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On the Statistical Arrow of Time

Andreas Henriksson

Published Apr 3, 2023• 1 citation
Publisher

Abstract

What is the physical origin of the arrow of time? It is a commonly held belief in the physics community that it relates to the increase of disorder, or entropy, as it appears in the statistical interpretation of the second law of thermodynamics. In this article, it is argued that the philosophical point of view that the arrow of time is a fundamental property of Nature is incompatible with the subjective information-theoretical interpretation of probability and entropy in statistical mechanics, where they arise due to the ignorance of the observer. This conclusion, however, relies on the premise that time's arrow has a statistical mechanical origin. If this assumption is abandoned, then there is no conflict between the belief in the fundamental character of time's arrow and the belief in the subjective information-theoretical interpretation.

DOI
10.32388/c9joj9.3

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What is the physical origin for the arrow of time? It is a commonly held belief in the physics community that it relates to the increase of disorder, or entropy, as it appears in the statistical interpretation of the second law of thermodynamics. In this article, it is argued that the philosophical point of view that the arrow of time is a fundamental property of Nature is incompatible with the subjective information-theoretical interpretation of probability and entropy in statistical mechanics, where they arise due to the ignorance of the observer. This conclusion, however, relies on the premise that time's arrow has a statistical mechanical origin. If this assumption is abandoned, then there is no conflict between the belief in the fundamental character of time's arrow and the belief in the subjective information-theoretical interpretation.
What is the physical origin of the arrow of time? It is a commonly held belief in the physics community that it relates to the increase of entropy as it appears in the statistical interpretation of the second law of thermodynamics. At the same time, the subjective information-theoretical interpretation of probability, and hence entropy, is a standard viewpoint in the foundations of statistical mechanics. In this article, it is argued that the subjective interpretation is incompatible with the philosophical point of view that the arrow of time is a fundamental property of Nature. The subjectivist can only uphold this philosophy if the role played by the second law of thermodynamics in defining time's arrow is abandoned.
What is the physical origin of the arrow of time? It is a commonly held belief in the physics community that it relates to the increase of entropy as it appears in the statistical interpretation of the second law of thermodynamics. At the same time, the subjective information-theoretical interpretation of probability, and hence entropy, is a standard viewpoint in the foundations of statistical mechanics. In this article, it is argued that the subjective interpretation is incompatible with the philosophical point of view that the arrow of time is a fundamental property of Nature. The subjectivist can only uphold this philosophy if the role played by the second law of thermodynamics in defining time's arrow is abandoned.
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In this article, the arrow of time as it appears in the statistical interpretation of the second law of thermodynamics is suggested to be of no relevance in understanding the true origin for the directionality of time. To arrive at this point of view, the theory of statistical mechanics is revisited, and restated in terms of the information content possessed by an observer of the system. By doing so, the statement that the arrow of time is due to the tendency of the entropy to increase with time, as encoded by the second law of thermodynamics, is argued to be equivalent to the statement that it is the increasing loss of information that causes time to flow towards the future.