论文标题
Quaternionic 3-Sphere模型中单线相关性的对称派生
Symmetric derivation of singlet correlations in a quaternionic 3-sphere model
论文作者
论文摘要
Using the powerful language of geometric algebra, we present an observationally symmetric derivation of the strong correlations predicted by the entangled singlet state in a deterministic and locally causal model, usually also referred to as a local-realistic model, in which the physical space is assumed to be a quaternionic 3-sphere, or $S^3$, available as the spatial part of a solution of Einstein's field equations of general相对论，并将其与贝尔的本地现实模型进行比较，以在平坦的Euclidean Space中设置的单元相关性$ {\ Mathrm {i \！r}^3} $。由于观察贝尔本地模型的测量结果的相对角度依赖性概率的定量详细表达似乎并未完全阐明，因此，我们的新颖分析利用了Quaternions的非交换性能的新分析，除了与Quaternionic 3-Sphere模型的比较外，还可以提供其他有用的模型。超确定性。除了保存零旋转角动量外，与贝尔的本地模型相比，$ s^3 $内强的单线相关性的主要属性是旋转符号会改变构成三个球体的四季度的内在变化。此外，我们还讨论了一个宏观实验，该实验原则上可以检验我们的三个球体假设。
Using the powerful language of geometric algebra, we present an observationally symmetric derivation of the strong correlations predicted by the entangled singlet state in a deterministic and locally causal model, usually also referred to as a local-realistic model, in which the physical space is assumed to be a quaternionic 3-sphere, or $S^3$, available as the spatial part of a solution of Einstein's field equations of general relativity, and compare it in quantitative detail with Bell's local-realistic model for the singlet correlations set within a flat Euclidean space ${\mathrm{I\!R}^3}$. Since the quantitatively detailed expressions of relative-angle-dependent probabilities of observing measurement outcomes for Bell's local model do not seem to have been fully articulated before, our novel analysis exploiting the non-commutative properties of quaternions, in addition to allowing the comparison with the quaternionic 3-sphere model, may also provide useful comparisons for other less compelling local-realistic models, such as those relying on retrocausality or superdeterminism. Apart from the conservation of zero spin angular momentum, the key attribute underlying the strong singlet correlations within $S^3$ in comparison with Bell's local model turns out to be the spinorial sign changes intrinsic to quaternions that constitute the 3-sphere. In addition, we also discuss anew a macroscopic experiment that can, in principle, test our 3-sphere hypothesis.
