A box of bombs, some live and some duds. A live one detonates if a single photon touches its trigger. Your task: find a guaranteed-live bomb without setting it off. Classically impossible. Quantum mechanically — Elitzur and Vaidman showed — routine.
↩ before you start · keep these handy
·From Ch. 16: with both arms open, interference sends every photon to the bright port D₀; the dark port D₁ never clicks.
·Also Ch. 16: the moment which path the photon took becomes knowable, interference dies and the ports go 50/50.
·From Ch. 3: anything that could record the path counts as a measurement.
🔑 symbol decoder · every new mark, in plain words
D₀ brightthe port that always clicks when interference is intact (a dud, or empty arms).D₁ darkthe port that can’t click with interference — so a click certifies a live bomb.which-patha live bomb acts as a detector of which arm the photon took.interaction-freea detection where no photon was actually absorbed by the bomb.inconclusivea bright click with a bomb present — it didn’t fire, but you learned nothing this shot.
feel
Learning from what does NOT happen
A dud bomb is transparent — a photon sails through, both arms stay open, and interference (chapter 16) sends every photon to the bright port. A live bomb is different: it watches its arm. Just by being able to absorb the photon, it acts as a which-path detector — and that destroys the interference. The tell-tale sign is a click at the dark port that should have been impossible. The photon that triggers it took the empty arm, so the bomb never fired — yet its mere presence announced itself.
🚨 everyday picture
Imagine two mirrors normally make a laser dance into a single perfect spot on the wall. Slip an opaque card into one beam-path and the perfect spot breaks up — a faint smear appears where light never used to land. You see the smear, learn the card is there, yet the photons making the smear went down the other path and never hit the card. The bomb is that card: its mere ability to block one path leaves a fingerprint at the dark port, with no photon spent on it.
recapA live bomb is a which-path detector; killing the interference lets the forbidden dark port click.
play
Fire single photons, watch the ports
Put a live bomb or a dud in the upper arm and fire photons one at a time. A click at the dark port D₁ — impossible for a dud — certifies a live bomb you have not detonated.
▸ interaction-free measurement{{ objLabel }}
D₀ bright{{ cD0 }}
D₁ dark · bomb found{{ cD1 }}
💥 detonated{{ cBoom }}
total fired{{ cTotal }}
{{ message }}
recapA dud only ever lights the bright port; a dark-port click is the live bomb signing its name, unharmed.
math
Where the probability leaks
With a live bomb in one arm, the photon’s fate splits at the first beam splitter:
½ → takes the bomb’s arm → absorbed → BOOM
½ → takes the clear arm → reaches BS2, now with no partner to interfere:
¼ → D₀ bright (inconclusive)
¼ → D₁ dark // impossible without a bomb → bomb certified, intact
per photon: P(detonate)=½, P(safe detection)=¼, P(inconclusive)=¼
Keep firing past the inconclusive bright clicks and a fraction ¼ of photons announce the bomb safely. Repeated runs, and cleverer multi-pass schemes, push the safe-detection rate arbitrarily close to 100% — you can be as sure as you like, having never risked the bomb on the photons that report.
✎ worked example · fire 100 photons at a live bomb
1.P(detonate) = ½ → about 50 photons set it off (these were the unlucky bombs).
2.P(bright, inconclusive) = ¼ → about 25 photons tell you nothing.
3.P(dark, safe detection) = ¼ → about 25 photons certify the bomb without firing it.
4.so a single live bomb is found intact with probability ¼ per attempt — and cleverer schemes push that toward 100%. ✓
recapPer photon: ½ boom, ¼ inconclusive, ¼ safe certification — a real measurement with nothing absorbed.
⚠ common misconception
“Nothing interacted with the bomb, so nothing could have measured it.” The bomb didn’t absorb a photon, but its capacity to absorb one is a physical fact that destroyed the interference. A measurement happened — the possible-but-unrealised path is just as real to quantum mechanics as the taken one. Absence of a click is information.
This is the same lesson as decoherence (chapter 09): coupling to anything that could record the path — bomb, environment, eavesdropper — collapses the interference. Next we make that idea precise: how to write down the state of just one half of an entangled pair.
✓ you can now
✓explain interaction-free measurement: detecting a bomb by the dark-port click it makes possible
✓split each photon’s fate into ½ boom, ¼ inconclusive, ¼ safe detection
✓see why a path that could have been taken is as real to QM as the one that was