| 4 Approved. Ear Release SDMUAI/ZE i GIARBE2G-00787R 009 200080052-7, APRIL 1972 ee 400 “200 fe} . N a ° g 5 a a a 5 2 -200 -400 6 PRONGS 400 10 < 200 o oe t & t a. Lo) « e) o 5 w a Qo 2 2 -200 ~400 8 PRONGS -4 -2 0 2 4 FIG, 4. (a) G, and (b) G, as defined in the text, The statistics on the eight-prong data are not good but show characteristics similar to those for six-prong. We present this dramatic behavior of the two m”’s as functions of their rapidity separation as a challenge to any theory of inclusive reactions. The author wishes to thank Richard Lander for his support-and encouragement. The author also appreciates the many useful discussions with him, David Pellett, and Philip Yager. He also benefit- ted from stimulating conversations with William Fraser and Rudolph Hwa. He is indebted to the following members of Group A at the Lawrence Berkeley Laboratory for generously allowing him to participate in the analysis of the K* exposure: M. Alston-Ganjost, A. Barbaro-Galtieri, P. J. Davis, S. M. Flatté, J. H. Friedman, G. R. Lynch, M. J. Matison, J. J. Murray, M. 8, Rabin, F. T. Solmitz, N. J. Uyeda, V. Waluch, and R, Wind- molders, *Work supported by the U. S. Atomic Energy Commis- : sion under Contract No, AT(04-3)=34 PA 191, 'kK, G. Wilson, Cornell University Report No, CLNS- , 131, 1970 (to be published), *w. R. Fraser et al., to be published, "H. D. L, Abarbanel, Phys, Rev, D 8, 2227 (1971), ‘RL C. Hwa, to be published, *D, Z. Freedman, C. E, Jones, F. E, Low, and J. E. Young, Phys, Rev. Lett. 26, 1197 (1971), °c. E, DeTar, Phys. Rev. D 8, 128 (1971). "A, Bassetto, M.-Toller, and L. Sertorie, Nucl, Phys, B34, 1 (1971), ~ TA, Mueller, Phys, Rev. D4, 150 (1971). *w. Ko and R. L, Lander, Phys. Rev. Lett. 26, 1064 (1971). a "J, Erwin, W. Ko, R. L, Lander, D. E. Pellett, and P. M. Yager, Phys, Rev. Lett, 27, 1534 (1971), “The correlation length.of about $ is even shorter than the short-range Mueller—Regge-theoretical value [R. C, Arnold, ANL Report No, ANL-HEP 7139, 1971 (unpublished), and Ref. 5}. In that theory a correlation length of % is only achieved for the center-center corre- lation if the intercept of exotic trajectories (as the 7m - a” channel has exotic quantum nuinbers) is — 1 [W. Ko, R. L, Lander, and C. Risk, Phys. Rev. Lett, 27, 1476 (1971)]. The correlation length of 1 or 2 is usually pre- dicted for fragment~center or fragment-fragment cor- relations. "1. 'T. Nieh and J, M. Wang, to be published, Experimental Test of Local Hidden-Variable Theories* Stuart J. Freedman and John F, Clauser Depariment of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, Californta 94720 (Received 4 February 1972) We have measured the linear polarization correlation of the photons emitted in an atom- ic cascade of calcium. It has been shown by a generalization of Bell's inequality that the - existence of local hidden variables imposes restrictions on this correlation in conflict | with the predictions of quantum mechanics. Our data, in agreement with quantum me- ; : chanics, violate these restrictions to high statistical accuracy, thus providing strong evi- . dence against local hidden-variable theories. Since quantum mechanics ae first developed, there have been repeated s ggestions that its sta- tistical features possibly might be described by an underlying deterministic substructure. Such ” ra’ 938 ne ear a The toys features, then, arise because.a quantum state . represents a statistical ensemble of “hidden- * variable states.” Proofs by von Neumann and others, demonstrating the impossibility of a hid-
