting. Chapter 1 showed that light comes in particles, photons. So what happens if you turn a light so dim that only one photon passes through Young's slits at a time?

Each photon lands on the screen as a single dot, in one place, like a particle. At first the dots look scattered at random. Keep going, and a pattern builds up: the dots pile up in bright stripes and avoid the dark ones. The same stripes Young saw, built one particle at a time.

Geoffrey Taylor first tried very faint light in 1909. Physicists did the same with single electrons in Bologna in 1974 and at Hitachi in Japan in 1989. In 2002 the readers of Physics World voted the single-electron double slit the most beautiful experiment in physics.

Chapter 2 introduced amplitudes: the parts of a quantum state that you square to get odds. Here's the extra fact that makes interference work. Amplitudes have a direction, like little arrows. Each possible path contributes its own arrow.

To find the odds of an outcome, you add the arrows from every path that leads there, then square the length of the total.

• If the arrows point the same way, they add up: a likely outcome. Bright stripe.
• If they point opposite ways, they cancel to nothing: an impossible outcome. Dark stripe.

That's all interference is. The particle is always detected in one place. The odds of each place come from adding up the arrows of every way it could have got there.

Neither word fits on its own, and you don't need both. Light is one thing, following one rule. It arrives in lumps (photons). The odds of where the lumps arrive follow the arrow rule, which behaves like waves adding and cancelling. "Wave-particle duality" is a historical name for two half-pictures of that one rule.

Electrons, neutrons and whole atoms all interfere. In 1999 a team in Vienna sent molecules of 60 carbon atoms, shaped like footballs, through a grating and got stripes. In 2019 another Vienna team did it with molecules of about 2,000 atoms.

There's no size at which the rule stops. What stops interference in practice is chapter 3's enemy: decoherence. The bigger the object, the harder it is to keep its surroundings from recording which path it took. Experiments with ever-larger molecules are pushing to see whether anything else ever gets in the way.

A quantum computer doesn't try every answer and pick the best. It arranges its calculation so that the arrows for wrong answers point in opposite directions and cancel, while the arrows for the right answer line up and add. When you measure at the end, the right answer is very likely. Every quantum algorithm, from Grover's search to Shor's factoring, is a carefully designed pattern of interference. Chapter 7 shows how.

Interference is also the most sensitive ruler ever built. Split a beam, send the two halves along different routes, and bring them back together. If anything changes one route's length by even a tiny amount, the arrows shift and the balance at the detectors changes.

The LIGO detectors in the US use laser beams in arms 4 kilometres long. On 14 September 2015 they caught a ripple in space itself, a gravitational wave from two black holes merging 1.3 billion years ago. The ripple changed the arms' length by about a thousandth of the width of a proton. That discovery won the 2017 Nobel Prize in Physics. Optional page 4b goes deeper.

Quantum sensors use the same idea with atoms instead of light. Atom interferometers measure gravity so precisely that they can sense tunnels, water and rock underground. Chapter 12 covers them.