On one set of runs (1“A,” 2 “C”) can measure correlation of A and C 10 km A C 1  2  SOURCE OF PAIRS ~ ~ B D SWITCH SWITCH A, B, C, D = ± 1. But for each pair, measure either A or B, and either C or D, not both. On one set of runs (1“A,” 2 “C”) can measure correlation of A and C A simple argument: For each particle 1, either A=+1 or A = -1, irrespective of whether A actually measured. Value of A unaffected by whether C or D was measured on “partner” (2) (etc.).  for each pair, quantities AC, AD, BC, BD exist, with A, B, C, D = ± 1 and A the same in (AC, AD) (etc.) Simple algebra  for each pair, Hence the correlations satisfy the inequality Obvious, right? So, let’s do the experiment. . . (“” = “cannot exceed”)

K cannot be greater than 2 (under any conditions) Recap: The simple argument says: K cannot be greater than 2 (under any conditions) Experiment finds that (under certain conditions) K is approximately 2 • 8! So, what has gone wrong? According to quantum mechanics, the idea that physical systems “have” definite properties even when these are not measured is just wrong. If we “inspect,” behavior is consistent with the “common-sense” idea that each system took either path 1 or path 2. If we do not “inspect,” behavior is NOT consistent with this assumption. INSPECTION “OPTIONAL” 1 SOURCE DETECTOR 2

PHOTONS In quantum mechanics, light comes in irreducible “chunks” —photons. A photon can have its “polarization” (direction of electric field) in any direction in the plane perpendicular to its motion. We can ask the photon “are you red or green?” with respect to any pair of perpendicular axes in the plane, eg. OR OR OR… If the photon polarization is exactly along red, it will answer “red..” If it is exactly along green, it will answer “green.” If the polarization is along some intermediate direction, e.g. Then it will sometimes answer “red” and sometimes “green.” . . . .

TWO IMPORTANT CONSEQUENCES OF QUANTUM MECHANICS FOR PHOTONS: “NO-CLONING” THEOREM: It is impossible to build a device which is guaranteed to take a photon of arbitrary (unknown) polarization and produce accurate copies of it. (e.g. with , can copy or but not ) EPR PAIRS: It is possible to produce pairs of photons such that for any choice of measurement direction, if 1 replies “red” (“green”) then so does 2. Note: photon polarization can be “mapped” onto two states of particle of spin ½ ( maps to “  ”, to “ ”)