One rope, two ends
An entangled pair drawn as one wave tied at two points. Turn the two analysers and compare two readings of the rope with the measured Bell tests.
Correlation at these angles: one reading for both ends · two ends each holding a fixed value
What end A sees on its own: up of the time, whatever B is turned to. Turning B never changes A's own counts, so no signal travels along the rope (no-signalling theorem).
A correlation of −1 means the two ends always read opposite; 0 means no relation. Angles are polariser angles as in the photon Bell tests (Aspect 1982): the correlation depends on twice the angle between the analysers.
Blue: the wave read once for both ends. Red: each end holds its own preset value. The two curves agree at 0°, 45°, 90°, 135° and 180°; they differ in between, which is where Bell tests look.
Settings A = 0°, 45° · B = 22.5°, 67.5°
- Read once for both ends: S = –
- Fixed values at each end: S = – (it can never exceed 2)
- Largest S any reading can give: 2√2 = 2.828 (Tsirelson 1980)
Pairs are generated by a fixed low-discrepancy sequence, not random numbers: the same button gives the same counts every time. Every measured S lies above 2, so a value fixed in advance at each end is contradicted; the wave read once for both ends stays inside the bound.
- Contradicted: each end carrying a value fixed in advance. It caps S at 2; every measurement above sits above 2 (Bell 1964, CHSH 1969).
- Contradicted: a rope that carries a push. Turning one end never changes the other end's own counts.
- Contradicted: a fourth direction for the rope to run through. No instrument reads one (Lee et al. 2020; CMS 2018), and the numbers above need none.
Sources: Clauser, Horne, Shimony, Holt 1969 (the S used); Freedman, Clauser 1972; Aspect, Grangier, Roger 1982, PRL 49, 91; Hensen et al. 2015, Nature 526, 682; Yin et al. 2017, Science 356, 1140; Tsirelson 1980. The correlation formulas shown are the textbook ones; nothing here goes beyond them.