CATCH THE PHOTON
Build your wave. Cancel theirs. Catch the photon. · Grades 6–8
Wave Board
Detectors
Waves played
Waves played
Hear a move
Pick a card, then hear the current wave, that card alone, and both together. A and B are played separately.
Wave Board
Add a wave
See the calculation
Silence the ghost · musical challenges
Choose a challenge. Listen, then try your answer.
Free play: add waves above, or start a challenge.
Try an example
Gray curves: separate waves. Red: their sum. Every wave plays the same tune; equal opposites cancel it. Sound uses a fixed scale, but perceived loudness is not a brightness meter.
How to play
Goal. Make your detector bright and your opponent's dark, then catch the photon.
Cards. The arrow gives the direction; the number is wave strength (amplitude) and tells you how many squares to move. ↑ up is blue, ↓ down red, → right purple, and ← left gold. There are 40 cards: seven strength-1 and three strength-2 cards per direction. The small plots all use the same scale and frequency.
- Choose. Start with three cards each. Secretly pick one card and either detector. Build your own wave or try to cancel your opponent’s.
- Reveal and move. Apply A’s card first, then B’s. Move the chosen token in the arrow’s direction by the full card strength. ↑2 and ↓1 leave ↑1; ↑2 and ↓2 cancel.
- Refill and repeat. Refill hands to three. Play 8 rounds. If both detectors end dark, play another round.
- Catch. Draw from exactly 64 equal-sized slips: blue equal to A’s brightness, purple equal to B’s, gray for the rest. Blue or purple wins. Return gray, mix, and send a new photon with the same settings. The browser handles retries.
Solo quick play. Click “Solo quick play” to show your hand and play against the computer. Each choice resolves both cards and starts the next round. “New game” keeps your play mode for an easy replay.
Passing one screen. The other player looks away before you show your cards. For a projector, open Play options → Open hands. Computer play and brightness hints are there too.
Edge of the board. Choose a full move that stays on the board. If A’s move makes B’s already-chosen move leave the board, B’s card is lost. Never make a partial move. With no legal move on either detector, discard the first card.
Hear a move. Pick a card, open “Hear a move”, then preview it on A or B before choosing its target. In Wave lab, try the musical challenges or open “Try an example”.
Why it works
The musical sound model. Every contribution shares the same three notes and timing. The arrow sets phase within each note, and strength sets amplitude. The app adds wave components before playback, using a fixed audio scale. Equal opposite contributions cancel the whole tune. The sound is an audible model of wave interference. Detector A and B are auditioned separately.
The arrow is a direction on the amplitude board, not the photon’s travel direction. It represents the phase: where a wave starts in its cycle. The number gives its amplitude. Up starts at a crest, down at a trough, right at zero rising, and left at zero falling. Adding these waves means adding their arrows tip to tail.
In-step amplitudes add. Opposite phases subtract; equal opposites cancel completely. Two equal waves a quarter-cycle apart have a combined amplitude about 1.4 times either one. The plots show a wave value over time, not the path of a photon.
At board position (x, y), brightness is x² + y². Each detector reaches at most 32, so together they use at most 64 slips. Per photon: A’s chance is A brightness ÷ 64, B’s is B brightness ÷ 64, and the missed chance is the remaining share. Brightnesses 25 and 9 give 25/64, 9/64, and 30/64. Among detections: A wins with chance 25/34 and B with 9/34. Replacing gray slips and sending identical new photons preserves those eventual-win odds. A missed photon is gone; the next attempt uses a new photon.
For teachers
| In the game | Math or science idea |
|---|---|
| The board is a grid around a center | Coordinate plane, four quadrants (CCSS 6.NS.C.8) |
| ↑1 + ↓1 = 0; →2 + ←2 = 0 | Opposite quantities combine to make 0 (CCSS 7.NS.A.1a) |
| Brightness = height × height | Whole-number exponents (CCSS 6.EE.A.1) |
| Brightness = distance² from the center | Pythagorean theorem and distance in the coordinate plane (CCSS 8.G.B.7–8) |
| The photon bar | Probability models (CCSS 7.SP.C.7); the Born rule of quantum physics |
| Twice the height, four times the brightness | Wave amplitude and energy (NGSS MS-PS4-1; that standard's assessment excludes light, so you can call these sound or water waves) |
A physical detection model. An ideal source sends one photon at a time into a 50:50 splitter. Each branch has an adjustable loss channel and an ideal detector. Set the branch transmissions to A brightness ÷ 32 and B brightness ÷ 32. Then the per-photon detection probabilities are exactly A brightness ÷ 64 and B brightness ÷ 64; all other photons leave through loss channels and are not detected at A or B. Both detectors can brighten as losses decrease.
What the cards represent. Cards add four-phase wave contributions on the amplitude board. The resulting brightness sets each branch’s transmission. This reproduces the stated detection probabilities; a card is not literally a newly opened optical path or a physical gate. The board is a wave-arithmetic teaching model, not a detailed optical interferometer. Interference can redirect light to other outputs; cancellation does not itself prove absorption. Real waves can have any phase; the cards use four.
Sound physics reference. Joe Wolfe, UNSW, Acoustics FAQ ↗: background on phase, reinforcement and cancellation.
Background. The arrow method comes from Feynman's QED (1985). Choudhary and Blair's "phasor wheels" (European Journal of Physics, 2021) use the same idea as a hands-on tool for middle school and up.
Catch the Photon · developed using QCaMP material · works offline in any browser.