Approved:kion Release QpA'03/28 : GIASRDR94-PO787RAQ9200080052-7, EE Ee ieee A 1972 4p? 's, 4p4s'p, 4s2 So FIG. 2. Level scheme of calcium. Dashed lines show the route for excitation to the initial state 4p's), that of Kocher and Commins.® A calcium atomic beam effused from a tantalum oven, as shown in Fig. 1. The continuum output of a deuterium arc lamp (ORIEL C-42-72-12) was passed through an interference filter [250 A full width at half-maxi- mum (FWHM), 20% transmission at 2275 A] and focused on the beam. Resonance absorption of a 2275-A photon excited calcium atoms to the 3d4p *P, state. Of the atoms that did not decay direct- ly to the ground state, about 7% decayed to the 4p°'S, state, from which they cascaded through the 4s4p Pp intermediate state to the ground state with the emission of two photons at 5513 A (4) and 4227 A (7,) (see Fig. 2). At the interac- tion region (roughly, a cylinder 5 mm high and 3 mm in diameter) the density of the calcium was - about 1x10° atoms/cm’, To avoid spherical aberrations which would have reduced counter ef- ficiencies, aspheric primary lenses (8.0 em diam, f=0.8) were used. Photons % were select- ed by a filter with 10 A FWHM and 50% transmis- sion, and y, by a filter with 6 A FWHM and 20% transmission, The requirement for large effi- cient linear polarizers led us to employ “pile-of- plates” polarizers, Each polarizer consisted of ten 0.3-mm-thick glass sheets inclined nearly at Brewster’s angle. The sheets were attached to hinged frames, and could be folded completely out of the optical path. A Geneva mechanism ro- tated,each polarizer through increments of 222°, The measured transmittances of the polarizers were €,'=0.9740.01, ©, =0.038+ 0.004, €,? =0.9640.01, and €,?=0.037+0.004. The photo- multiplier detectors (RCA C31000E, quantum ef- ficiency ~0.13 at 5513 A; and RCA 8850, quantum efficiency = 0.28 at 4227 A) were cooled, reducing dark rates to 75 and 200 counts/sec, respective- ly. The measured counter efficiencies with po- 940 larizers removed were 7, *1,7X 10°° and 9, =1.5 x1078,9 A diagram of the electronics is included in Fig. 1, The overall system time resolution was about 1.5 nsec, The short intermediate state lifetime (~5 nsec) permitted a narrow coincidence window (8.1 nsec). A second coincidence channel dis- placed in time by 50 nsec monitored the number of accidental coincidences, the true coincidence rate being determined by subtraction.’° A time~ to-amplitude converter and pulse-height analyzer measured the time-delay spectrum of the two photons. The resulting exponential gave the in- termediate state lifetime, The coincidence rates depended upon the beam and lamp intensities, the latter gradually decreas- ing during a run. The typical coincidence rate with polarizers removed ranged from 0.3 to 0.1 _ countx/sec, and the accidental rate ranged from 0.01 to 0.002 counts/sec. Long runs required by the low coincidence rate necessitated automatic data collections. — The system was cycled with 100-sec counting periods, Periods with one or both polarizers in- serted alternated with periods in which both po-: larizers were removed, Both polarizers rotated according to a prescribed sequence, For a given run, R(v)/R, was calculated by summing counts for all configurations corresponding to angle ¢ and dividing by half the sum of the counts in the adjacent periods of the sequence in which both polarizers were moved, Data for R,/R, and R,/ R, were analyzed in a similar fashion. The val- ues given here are averages over the orientation of the inserted polarizer, This cycling and aver- aging procedure minimized the effects of drift and apparatus asymmetry. The results of the measurements of the corre- lation R(¢)/R,, corresponding to a total integra- tion time of ~ 200 h, are shown in Fig. 3, All er- ror limits are conservative estimates of 1 stan- dard deviation, Using the values at 222° and 674°, we obtain 5 =0.050 + 0.008 in clear violation of inequality (3).17 Furthermore, we observe no evidence for a deviation from the predictions of quantum mechanics, calculated from the mea- sured polarizer efficiences and solid angles, and shown as the solid curve in Fig. 3. We consider these results to be strong evidence against local hidden-variable theories, The authors wish to express their sincerest ap- preciation for guidance and help from Professor Eugene Commins, to Professor Charles Townes for his encouragement of this work, and to M. Sim-
