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arXiv:1102.2988

Reality is both digital and analog

Alan Forrester

Published Feb 15, 2011• 0 citations
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Abstract

I argue that both digital and analog information are important in the foundations of quantum physics. If it is possible for information present in one system to become present in others without being erased in the original system I will say that this information can be copied. I argue that copying is important for understanding issues like causality and that all information that can be copied is digital. I then explain that analog information that cannot be copied can be understood in terms of decision theoretic probability. Finally, I argue that these ideas can help explain the second law of thermodynamics. The arrow of time we experience is the knowledge arrow of time -- the present contains more knowledge, that is, useful or explanatory information, than the past. That knowledge is created by evolutionary processes that involve copying, variation and selection and such processes increase entropy.

DOI
10.48550/arxiv.1102.2988

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I argue that both digital and analog information are important in the foundations of quantum physics. If it is possible for information present in one system to become present in others without being erased in the original system I will say that this information can be copied. I argue that copying is important for understanding issues like causality and that all information that can be copied is digital. I then explain that analog information that cannot be copied can be understood in terms of decision theoretic probability. Finally, I argue that these ideas can help explain the second law of thermodynamics. The arrow of time we experience is the knowledge arrow of time -- the present contains more knowledge, that is, useful or explanatory information, than the past. That knowledge is created by evolutionary processes that involve copying, variation and selection and such processes increase entropy.
Most attempts to argue for the second law of thermodynamics fail because (1) they use the unviable frequency theory of probability and (2) they do not explain why the arrow of time seen in experiments is aligned with the thermodynamic arrow of time. I use the decision theoretic interpretation of quantum probability from the many worlds interpretation of quantum mechanics to solve the probability problem. I then derive a correlation between the knowledge arrow of time and the entropy arrow of time using physical constraints on knowledge creation imposed by Popper's evolutionary theory of knowledge and the many worlds interpretation.
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.
The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.
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.
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.