Abstract

The aim of this work is to discuss concisely the modern paradigm of the concept of time and to analyze its relevance and applicability in the context of classical and relativistic physics. We are touching briefly the different notion of time in classical and quantum mechanics and in special and general relativity to analyze their compatibility or incompatibility. In quantum mechanics we deal with the absolute character of Newtonian (dynamical) time, whereas in quantum field theories we consider the Minkowski metric as the background space-time (at least partially). Classical general relativity is characterized by a dynamical spacetime, but as regards to the quantum gravity the situation is more complicated. We discussed the consequences which these circumstances cause in the quantum gravity theory (“time paradox”) when attempt to operate with both the dynamical spacetime and the so-called “non-dynamical” time. We analyzed critically whether the last notion may be justified with the aid of an analogy with the “coarse grain” averaging procedure in statistical thermodynamics.

中文翻译：

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复杂系统的时间行为：从微观世界到宏观世界

摘要

这项工作的目的是简明地讨论时间概念的现代范式，并分析其在经典和相对论物理学背景下的相关性和适用性。我们将简要介绍经典力学和量子力学以及狭义相对论和广义相对论中不同的时间概念，以分析它们的兼容性或不兼容性。在量子力学中，我们处理牛顿（动力学）时间的绝对特征，而在量子场论中，我们将闵可夫斯基度量视为背景时空（至少部分）。经典广义相对论的特点是动态时空，但对于量子引力而言，情况更为复杂。我们讨论了当尝试同时处理动态时空和所谓的“非动态”时间时，这些情况在量子引力理论（“时间悖论”）中造成的后果。我们借助与统计热力学中“粗粒”平均过程的类比，批判性地分析了最后一个概念是否合理。