Delaychoice

Delaychoice, an hourglass seer of the Paradox Parlour, decides whether to put the last beam splitter in place only after the photon has entered her interferometer.

The Physics

In a Mach–Zehnder interferometer, a single photon meets a first beam splitter and then two paths. If a second beam splitter recombines the paths, the photon shows interference: which detector clicks depends on the phase difference. If the second splitter is removed, each detector clicks half the time, as if the photon took one path. John Wheeler proposed in 1978 making this choice after the photon has passed the first splitter. Jacques et al. (Science 315, 966, 2007) did it with single photons and a random choice that was space-like separated from the photon's entry.

with splitter: P₁ = cos²(φ/2), P₂ = sin²(φ/2); without: P₁ = P₂ = ½

• P₁, P₂: probabilities that detector 1 or 2 clicks
• φ: phase difference between the two arms (rad)

The results agree exactly with standard quantum mechanics: the statistics depend only on the setup at the moment the photon is detected.

Honest caveat: No signal goes back in time, and nothing about the photon's past is rewritten. That reading only arises if you insist the photon “really” took one path or both before it was measured. Quantum mechanics assigns no such definite past, and the experiment does not need retrocausality. What the result means for the nature of the photon depends on your interpretation (Copenhagen, many-worlds, pilot-wave and others), and that is unsettled; all of them predict the same counts. Quantum-eraser versions also give no signal, because the pattern only shows after matching with data from the other detector.

On the sticker

Delaychoice holds up her glowing cyan Mach–Zehnder light maze, with its removable splitter crystal. Printed text: DELAYCHOICE with the line CHOOSE LATER. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.