量子力学与最小基经济原理
Quantum Mechanics and the Principle of Least Radix Economy
摘要：
提出了一种新的变分方法--最小基经济原理。基数经济的数学和物理相关性，也被称为数字容量，建立，显示如何物理定律可以从这个概念中得到一个统一的方式。该原理重新解释和推广了最小作用量原理，产生了两类物理解：最小作用量路径和量子波函数。然后完成了量子力学的希尔伯特空间的一个新的物理基础，并利用它导出了薛定谔方程和狄拉克方程以及时空几何对易性的破缺。该公式解释了决定论和随机统计行为如何在时空中共存，并建立了一个框架，使动力学过程可以用数字链来表示。这些方法为洛伦兹变换和狭义相对论提供了一个新的（前几何的）基础。帕克-罗德斯组合层次包含在我们的方法中，这导致电磁力和引力的相互作用强度的估计与实验值一致，误差小于千分之一。最后，它是如何显示的原则，最小基数经济自然产生玻尔兹曼的原则，经典的统计热力学。提出了一种新的满足热力学第二定律的广义非平衡熵的表达式。
英文摘要：
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.
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