Plate I

On the Correlation of Divided Pairs

being the apparatus of Bell, drawn to the life, with its readings taken under two suppositions

Classical Quantum

the supposition under which the pairs are decided

4 pairs / sec.

turn to set the oven's pace

Fig. 1. — The oven, which divides an atom into a pair and sends one each way through a slit. Each pair carries one secret, or none, as the supposition holds.

0°

turn to rotate the magnet

Fig. 2. — Magnet A, of Stern and Gerlach: a wound yoke, a knife-edge pole above the beam and a channelled pole beneath, turned in its ring.

45°

turn to rotate the magnet

Fig. 3. — Magnet B, the same, set on the far side of the oven and turned as the reader pleases.

0 above · 0 below

Fig. 4. — The plate behind Magnet A. Each atom leaves a grain, above or below the line.

0 above · 0 below

Fig. 5. — The plate behind Magnet B.

The Ledger of Coincidences

both above	0
A above, B below	0
A below, B above	0
both below	0
pairs	0

—of pairs answered alike, the magnets 45° apart

the classical supposition expects 25% divergence from it — the quantum supposition expects 15% divergence from it —

classical: a hidden directionquantum: one wave functionas measured

Fig. 6. — The correlation of the two answers against the angle between the magnets. A dot is set down for every angle tried, once twenty-five pairs have crossed it.

Of the apparatus. The oven divides an atom into two and sends one each way. Each magnet sorts its atom to the upper pole or the lower, along the magnet's own axis, and the atom leaves its grain on the plate behind. Turn a dial and the magnet turns in its ring. The ledger counts how often the two plates agree, and the chart sets down that agreement as a dot for every angle the reader has tried.

The classical supposition. Each pair leaves the oven with one hidden direction, drawn by lot. Each atom answers with the pole nearest that direction. Nothing about Magnet A can reach Magnet B. This is the best any local story can do, and it draws the straight dashed line: the agreement changes evenly with the angle.

The quantum supposition. The pair is one wave function. Whichever atom is measured first collapses it, and the other then answers with odds that follow the cosine of the angle between the magnets. That is the solid curve. At 45° apart it parts from the straight line by a fifth, and no hidden direction can be drawn that lands there.

The proof. Set the magnets 45° apart and move the slider. Let the plates fill. The dot settles on one curve or the other, and in the laboratory it settles on the cosine. Bell showed that no story in which each atom carries its own answer from the oven can bend the line so far. Something of the pair is shared at the moment of measurement, however far apart the magnets stand.

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