Bell's inequality and the coincidence-time loophole

¹ Matematiska Institutionen, Linköpings Universitet - SE-581 83 Linköping, Sweden
² Department of Mathematics, University of Utrecht Box 80010, NL-3508 TA Utrecht, The Netherlands
³ EURANDOM - P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands

Corresponding author: jalar@mai.liu.se

Received: 19 March 2004
Accepted: 21 June 2004

Abstract

This paper analyzes effects of time dependence in the Bell inequality. A generalized inequality is derived for the case when coincidence and non-coincidence (and hence whether or not a pair contributes to the actual data) is controlled by timing that depends on the detector settings. Needless to say, this inequality is violated by quantum mechanics and could be violated by experimental data provided that the loss of measurement pairs through failure of coincidence is small enough, but the quantitative bound is more restrictive in this case than in the previously analyzed “efficiency loophole”.