ARb»MM£su; %eieasemw?%iymmw&m200080052 -7
3 April 1972
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. Flatte,
J. H. Friedman,
G. R. Lynch,
M.
J. Matison,
J.
J. Murray, M.
S. Rabin,
F. T.
Solmitz,
N.
J. Uyeda,
V. Waluch,
and R. Wind-
molders.
FIG. 4,
(a) G 2 and (b) G s 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
ir"’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
*Work supported by the U. S. Atomic Energy Commis-
sion under Contract No. AT(04-3)-34 PA 191.
K. G. Wilson,
Cornell University Report No, CLNS-
131,
1970 (to be published).
2W. R. Fraser et dl„
to be published.
H. D.
I. Abarbanel, Phys. Rev. D 3, 2227 (1971).
Il. C. Hwa,
to be published.
5D. Z. Freedman,
E.
C. E. Jones, F. E. Low, and J
Young, Phys. Rev. Lett. 26,
1197 (1971),
6 C. E. DeTar, Phys. Rev. D 3, 128 (1971).
7A. Bassetto, M. Toller, and L. Sertorie, Nucl. Phys
B34,
1 (1971).
®A. Mueller, Phys. Rev. D 4,
150 (1971).
9W. Ko and R. L. Lander, Phys. Rev. Lett. 26, 1064
(1971).
—
10J. Erwin, W. Ko, R. L. Lander, D. E. Pellett, and
P. M. Yager, Phys. Rev. Lett. 27, 1534 (1971).
11 The correlation length, of about I 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(unpublished), and Ref.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 2
is only achieved for the center-center corre-
lation if the intercept of exotic trajectories (as the ir"-
ir
channel has exotic quantum numbers) 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.
I1. T. Nieh and J. M. Wang,
to be published.
Experimental Test of Local Hidden-Variable Theories*
Stuart J. Freedman and John F. Clauser
eparmen
of P ysics and Lawrence Berkeley Laboratory,
University of California, Berkeley,
California 94720
(Received 4 February 1972)
We have measured the linear polarization correlation of the photons emitted in an atom-
.
ie 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 was first developed,
there have been repeated suggestions that its sta-
tistical features possibly might be described by
an underlying deterministic substructure.
Such
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-
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FIG. 2.
Level scheme of calcium.
Dashed lines show
the route for excitation to the initial state 4p
lS0 .
that of Kocher and Commins .
8 A calcium atomic
beam effused from a tantalum oven,
as shown in
I*
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
.Pj state.
Of the atoms that did not decay direct-
ly to the ground state,
about 7% decayed to the
4p
z lS0 state, from which they cascaded through
the 4s4p lP l intermediate state to the ground
state with the emission of two photons at 5513 A
(Fi) and 4227 A (y2 ) (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 1 XIO10 atoms/cm 3
.
To avoid spherical
aberrations which would have reduced counter ef-
ficiencies,
aspheric primary lenses
(8.0 cm
diam, f
0.8) were used.
Photons yl were select-
ed by a filter with 10 A FWHM and 50% transmis-
sion, and
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 22 j°.
The measured transmittances of the polarizers
were e/ =0.97
±
0 . 01
,
em
l =0.038 ± 0.004, e/
-0.96±0.01, and e m
2 =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-
larizers removed were
77 , ~ 1.7X10
‘ 3 and n -15
xiQ-s.a
' 2
'
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 . 10 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 . 11
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(<p)/R0 was calculated by summing counts
for all configurations corresponding to angle
<p
and dividing by half the sum of the counts in the
adjacent periods of the sequence in which both
polarizers were moved.
Data for RjR0 and RJ
R0 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(<p)/R0 , 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 22£° and
67|-
, we obtain 6 =0.050 ±0.008 in clear violation
of inequality (3 ). 12
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-
I
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VcKfiME 28HNUMBER 14
^PHYSICAL REVIEW LETTERS^
3 April 1972
• 5
r
FIG. 3.
Coincidence rate with angleV between the
polarizers, divided by the rate with both polarizers re-
moved,
plotted versus the angle
</>.
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.
1The best-known proof is by J. von Neumann, Mathe-
matische Grundlagen der Quanlemechanik (Springer,
Berlin,
1932) [Mathematical Foundations of Quantum
Mechanics (Princeton Univ. Press. Princeton, N. J.,
1955)1.
For a critical review of this and other proofs
see J. S. Bell, Rev. Mod. Phys. 38, 447 (1966).
2J. S. Bell,
Physics (Long Is. City,
N.Y.)
1,
195
(1964).
3J. Clauser, M. Horne, A. Shimony, and R. Holt,
Phys. Rev. Lett. 23,
880 (1969).
4A hidden-variable theory need not require that R t and
•ft 2 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
fti and R 2 being independent of angle, and for simplicity
they are so denoted.
5M. 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).
eThis assumption is much weaker than the assumption
made by L. R. Kasday,
J. Ullman, and C. S. Wu,
Bull.
Amer. Phys. Soc. 16, 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).
7 The inequality A((p) =£ 0 is 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)
.
SC. 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).
9The counter efficiencies are given by
i
i
t = (ft (/4r)Tj
Xe j£(, where
is the solid angle, T
i is the transmis-
sion of the filter,
e
4 is the quantum efficiency, and Lt
accounts for other losses.
The measurement of
J) 2 was
made, employing the properties of the calcium cascade,
by comparing the coincidence rate and the y 1 singles
rate after suitable background correction;
ij t was then
inferred from the known quantum efficiencies and filter
transmissions assuming that
and L i were the same
for both detector systems.
10An 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
for the data presented.
“Resonance trapping, encountered at high beam densi-
ties,
resulted in a lengthening of the observed lifetime
and a slight decrease in the polarization correlation am-
plitude, see J. P. Barrat, J. Phys. Radium 20, 641, 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. S. National Bureau of Stan-
dards Reference Data Series—22 (U.S. GPO, Washing-
ton,
D.C.,
1969), Vol. 2.
12The results that are of interest in comparison with
the hidden-variable inequalities are A i/R 0 = 0.497 ±0.009,
•ft
/ft 0 = 0.499 ±0.009, R(224°)/A 0 = 0.400 ±0.007, and
R(67-f°)/fto =0.100 ±0.003. We thus obtain A(22-i°)
= 0.104 ±0.026 and A(67-£°) =— 1.097 ±0.018,
in violation
of inequalities
(2)
.
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