论文标题
分辨率相对论中非差异动力学路径的病毒定理
The virial theorem for non-differentiable dynamical paths in resolution-scale relativity
论文作者
论文摘要
病毒定理是在以扩散常数为特征的随机动力学的分辨率相对性的框架中确定的。它仅像经典病毒定理一样依赖于简单的时间平均值，而量子机械病毒定理涉及观察值的预期值。然而，由于出现了量子样的潜在项，分辨率尺度病毒定理还包括识别HBAR <-> 2MD下的量子机械动力学。这为标准量子力学的基础提供了相对论方法的说明。此外，指出的是，如果分辨率规模的相对性原理是在复杂和/或混乱的宏观系统中实现的，则在分析天体物理系统动力学中，将经典病毒定理的应用忽略了分辨率相对量价量子型的贡献。结果表明，这种类似量子的电位可以解释暗物质假设的一部分。
The virial theorem is established in the framework of resolution-scale relativity for stochastic dynamics characterized by a diffusion constant D. It only relies on a simple time average just like the classical virial theorem, while the quantum mechanical virial theorem involves the expectation values of the observables. Nevertheless, by the emergence of a quantum-like potential term, the resolution-scale relativity virial theorem also encompasses quantum mechanical dynamics under the identification hbar <--> 2mD. This provides an illustration of the scale relativistic approach to the foundation of standard quantum mechanics. Furthermore, it is pointed out that, if the resolution-scale relativity principle is implemented in macroscopic systems that are complex and/or chaotic, then the application of the classical virial theorem in the analysis of the dynamics of astrophysical systems neglects the contribution from a resolution-scale relativistic quantum-like potential. It is shown that this quantum-like potential could account for some fraction of the dark matter hypothesis.
