Two slits. Stripes mean waves

Every kind of wave does this, and it has a name: interference. Each calm line follows the points where one ripple has travelled exactly half a wave further than the other, or one and a half, or two and a half. There a crest always meets a trough. Noise-cancelling headphones use the same trick with sound. A microphone hears the noise around you, and the headphone plays it back flipped, troughs for crests, so the two cancel in your ear.

At a point a distance r₁ from one slit and r₂ from the other, the two ripples add:

The difference r₂ − r₁ is always less than the gap d, so the number of calm lines is twice the count of ½, 1½, 2½, … that are smaller than d/λ. The ripples here weaken as 1/√r, as circular waves on water do.

Thomas Young first showed light making stripes, between about 1801 and 1803. He let sunlight into a dark room through a pinhole, split the thin beam in two and saw bands where the two halves overlapped. From the spacing of the bands he worked out how long light waves are, and found them tiny, less than a thousandth of a millimetre. Many physicists stayed doubtful until Augustin Fresnel's work in France in the 1810s.

Bright stripes sit where the extra distance is a whole number of wavelengths. On a wall a distance L away they are spaced Δy apart:

The full brightness, for slits of width a (here a = 0.05 mm and L = 1 m):

With both slits open, the bright stripes are not twice as bright as one slit's glow but four times, and the dark stripes get nothing. Averaged over the wall it comes to exactly twice, so no light is lost or made. It is only moved. For water waves none of this is strange. For light it is, because light also comes in coins, and a single coin cannot be half cancelled. Page 12 sends particles through one at a time to see what happens.

Waves add their heights first, and brightness is the height squared. With a wave of height E from each slit:

Two slits give twice one slit's light overall, but four times at a bright stripe and nothing at a dark one.

This is not a clumsy detector bumping the light. In 1998 Gerhard Rempe's group in Germany sent atoms along two paths and tagged each path by gently changing a state inside the atom, far too gently for any kick to matter. The stripes still vanished. For light, the tag can be a polarising filter on each slit, like the ones in some sunglasses, set to let through different directions of wiggle. The book draws the result as one even glow (pp. 11, 14 and 17). Cartoons often show two neat bands behind the slits instead, but with slits as narrow as these each glow spreads so wide that the two overlap into one.

V is the stripe contrast and D how well the tag tells the two paths apart. With tag states t_L and t_R:

A best guess of the slit from the tag is right with chance (1 + D)/2.

For decades the usual story was a clumsy kick: to see the path you must bounce something off the light, and the bounce scrambles the stripes. Werner Heisenberg explained the limits of measuring in this way in 1927. Experiments like Rempe's show the kick is not needed. What counts is whether a record of the path exists anywhere. Whether a mind plays any deeper part in quantum physics is still argued, and the book comes back to it.

The stripes' contrast is the overlap of the two tag states:

Nothing in the formula asks whether anyone reads the tag.