- ete MBER ved For Release 2001/03/26 : GIA RDP96- ‘00787 RQQ9200080052-7 3 AprIL 1972 = ) 22% «45 674 90 ANGLE ¢@ IN DEGREES FIG. 3. Coincidence rate with angle y between the polarizers, divided by the rate with both polarizers re- moved, plotted versus the angle y. The solid line is the prediction by quantum mechanics, calculated using the measured efficiencies of the polarizers and solid angles of the experiment. mons for helpful suggestions. ‘Work supported by U.S. Atomic Energy Commission. ‘The best-known proof is by J. von Neumann, Mathe~ matische Grundlagen der Quantemechanik (Springer, Berlin, 1932) [Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press. Princeton, N. J., 1955)]. For a critical review of this and other proofs see J. &. Bell, Rev. Mod. Phys. 38, 447 (1966). *J. S. Bell, Physics (Long Is. City, N.Y.) 1, 195 (1964). ay, Clauser, M. Horne, A. Shimony, and R. Holt, Phys. Rev. Lett. 23, 880 (1969). 44 hidden-variable theory need not require that R, and R, be independent of the orientation of the inserted po- larizer, and we do not assume this independence in our data analysis. However, the results are consistent with R, and R» being independent of angle, and for simplicity they are so denoted. °M. Horne, Ph. D. thesis, Boston University, 1970 (unpublished). See also A. Shimony, in “Foundations of Quantum Mechanics, Proceedings of the International School of Physics ‘Enrico Fermi,’ Course IL” (Academ- ic, New York, to be published). ®This assumption is much weaker than the assumption made by L. R. Kasday, J. Ullman, and C. 8. Wu, Bull. Amer. Phys. Soc. 15, 586 (1970), in their discussion of the two-y decay of positronium; see L. R. Kasday, in “Foundations of Quantum Mechanics, Proceedings of the International School of Physics ‘Enrico Fermi,’ Course IL” (Academic, New York, to be published). "The inequality A(y) <0 ig derived in Refs. 3 and 5. The other forms of the hidden-variable restriction are obtained by similar arguments; see S. Freedman, Ph. D. thesis, University of California, Berkeley, Lawrence Berkeley Laboratory Report No. LBL-391, 1972 (un- published). : 5G. A. Kocher and E. D. Commins, Phys. Rev. Lett. 18, 575 (1967); C. A. Kocher, Ph. D. thesis, University of California, Berkeley, Lawrence Berkeley Labora- tory Report No. UCRL-17587, 1967 (unpublished). "The counter efficiencies are given by = (Q,/40)T, x€,L,, where Q, is the solid angle, 7; is the transmis- sion of the filter, €, is the quantum efficiency, and ly accounts for other losses. The measurement of 7, was made, employing the properties of the calcium cascade, by comparing the coincidence rate and the 7; singles rate after suitable background correction; 7; was then inferred from the known quantum efficiencies and filter transmissions assuming that Q; and L; were the same for both detector systems. ‘an estimate of the accidental rate was also obtained from the singles rates. The two estimates gave consis- tent results. In fact, our.conclusions are not changed if accidentals are neglected entirely; the signal-to-ac- cidental ratio with polarizer removed is about 40 to 1 for the data presented. ‘tResonance trapping, encountered at high beam densi- ties, resulted in a lengthening of the observed lifetime and a slight decrease in the polarization correlationam-~ plitude, see J. P. Barrat, J. Phys. Radium 20, 541, 633 (1959). At low beam densities the measured lifetime is consistent with previously measured values. See W. L. Weise, M. W. Smith, and B. M. Miles, Atomic Transition Probabilities, U. 8. National Bureau of Stan- dards Reference Data Series—22 (U.S. GPO, Washing- ton, D.C., 1969), Vol. 2. the results that are of interest in comparison with the hidden-variable inequalities are R,/R)=0.497 £0,009, R,/R = 0.499 0.009, R(224°)/R,=0.400 +0.007, and R(674°)/Ry=0.100 +0.003. We thus obtain A(2244 =0.104+0.026 and A (6749 =—1.09740.018, in violation of inequalities (2). 941