Elze Hans-Thomas
Dipartimento di Fisica "Enrico Fermi", Universitá di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy.
Entropy (Basel). 2025 Apr 7;27(4):395. doi: 10.3390/e27040395.
The cornerstones of the Cellular Automaton Interpretation of Quantum Mechanics are its underlying ontological states that evolve by permutations. They do not create would-be quantum mechanical superposition states. We review this with a classical automaton consisting of an Ising spin chain which is then related to the Weyl equation in the continuum limit. Based on this and generalizing, we construct a new "Necklace of Necklaces" automaton with a torus-like topology that lends itself to represent the Dirac equation in 1 + 1 dimensions. Special attention has to be paid to its mass term, which necessitates this enlarged structure and a particular scattering operator contributing to the step-wise updates of the automaton. As discussed earlier, such deterministic models of discrete spins or bits unavoidably become quantum mechanical, when only slightly deformed.
量子力学的元胞自动机诠释的基石是其通过排列演化的潜在本体状态。它们不会产生准量子力学叠加态。我们用一个由伊辛自旋链组成的经典自动机来回顾这一点，该自动机在连续极限下与外尔方程相关。基于此并进行推广，我们构建了一个具有环面状拓扑结构的新“项链之项链”自动机，它适合于表示1 + 1维的狄拉克方程。必须特别注意其质量项，这需要这种扩大的结构以及一个特定的散射算子来促进自动机的逐步更新。如前所述，这种离散自旋或比特的确定性模型在仅稍有变形时就不可避免地会变成量子力学的。
