Joint reality and Bell inequalities for consecutive measure - ments

– Some new Bell inequalities for consecutive measurements are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes the non-invasive measurability hypothesis advantageously, provided that the system satisfies the perfect correlation property. The new inequalities are violated quantically. This violation can be expected to be more severe than in the case of precedent temporal Bell inequalities. Some microscopic and mesoscopic situations, in which the new inequalities could be tested, are roughly considered. 1. Introduction. – Besides the ordinary Bell inequalities [1, 2] for entangled systems, there also exist so-called temporal Bell inequalities [3-5] for a single system. In the seminal paper of Leggett and Garg [6], the authors consider a macroscopic system and make two general assumptions: i) Macroscopic realism: " A macroscopic system with two or more macroscopically distinct states available to it will at all times be in one or the other of these states ". ii) Noninvasive measurability (NIM): " It is possible, in principle, to determine the state of the system with arbitrarily small perturbation in its subsequent dynamics ". With these two assumptions, these authors prove some temporal Bell inequalities for such a macroscopic system, where the measurement times, t i , play the role of the polarizer settings in the ordinary Bell inequalities. NIM assumption is obviously not valid for quantum systems, and has been criticized for macroscopic systems [7]. In spite of these criticisms, it seems that the idea of an ideal negative experiment, or alternatively the coupling of the system to a microscopic probe, as explained in [6], can change NIM into a reasonable assumption. Whatever it be, the main purpose of the present paper is to prove some new Bell inequalities for consecutive measurements, retaining the realism of assumption i), but changing the NIM for a new assumption, that encompass the above assumption i), and becomes extremely natural and plausible if NIM is assumed, but not necessarily the reverse way. We will call this new assumption the joint reality assumption and we will state it below. Contrarily to what happens