File:Bell.svg

The best possible local realist imitation (red) for the quantum correlation of two spins in the singlet state (blue), insisting on perfect anti-correlation at zero degrees, perfect correlation at 180 degrees. Many other possibilities exist for the classical correlation subject to these side conditions, but all are characterized by sharp peaks (and valleys) at 0, 180, 360 degrees, and none has more extreme values (+/-0.5) at 45, 135, 225, 315 degrees. These values are marked by stars in the graph, and are the values measured in a standard Bell-CHSH type experiment: QM allows , local realism predicts or less. svg("Bell.svg", width = 7, height = 6)

plot(0, 0, xlim = c(0, 2), ylim = c(-1, 1), type = "n", axes = FALSE, ylab="", xlab = "", mar = c(1, 1, 1, 1))

x <- seq(from = 0, to = 2, length = 181)

lines(x, -cos(pi*x), col = "blue", lwd = 2)

lines(c(0, 1, 2), c(-1, 1, -1), col = "red", lwd = 2)

lines(c(0, 2, 2, 0,0), c(-1, -1, 1, 1, -1))

abline(h=0)

legend(0.05, 0.95, legend = c("Quantum", "Classical"), lwd = c(2, 2), col = c("blue", "red"))

text(c(0, 1/2, 1, 3/2, 2), -0.1, labels = c(0,90, 180, 270, 360), cex = 1.5 )

text(-0.05, c(-1, 0, 1), c(-1, 0, 1), cex=1.5)

text(-0.2, 0, "Correlation", srt = 90, cex = 1.5, pos = 1, xpd = NA)

text( 1.0, -1.1, "Angle between detectors (in degrees)", cex = 1.5, pos = 1, xpd = NA)