426 The Einstein-Podolsky-Rosen Paradoxthe University of Geneva and his collaborators performed theexperiment with detectors in the Swiss villages of Bellevue andBernex, separated by nearly seven miles.6.2 Experiment 6.2: Random distant measurementsThis experiment is called the "test of Bell's theorem". The reasoning isintricate, so I give an outline here before plunging into the details. Wewill build an apparatus much like the previous one with a central sourcethat produces a pair of atoms, and with two detector boxes. Mountedatop each detector box are a red lamp and a green lamp. Every timethe experiment is run, a single lamp on each detector box lights up. Onsome runs the detector on the left flashes red and the detector on theright flashes green, on other runs both detectors flash red, etc. When theof each detector flashing a different color is. But we can also analyzeapparatus is analyzed by quantum mechanics, we find that the probabilitythe apparatus under the assumption of local determinism. This analysisshows that the probability of each detector flashing a different color isor more. (Exactly how much more depends on exactly which localdeterministic scheme is employed, see problem 6.4.) Experiment agreeswith quantum mechanics, so the assumption of local determinism, naturalthough it may be, is false. Any local deterministic scheme, including thesecond alternative interpretation mentioned on page 38, must be wrong.The apparatusThis experiment uses the same source as the previous experiment, butnow the detectors are not regular Stern-Gerlach analyzers, but the tiltingStern-Gerlach analyzers described in section 5.3 (page 33). Each of thetwo analyzers has probability of being oriented as A, B, or C. If youwish, you may set the detector orientations and then have the sourcegenerate its pair of atoms, but you will get the same results if you firstlaunch the two atoms and then set the detector orientations while theatoms are in flight. Mounted on each detector are two colored lamps. Ifan atom comes out of the + exit, the red lamp flashes; if an atom comesout the exit, the green lamp flashes.<<-0source06.2 Experiment 6.2: Random distant measurementsThe prediction of quantum mechanicsIf the two detectors happen to have the same orientation, then thisexperiment is exactly the same as the previous one, so exactly the sameresults are obtained: the two detectors always flash different colors. Onthe other hand, if the two detectors have different orientations, then theymight or might not flash different colors.What is the probability that the two detectors flash different colors ingeneral, that is, when the two detectors might or might not have thesame orientation? Suppose the detector on the left is closer to the sourcethan the detector on the right. If the left detector were set to A andflashed green (that is, -), then the atom on the right has m = +mB.In the previous chapter we saw that when such an atom enters the rightdetector, it has probability of causing a red flash and probability ofcausing a green flash. You can readily generalize this reasoning to showthat regardless of orientation, the two detectors flash different colors withprobability.We conclude that:43(1) If the orientation settings are the same, then the two detectorsflash different colors always.(2) If the orientation settings are ignored, then the two detectorsflash different colors with probability.And these results are indeed observed!The prediction of local determinismIn any local deterministic scheme, each atom must leave the source alreadysupplied with an instruction set that determines which lamp flashes foreach of the three orientation settings. For example, an instruction setmight read (if set to A then flash red, if set to B then flash red, if setto C then flash green), which we abbreviate as (RRG). One natural wayto implement an instruction set scheme would be through the atom'sassociated magnetic arrow: if the detector is vertical (orientation A) andthe atom's arrow points anywhere north of the equator, then the atomleaves through the + exit, while if the atom's arrow points anywhere southof the equator, then the atom leaves through the exit. Similar rules holdfor orientations B and C: the atom always leaves through the exit towardswhich its arrow most closely points. The argument that follows holds forThis postulated scheme is inconsistent with quantum mechanics because it assumes that an atom'smagnetic arrow points in the same manner that a classical stick does, with definite values for allthree projections my, my, and m, simultaneously. 6.3 A probability found through quantum mechanics. In the test of Bell'stheorem, experiment 6.2, what is the probability given by quantummechanics that, if the orientation settings are different, the twodetectors will flash different colors?

In the test of Bell's theorem, the probability given by quantum mechanics that the two detectors…

Answered: 3 A probability found through quantum…