Bell's theorem : experimental tests and implications - Physics at ...

Bell's theorem: experimental tests and implications 19095.3.1. Experiment by Freedman and Clauser (1972). Freedman and Clauser (1972, seealso Freedman 1972) observed the 5513 a and 4227 A pairs produced by the4p2 1So+4p4s 1P1+4sz IS0 cascade in calcium. Their arrangement is shown schematicallyin figure 5. Calcium atoms in a beam from an oven were excited by resonanceabsorption to the 3d4p 1P1 level, from which a considerable fraction decayed to the4p2 WO state at the top of the cascade. No precaution was necessary for eliminatingisotopes with non-zero nuclear spin, since 99.855% of naturally occurring calcium haszero nuclear spin. Pile-of-plates polarisation analysers were used, with transmittances~~1=0.97 k 0.01, ~~1=0*038 & 0.004, €$=Om96 k 0.01, ~,2=0*037 f 0.004. Eachanalyser could be rotated by angular increments of n/8, and the plates could be foldedout of the optical path on hinged frames. The half-angle 6 subtended by the primarylenses was 30". Coincidence counting was done for 100 s periods; periods duringwhich all plates were removed alternated with periods during which all were inserted.In each run the ratios R(n/S)/Ro and R(3n/8)/& were determined. Corrections weremade for accidental coincidences, but even without this correction, the results stillsignificantly violated inequality (5.6). The average ratios for roughly 200 h of runningtime are:[R(n/S)/Ro]expt= 0.400 & 0.007[R(3~/8)/Ro]expt= 0.100 f 0.003and therefore:[R(n/8)/Ro - R(3~/8)/Ro]expt= 0.300 f 0.008in clear disagreement with inequality (5.6). The quantum-mechanical predictionsare obtained from equation (5.15) (with allowances for uncertainties in the measurementof the transmittances and the subtended angle) :[R(n/8)/Ro-R(3n/8)/Ro]QM=(0'401 & 0*005)- (0.100 & 0*005)=0*301 f 0,007.The agreement between the experimental results with the quantum-mechanicalpredictions is excellent. Agreement is also found for other values of the angle $, aswell as for measurements made with only one or the other polariser removed.5.3.2. Experiment by Holt and Pipkin (1973). Holt and Pipkin (1973, see also Holt1973) observed 5676 A and 4047 A photon pairs produced by the 91P1-+73S1+63Pocascade in the zero nuclear-spin isotope 198Hg (see figure 6 for a partial level diagramof mercury). Atoms were excited to the glP1 level by a 100 eV electron beam. Thedensity matrix of the glP1 level was found to be approximately Q I by measurementsof the polarisation of the 5676 A photons, so that equation (5.15) with Fl(6) replacedby - F2(f) is used to calculate the quantum-mechanical predictions for the coincidencecounting rates. Calcite prisms were employed as polarisation analysers, withmeasured transmittances :~~1=0*910 2 0.001 €M2=0*880 & 0.001< 10-4 10-4.The half-angle f was taken to be 13 O (F413") = 0.9509). The quantum-mechanicalprediction is :[R(3n/8)/RO- R(n/8)/Ro]QM=0*333 - 0*067= 0.266which only marginally exceeds the value & allowed by inequality (5.6). The experimentalresult in 154.5 h of coincidence counting, however, is:[R(3n/8)/Ro-R(.rr/8)/Ro],xpt=0.316 5 0.011 -0.099 & 0*009=0.216+ 0.013