论文标题
随机变量和免费定理的系统
Systems of random variables and the Free Will Theorem
论文作者
论文摘要
标题是指康威(Conway)和科钦(Kochen)的自由遗嘱定理,其浮华配方是:如果实验者拥有自由意志,那么粒子也是如此。从更谦虚的角度来看,定理说,只要对所有测量设置选择,确定性系统都不能描述单个间距分离的粒子对。我们从随机变量的系统中重新调整和推广了自由遗嘱定理,并表明证明是基于两个观察结果:(1)某些复合系统是上下文(非本地),并且(2)任何具有空中式分离组件的确定性系统是无标志性的。两者之间的矛盾是通过证明非信号确定性系统的混合物(如果存在的)始终是非秘密的。证明不需要“实验者的自由意志”(独立性)假设:通过上述假设(1)使其对证明至关重要。接下来,我们认为,确定性系统不描述单个粒子的原因比在自由意志定理中更为基础。一个系统或不确定性的系统,包括设置的几种选择,每个设置都可以在不更改系统的情况下实际使用。单个颗粒只能为单个选择的随机变量提供单一的实现。有了这个概念化,“实验者的自由意志”甚至无法得到有意义的表述,而确定论和“粒子自由意志”之间的选择变得任意和无关紧要。
The title refers to the Free Will Theorem by Conway and Kochen whose flashy formulation is: if experimenters possess free will, then so do particles. In more modest terms, the theorem says that individual pairs of spacelike separated particles cannot be described by deterministic systems provided their mixture is the same for all choices of measurement settings. We reformulate and generalize the Free Will Theorem theorem in terms of systems of random variables, and show that the proof is based on two observations: (1) some compound systems are contextual (non-local), and (2) any deterministic system with spacelike separated components is non-signaling. The contradiction between the two is obtained by showing that a mixture of non-signaling deterministic systems, if they exist, is always noncontextual. The "experimenters' free will" (independence) assumption is not needed for the proof: it is made redundant by the assumption (1) above, critical for the proof. We next argue that the reason why an individual pair of particles is not described by a deterministic system is more elementary than in the Free Will Theorem. A system, contextual or not and deterministic or not, includes several choices of settings, each of which can be factually used without changing the system. An individual pair of particles can only afford a single realization of random variables for a single choice of settings. With this conceptualization, the "free will of experimenters" cannot be even meaningfully formulated, and the choice between the determinism and "free will of particles" becomes arbitrary and inconsequential.