量子理论中的自由选择:一个极端的观点
1Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia.
Entropy (Basel, Switzerland)
|May 27, 2023
概括
现实在最小尺度上的性质 - - 无论是离散的还是连续的 - - 都取决于用于解释测量数据的数学工具. 本研究探讨了用于建模物理系统的p-adic分析和Mealy机器.
科学领域:
- 数学物理学的数学物理.
- 量子力学就是量子力学.
- 数学理论 数学理论
背景情况:
- 由于测量错误,物理学中的观测数据是理数.
- 对这些数据的解释可能会导致关于现实的基本性质的不同结论.
- 现有的模型通常依赖于实数分析.
研究的目的:
- 严格证明,衡量的选择 (真实或p-adic) 决定了自然是否看起来是离散的或连续的.
- 引入p-adic 1-Lipschitz地图和Mealy机器作为物理建模的工具.
- 在这个框架内构建波函数并证明不确定性关系.
主要方法:
- 使用p-adic 1-Lipschitz地图,这些地图与p-adic度量相比是连续的.
- 使用连续的Mealy机来定义在离散时间内的因果函数.
- 将这些地图扩展到连续的实函数,用于模拟开放的物理系统.
主要成果:
- 证明真实和p-adic指标之间的选择决定了物理现实的感知性质.
- 成功构建波函数并证明了的不确定性关系.
- 展示了梅利机器和量子力学的p-adic分析的适用性.
结论:
- 在最小的尺度上,自然的基本性质不是固有的,而是取决于对实验数据应用的数学框架.
- p-adic数学物理学为传统的基于实数的方法提供了一个可行的替代方案.
- 这项工作为量子力学提供了一个新的视角,与超决定论概念相一致.
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