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Information Theoretic Description of Time

Bharath Ron

Published Apr 3, 2017• 0 citations
OpenAlex

Abstract

Physics is studying a system based on the information available about it. There are two approaches to physics deterministic and the nondeterministic. The deterministic approaches assume complete availability of information. Since full information about the system is never available nondeterministic approaches such as statistical physics and quantum physics are of high importance. This article is concerned with informational foundations of Physics and a description of time in terms of information. This article addresses the problem of time and a cluster of problems around measurement in quantum mechanics. It gives an interpretation for time in terms of information. The thermal time is shown to be emergent from the noncommutativity of quantum theory.

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We shall draw an affirmative answer to the question posed in the title.The key point will be a quantum description of physical reality.Once fixed at ontic level two basic elements, namely the laws of physics and the matter, we argue that the underlying physical reality emerges from the interconnection between these two elements.We consider any physical process, including measurement, modeled by unitary evolution.In this context, we will deduce quantum randomness as a consequence of inclusion of the observer into the quantum system.The global picture of the universe is in a sense deterministic, but from our own local perspective (as part of the system) we perceive quantum mechanical randomness.Then, the notion of "information" turns out to be a derivative concept.I've spent much more time thinking about the photon problem [i.e., about quantum theory] than about relativity. A. Einstein

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On Quantum Mechanics

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We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION THEORY. We propose three different postulates out of which the formalism of the theory can be reconstructed; these are based on the notion of information about each other that systems contain. All systems are assumed to be equivalent: no observer-observed distinction, and information is interpreted as correlation. We then suggest that the incorrect notion that generates the unease with quantum mechanichs is the notion of OBSERVER INDEPENDENT state of a system.

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Physics is studying a system based on the information available about it. There are two approaches to physics deterministic and the nondeterministic. The deterministic approaches assume complete availability of information. Since full information about the system is never available nondeterministic approaches such as statistical physics and quantum physics are of high importance. This article is concerned with informational foundations of Physics and a description of time in terms of information. This article addresses the problem of time and a cluster of problems around measurement in quantum mechanics. It gives an interpretation for time in terms of information. The thermal time is shown to be emergent from the noncommutativity of quantum theory.
Physics is studying a system based on the information available about it. There are two approaches to physics, deterministic and the nondeterministic. The deterministic approaches assume everything is known about the system. Since everything about the system is almost never known, nondeterministic approaches such as statistical physics and quantum physics are of high importance. After a tour through informational interpretation of quantum physics and required mathematical tools, we go into the notion of time. We address the problem of time and a cluster of problems around measurement in quantum mechanics. I present a new approach to interpreting time in terms of information changes. Time will emerge from the non-commutativity of quantum theory. In the third section we review information thermodynamics and later derive some relations between our notion of time and the thermal time.
Abstract: A suitable unified statistical formulation of quantum and classical mechanics in a ∗-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer’s information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer’s information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process. 1.
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the covariant formalism, and use it to interpret the measurement process. We find that the time ordering of measurements emerges as an entropy relationship in the state of the observers, giving unique probabilities for multiple measurements. This approach suggests a new, fully self-contained probability interpretation for generally covariant quantum physics, which makes use of a quantum mechanical description of the observer, in contrast to standard quantum mechanics which assumes an external, classical observer.
The description of physical systems obtained in the classical limit of quantum mechanics is not consistent with the one given by classical statistical mechanics. In qantum mechanics the complete description of a physical system is given by specifying the wave function, which evolves completely deterministically. Probability comes into play only when a measurement is made. Classical statistical mechanics, on the contrary, concerns systems whose description is not complete and where probability enters as a consequence of a lack of knowledge. We show that Nelson's stochastic mechanics, whose predictions are identical with those of quantum mechanics, provides nevertheless a unified description of the deterministic and random aspects of quantum mechanics which eliminates the inconsistency outlined above and gives a simple and satisfactory solution to the measurement problem.
We shall draw an affirmative answer to the question posed in the title.The key point will be a quantum description of physical reality.Once fixed at ontic level two basic elements, namely the laws of physics and the matter, we argue that the underlying physical reality emerges from the interconnection between these two elements.We consider any physical process, including measurement, modeled by unitary evolution.In this context, we will deduce quantum randomness as a consequence of inclusion of the observer into the quantum system.The global picture of the universe is in a sense deterministic, but from our own local perspective (as part of the system) we perceive quantum mechanical randomness.Then, the notion of "information" turns out to be a derivative concept.I've spent much more time thinking about the photon problem [i.e., about quantum theory] than about relativity. A. Einstein
We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION THEORY. We propose three different postulates out of which the formalism of the theory can be reconstructed; these are based on the notion of information about each other that systems contain. All systems are assumed to be equivalent: no observer-observed distinction, and information is interpreted as correlation. We then suggest that the incorrect notion that generates the unease with quantum mechanichs is the notion of OBSERVER INDEPENDENT state of a system.