Riek Roland
Laboratory of Physical Chemistry, ETH Zuerich, Wolfgang-Pauli-Strasse 10, HCI F 225, CH-8093 Zurich, Switzerland.
Entropy (Basel). 2020 Jun 10;22(6):647. doi: 10.3390/e22060647.
The second law of thermodynamics, with its positive change of entropy for a system not in equilibrium, defines an arrow of time. Interestingly, also, causality, which is the connection between a cause and an effect, requests a direction of time by definition. It is noted that no other standard physical theories show this property. It is the attempt of this work to connect causality with entropy, which is possible by defining time as the metric of causality. Under this consideration that time appears only through a cause-effect relationship ("measured", typically, in an apparatus called clock), it is demonstrated that time must be discrete in nature and cannot be continuous as assumed in all standard theories of physics including general and special relativity, and classical physics. The following lines of reasoning include: (i) (mechanical) causality requests that the cause must precede its effect (i.e., antecedence) requesting a discrete time interval >0. (ii) An infinitely small time step d t > 0 is thereby not sufficient to distinguish between cause and effect as a mathematical relationship between the two (i.e., Poisson bracket) will commute at a time interval d t , while not evidently within discrete time steps Δ t . As a consequence of a discrete time, entropy emerges (Riek, 2014) connecting causality and entropy to each other.
热力学第二定律表明，对于非平衡系统，其熵会发生正向变化，该定律定义了时间箭头。有趣的是，因果关系（即原因与结果之间的联系）从定义上也要求时间具有方向性。需要注意的是，没有其他标准物理理论具有这一特性。本研究试图将因果关系与熵联系起来，这可以通过将时间定义为因果关系的度量来实现。基于时间仅通过因果关系出现（通常在称为时钟的装置中“测量”）这一考虑，证明了时间在本质上必然是离散的，而不是像包括广义相对论、狭义相对论以及经典物理学在内的所有标准物理理论所假设的那样是连续的。以下推理思路包括：（i）（机械）因果关系要求原因必须先于其结果（即先后顺序），这就需要一个大于0的离散时间间隔。（ii）因此，一个无限小的时间步长dt>0不足以区分原因和结果，因为两者之间的数学关系（即泊松括号）在时间间隔dt内将是可交换的，而在离散时间步长Δt内则不明显。由于时间是离散的，熵就出现了（里克，2014年），从而将因果关系和熵相互联系起来。
