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arXiv:2409.11594

A remark on quantum measuring systems and the holographic principle

Konishi, Eiji

Published Sep 17, 2024• 0 citations
arXivHTMLPDF

Abstract

It is a sort of ultimate question to examine the continuity of a quantum measurement subject theoretically and has not yet been resolved within a scientific framework. In this article, we approach this question and argue that the continuity of a quantum measurement subject follows as a fundamental consequence of the holographic principle after the classicalization of the quantum state of the bulk space.

DOI
10.48550/arxiv.2409.11594

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It is a sort of ultimate question to examine the continuity of a quantum measurement subject theoretically and has not yet been resolved within a scientific framework. In this article, we approach this question and argue that the continuity of a quantum measurement subject follows as a fundamental consequence of the holographic principle after the classicalization of the quantum state of the bulk space.
In quantum mechanics without application of any superselection rule to the set of the observables, a closed quantum system temporally evolves unitarily, and this Lorentzian regime is characterized by von Neumann entropy of exactly zero. In the holographic theory in the classicalized ground state, we argue that the unitary real-time evolution of a non-relativistic free particle with complex-valued quantum probability amplitude in this Lorentzian regime can be temporally analytically continued to an imaginary-time classical stochastic process with real-valued conditional probability density in the Euclidean regime, where the von Neumann entropy of the classicalized hologram and the information of a particle trajectory acquired by the classicalized hologram are positive valued. This argument could shed light on the Euclidean regime of the holographic Universe.
We show in this pedagogical review that far from being an apparent law of physics that stands by itself, the holographic principle is a straightforward consequence of the quantum information theory of separable systems. It provides a basis for the theories of measurement, time, and scattering. Utilizing the notion of holographic screens, which are information encoding boundaries between physical subsystems, we demonstrate that the physical interaction is an information exchange during which information is strictly conserved. Then we use generalized holographic principle in order to flesh out a fully-general quantum theory of measurement in which the measurement produces finite-resolution, classical outcomes. Further, we show that the measurements are given meaning by quantum reference frames and sequential measurements induce topological quantum field theories. Finally, we discuss principles equivalent to the holographic principle, including Markov blankets and the free-energy principle in biology, multiple realizability and virtual machines in computer science, and active inference and interface theories in cognitive science. This appearance in multiple disciplines suggests that the holographic principle is not just a fundamental principle of physics, but of all of science. Quanta 2022; 11: 72–96.
I am very grateful to the Master and Fellows of Trinity College for inviting me to give the Tarner Lectures. What I want to do in this book, stated boldly and baldly, is to consider the relevance of developments in modern theoretical physics to metaphysical questions about the ultimate nature of reality. By metaphysical questions I mean the very general sorts of questions that arise out of a critical examination of the principles, concepts and fundamental presuppositions that lie behind modern physics. How should we interpret the claims that physicists seem to be making about the world? Are they intended to be understood as literally true, for example, and exactly what are those claims, given that the pages of theoretical physics monographs are largely filled with abstract mathematical formalism? In the first chapter, I shall be looking at a range of philosophical points of view in the framework of which such questions can be addressed, and attempt the difficult task of adjudicating between the different approaches. At the end of the day I shall be arguing for a pretty straightforward metaphysical realism, that the external world exists independently of our knowledge of it. In the second chapter I shall look at arguments from various branches of modern physics that are sometimes claimed to bring in an essential role for subjectivity in physics, bringing the observer into a central role, creating his own reality.
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches - that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism - fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel conceptual framework from which to conduct this analysis.
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this dilemma have been proposed and this article tries to describe how a now-century-long discussion has led to new insights about the transition from the quantum to the classical world. Starting from the pioneer’s view of the quantum measurement problem, it follows the development of formalisms, the interest from philosophers for its new aspects on reality and how different interpretations of quantum mechanics have tried to support our classically working brains in understanding quantum phenomena. Decoherence is a main topic and its role in measurement processes exemplified. The question of whether the quantum measurement problem is now solved is left open for the readers’ own judgment.