BELL’S INEQUALITY: A Distinction between Local Reality and Quantum Mechanics Theory | Quantum Science Philippines
Quantum Science Philippines

BELL’S INEQUALITY: A Distinction between Local Reality and Quantum Mechanics Theory

Marichu M. Tompong-Miscala

Local realism is the idea that an object has definite properties or assumes a definite state without being affected by the act of measurement [1]. This belief is especially contrary to the probabilistic ( not deterministic ) characteristic of quantum mechanics.

In 1965, John S. Bell had proposed a mathematical proof or designed several experiments that would test the consistency of quantum mechanics, and hence the inconsistency of the local reality. This has brought the idea that quantum mechanics is an incomplete theory. That is, physical properties such as momentum and position were absolute values and that when they exist, whether they were measured or not, an inequality ( Bell’s inequality), would then be satisfied. But later on this theory was the subject of considerable interests and debates, and loopholes are uncovered by the much refined experiments. Moreover, several proposals for closing this loophole have been made as well, and previous investigation was reported.

Early experiments such as the experiment in the correlation measurements in the classical properties of massive entangled particles Be+ ions, were made to test Bell’s inequalities and these were subject to two primary loopholes. The first primary loophole might be termed as ‘locality’ or ‘lightcone’ loophole, in which the correlations of apparently separate events, could result from unknown subluminal ‘signals’ propagating between different regions of the apparatus. These correlations violate a form of Bell’s inequality which was obtained by a complete set of measurements. Here, the appropriate ‘Bell’s signal’ is  2.25 +/- 0.03, whereas a value maximum of 2 is the only allowable value by local realist. Similar results have also been reported for the Geneva experiment [2]. The second loophole is usually referred to as the detection loophole. Here, every experiments is assumed to have had detection efficiencies low enough to allow the possibility that the sub-ensemble of detected events agrees with quantum mechanics even though the entire ensemble satisfies Bell’s inequalities. Conversely saying, the detected events thus represent the entire ensemble; a fair-sampling hypothesis. Thus, in the presence of an ‘accurate set’ of measurements, Bell’s inequalities are violated. Meaning, as a way of eliminating the so-called “detection-loophole”, more high-detection efficiency experiments were designed that would put distinction between what local realism is, and when the quantum mechanics theory should be applied.

[1]  M.A. Rowe, D. Kielspinski, V. Meyer, C.A. Sackett, W.M. Itano, C. Monroe, and D.J. Wineland. Experimental violation of a Bell’s inequality with efficient detection. Letters to nature. Nature 791, Vol 409 (2001)

[2]  Tittel, W., Brendel J., Zbinden H. and Gisin N. Violation of Bell’s Inequalities by photons more than 10 km apart. Phys. Rev. Lett. 81, 3563-356 (1998)


M.T. Miscala is an aspiring MS Physics student of Mindanao State University-Iligan Institute of Technology. Her research interests include structural acoustics, nanotechnology and high energy physics research.

Leave a Reply