Which path?

Chapter 3 made it look like a switch: watch the slits and the fringes die. It is not a switch. It is a dial. Look a little and the fringes fade a little; the trade between fringe contrast and path knowledge is exact, and quantum mechanics will not let you cheat it. This is complementarity made quantitative.

The detector below couples to the passing particle with adjustable strength. What matters is the overlap γ of the records it keeps for the two paths: γ = 1 means no usable record, γ = 0 a perfect one. The curve is computed live as the coherent cross-term scaled by γ. Nothing else changes.

Recovering the cartoon

Chapter 3's detector left one smooth band, not the two neat stripes of the textbook cartoon, because 10 µm slits diffract far wider than their separation. The cartoon is not wrong, it is a limit: keep the detector on and widen the slits toward the Fresnel scale √(λL) ≈ 0.74 mm, and geometry takes over from diffraction. Slide it yourself:

6.00 mm (fixed)

Things to notice

The trade is exact

Half-strength detection does not halve the fringes on some vague curve: V and D sit on a circle. Watch the V² + D² readout as you slide: it pins to 1.

The inequality

Gentleness doesn't help

The dial is the quality of the record, not how hard you poke the particle. Any apparatus whose state ends up different for the two paths costs fringes, even one nobody ever reads.

Records, not observers

The cartoon recovered

At 10 µm the two humps merge into one band; past a few hundred µm they pull apart into the two stripes everyone draws. Classical shadows are quantum optics in a limit.

Where geometry wins