Open a second door, and fewer photons get through

Here is a machine that breaks common sense. A single photon enters a splitter and has two routes to one detector — call them A and B. Block route B, so the photon can only travel via A: of the photons that get through, the detector catches half. Block A instead and again it catches half. Common sense — and not just common sense, but the entire mathematics of probability — now makes a firm prediction about opening both routes. If a photon has some chance of arriving via A and some chance via B, the chances add. More ways to arrive can never mean fewer arrivals. A second open door cannot subtract.

Run the experiment, and at certain path lengths the detector stops clicking altogether — not less often, but not at all. Physicists call such a setting a dark fringe, after the dark bands that appear where overlapping water ripples cancel. Photons that arrived reliably through one open door stop arriving the moment you open a second one, and close either door again and the clicks resume. Nor can this be blamed on photons crowding each other out of the way, because the experiment is routinely done one photon at a time. Each photon, travelling alone, somehow “knows” whether the door it didn’t use was open.

The diagnosis is that nature does not run on probabilities at all. It runs on something one level beneath them: amplitudes — numbers that carry a direction as well as a size (mathematically, complex numbers). What predicts the click rates is this recipe: add the amplitudes of every route to an outcome, then square the length of the result. Amplitudes pointing the same way reinforce each other, and amplitudes pointing opposite ways cancel. Probabilities could never do that — squares are never negative — but the quantities underneath them can. And the knob you turn to swing them between those extremes is the difference in path lengths, which sets the angle between the two amplitudes: their relative phase.

Whether those squared lengths deserve the name “probability” at all is a deep question we are saving for later in this strand; for now, notice only that the recipe works and probability theory’s own arithmetic does not. The model below is the real calculation, not a cartoon: two routes, one amplitude each, added and then squared.

Run it and notice the three facts that any account of the world now has to explain. One: with a single route open, amplitudes and probabilities agree exactly — half the photons arrive. The strangeness only appears when there are two ways to do the same thing. Two: the dark fringe is paid for. Average the amplitude curve over all phases and you get exactly the classical rate — interference never destroys photons, it redistributes them from the dark places to the bright ones, where the arrival rate is double what probability allows. Three: the cancellation is between routes the photon didn’t detectably take. Something travelled route B — something capable of exactly cancelling the contribution of route A — even though every time you look, you find one whole photon on one route.

That third fact is the doorway this strand walks through. David Deutsch’s argument, in The Fabric of Reality, starts precisely here: something interferes with the photon, it behaves in every respect like a photon on the other path, and no theory that denies its existence predicts the silence. The amplitude for “photon on route B” is not a statement about our ignorance — it is a piece of the state of the world, as real as the route-A piece, because the detector’s silence is manufactured out of both. Quantum theory’s central object, the thing the amplitudes describe, is called the state vector, and the interferometer forces the question this strand exists to answer: if both components of the state are real enough to cancel each other here, what happens when they stop being able to meet — when each component drags a measuring device, an observer, a world along with it?

That question has a precise, unmysterious answer, and it is not “the wave collapses”. It’s called decoherence, it’s ordinary quantum mechanics applied honestly, and it is three essays away — with one waypoint beyond it, the Born rule: the question of why the square of an amplitude earns the name “probability” at all, which is the hardest and best part of the Everett story. Next, though, we need the second ingredient: what amplitudes do when two particles share them — entanglement, where the state stops describing particles separately and the Everett picture starts coming into focus.