任意自旋量系统的贝尔不等式

Bell's Inequalities for Any Spin System

贝尔不等式是明显区别爱因斯坦局域原理与量子力学非局域观点的一个关系式.通过推导给出了两粒子任意自旋S(S是整数或半整数)单重态贝尔不等式的普遍性的描述.这个不等式是判断自旋两个可能方向夹角θ的函数.另外还发现:对任意半整数自旋系统,θ在某区间内是违反贝尔不等式的,这个区间的右边界固定且等于π/2,随着自旋量的增加,左边界越来越靠近右界,违反贝尔不等式的范围按照1/S^(1/2)比例渐近减少趋于0;对于有限整数自旋存在类似现象.因此对于大数自旋系统,爱因斯坦局域原理与传统量子力学非局域观点趋于一致.

Bell＇ s inequality is a relationship among observables that discriminates between Einstein＇ s locality principle and the nonlocal point of view of orthodox quantum mechanics. By making natural induction, a generalization for Bell＇ s inequality for any two spin-s particles in a singlet state （ s integer or half-integer）. This inequality is expressed as a function of a 0 parameter, which is a measure of the angle between two possible directions in which the spin is measured. Besides the expression for this general ine- quality we have found that for any finite half-integer spin Bell＇ s inequality is violated for some interval of the 0 -parameter. The right limit of this interval is fixed and equal to ~r/2, while the left one comes closer and closer to this value as spin number grows. A func- tion fit shows clearly that the size of this 0-interval over which Bell＇ s inequality is violated diminishes asymptotically to zero as 1 l/ST. Besides, the behavior for any finite integer spin is analogous. So the greater the spin number, the more agree between Ein- stein＇ s locality principle and the non-local point of view in orthodox quantum mechanics disappears.