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There are two main avenues of escape from the logic of Bell's Theorem
in quantum physics with its implication of "quantum nonlocality". One
can either argue that Bell's logic was wrong and his inequality can be infringed without implying nonlocal effects; or one may
challenge the experimental evidence and the correctness of the quantum-mechanical prediction. The whole topic has come to be
known as "loophole-hunting", but this page is concerned only with the latter: the experimental loopholes.
The Bell tests (tests designed to discriminate between quantum theory with its "entanglement" of separated particles and "local realism") performed in the actual "EPR" experiments are not quite the original ones that Bell proposed. Most experiments in
practice have been done using light, and this cannot be detected with 100% efficiency. In consequence the test had to be
modified, and along with the modification went certain assumptions.
There are currently two main groups of test in use, the most popular being known
as the CHSH test. This is named after Clauser, Horne, Shimony and Holt, who wrote the 1969 paper to which the test is attributed,
though they never in fact supported its use in the way that has become customary (cf. CHSH inequality). The "visibility" test and similar are related to this test. All in the group require the
assumption of "fair sampling". The other group of tests I shall refer to as the CH74 tests, after the 1974 paper in which Clauser
and Horne specified it. This test assumes "no enhancement" but does not, despite common belief by almost everyone concerned,
require fair sampling.
The fair sampling loophole (otherwise known as the detection, efficiency or
variable detection probability loophole) can readily be shown to be a genuine problem, liable to bias the CHSH
test. If the logic of the experiments is studied in conjunction with the geometry it can be seen that, given the low
detection efficiencies achieved in the actual experiments, the set of detected pairs is unlikely in general to be a fair sample
of those emitted (see the "Chaotic Ball" model ). No enhancement, on the other hand, merely
means that the insertion of a polariser does not increase the chance of detection. This is a far more acceptable assumption, and
the CH74 test was in fact the one of choice for all experiments prior to Alain Aspect's "two-channel" one (Aspect, 1982a ).
In the optical Bell tests there are in addition other experimental loopholes, associated with the failure of
various assumptions , whether explicit or implicit in
the experimental design. The subtraction of accidentals loophole -- in a few experiments potentially of great
importance -- is discussed in detail in a paper referenced below, together with a brief summary of several others.
Apart from the fair sampling one, loopholes gain on the whole little attention, not being in themselves of any great
theoretical interest. The only other loophole likely to be encountered in the literature is one that does not quite qualify to be
called an "experimental loophole", since its failure does not lead to any realistic explanations and there is no a
priori reason to expect its presence. It is the timing, locality or light
cone one, whereby the violation of the inequality is supposed to be due to exchange of signals between the detectors
during flight of the "photons". Elaborate experiments (Aspect,1982b ;Weihs 1998
) have been conducted to rule this possibility
out.
Recently experiments have been conducted that use detectors that are almost 100% efficient, thus avoiding the fair sampling
loophole. They are claimed to depend on entanglement between two ions in the same linear laser trap. Though it would be
satisfying to provide physical explanations for the violation of Bell tests here, the urgency is not so great: the ions are so
close together that Bell's basic assumption -- that the two measurements should be made on particles that are too far apart to
interact by normal methods -- is not met. All Bell tests depend on the assumption that the detection events are, once the "hidden
variable" values and detector settings are given, conducted independently on the two particles.
Conclusion
The fair sampling loophole casts doubt on the majority of claims for experimental support for quantum entanglement. Where it
does not apply, other loopholes are present. For convincing comfirmation of the phenomenon, all loopholes must be closed
at once. The search for a loophole-free experiment continues.
Further external references
Practical Versions of the Bell test:
- J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Proposed experiment to test local hidden-variable theories,
Physical Review Letters 23, 880-884 (1969)
- J. F. Clauser and M. A. Horne, Experimental consequences of objective local theories, Physical Review D, 10, 526-35
(1974)
Loopholes:
- Caroline Thompson's Physics Site
- C. H. Thompson, Setting the Record Straight on Quantum
Entanglement (2004). This not only
explains the detection loophole intuitively (via the Chaotic Ball model) but also puts the matter in context, explaining why the
loopholes are so poorly understood even amongst the experts.
- T. W. Marshall, E. Santos and F. Selleri, F, Local Realism has not been Refuted by Atomic-Cascade Experiments,
Physics Letters A, 98, 5-9 (1983)
- C. H. Thompson, Subtraction of 'accidentals' and the validity of Bell tests , Galilean Electrodynamics 14 (3), 43-50 (May 2003)
Experiments on trapped ions:
- M. Rowe et al.,Experimental violation of a
Bell’s inequality with efficient detection ,
Nature 409, 791 (2001)
- D. Kielpinski, David et al, Recent Results in Trapped-Ion Quantum Computing (2001)
- L. Vaidman, Bell's inequality: more tests are needed (2001)
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