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A variable behaving as a quantum in economic system

Kazuyoshi Kitazawa

Published Oct 19, 2020• 0 citations
OpenAlex

Abstract

A variable behaving as a quantum in economic system is studied on the basis of quantum mechanics. The several formulas of relevant variable are derived along with this speculation. Thus a possible value for the common constant which may be understood as Planck constant in economic system is calculated. There, a concerned variable seems to exhibit a quantum behavior.Recently it has been pointed out that there might be a similarity between the rational expectation hypothesis in economics and quantum mechanics, where their observers are both in respective systems. Nevertheless, on the other hand, the principle of uncertainty in economics has not yet been discovered so far. Therefore we will study on this problem by starting to formulate the basic equations respective which correspond to quantum mechanics. Here we pursue solely a behavior of certain representative variable with which an important econophysical quantity is newly introduced, and then discuss about Planck constant in economic system.

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A variable behaving as a quantum in economic system is studied on the basis of quantum mechanics. The several formulas of relevant variable are derived along with this speculation. Thus a possible value for the common constant which may be understood as Planck constant in economic system is calculated. There, a concerned variable seems to exhibit a quantum behavior.Recently it has been pointed out that there might be a similarity between the rational expectation hypothesis in economics and quantum mechanics, where their observers are both in respective systems. Nevertheless, on the other hand, the principle of uncertainty in economics has not yet been discovered so far. Therefore we will study on this problem by starting to formulate the basic equations respective which correspond to quantum mechanics. Here we pursue solely a behavior of certain representative variable with which an important econophysical quantity is newly introduced, and then discuss about Planck constant in economic system.
The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance has produced valuable results. The principal movement which has steered this research direction is known under the name of `econophysics'. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under `uncertainty' in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as `quantum probability') enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.
Approaching physics as the way to predict the results of experiments is good enough for physics as it is. However the transition of its notions and mathematical apparatus to systems of different nature requires obligatory in-depth analysis of its initial concepts. Econophysics is a young interdisciplinary scientific field, which developed and acquired its name at the end of the last century. Quantum econophysics, a direction distinguished by the use of mathematical apparatus of quantum mechanics as well as its fundamental conceptual ideas and relativistic aspects, developed within its boundaries just a couple of years later, in the first decade of the 21-st century. In this paper from quantum econophysics positions, attained by moderntheoretical physics in understanding of the universe bases, the methodological and philosophicalanalysis of fundamental physical concepts and their formal and informal connections with thereal economic measurings is carried out. The possibility of introducing economic equivalents ofphysical quantities in order to describe socio-economic processes using the quantum uncertaintyprinciple is shown. Procedures for heterogeneous economic time determination, normalizedeconomic coordinates and economic mass are offered, based on the analysis of time series, theconcept of economic Plank's constant is proposed. A theory is approved on the real economicdynamic's time series, including crises stock market indices. It is shown that the effective mass ofthe time series universally decreases before the crisis period, which may be an indicator of thecrisis phenomena.
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that were described before through the replicator dynamics. Quantum mechanics could be used to explain more correctly biological and economical processes and even it could encloses theories like games and evolutionary dynamics. This could make quantum mechanics a more general theory that we had thought. Although both systems analyzed are described through two apparently different theories (quantum mechanics and game theory) it is shown that both systems are analogous and thus exactly equivalents. So, we can take some concepts and definitions from quantum mechanics and physics for the best understanding of the behavior of economics and biology. Also, we could maybe understand nature like a game in where its players compete for a common welfare and the equilibrium of the system that they are members.
Abstract Foundations of Quantum Economics unfolds a coherent theoretical thread, replacing the rational-agent premise of mainstream economics with the quantum-person hypothesis: before observation, decision-makers sustain multiple conflicting options encoded in probability amplitudes, and a decision corresponds to collapse triggered by measurement. The book first lays cognitive and mathematical foundations, demonstrating that human judgement inherently exhibits quantum features including superposition, interference and order dependence. Classical probability theory fails for non-commutative economic events, making Hilbert spaces and probability amplitudes indispensable languages for economic inquiry. It then reconstructs causality, information, uncertainty and risk, arguing that economic causes are not uniquely fixed before the collapse of consensus; uncertainty is endogenous to the system, and risk represents the spread of superposed distributions rather than exogenous noise. Built upon this architecture, the work revisits core microeconomic notions such as value, utility, game interaction, supply and demand, property rights, institutions and innovation. All conventional theories are recovered as special limits under zero interference and single eigenstates, while superposition and entanglement furnish fresh explanatory power for economic anomalies. The analysis further expands into macroeconomics, interpreting growth, business cycles, money, fiscal policy, trade and welfare as coherent superposition, phase transition and collapse of collective cognition and consensus, and concludes with the renovation of econometrics and economic governance. The book’s central thesis holds that superposition, interference, observation and collapse are not metaphors borrowed from quantum physics, but intrinsic properties of human cognition and economic practice. Economic realities are not predetermined facts waiting to be discovered; instead, they are generated through human cognition, consensus and practice in the act of measurement. Quantum economics is far more than a cosmetic revision of existing models. It constitutes a shift of research programme, abandoning Laplacian determinism and reconceiving the economy as an open, generative process. The book articulates five interconnected layers: the quantum person as ontological starting point, quantum features of cognition, superposition of collective consensus, endogenous uncertainty, and quantuminformed governance. It reminds researchers and policymakers that economic observation and policy intervention are performative, capable of reshaping the very system they examine. Economics abandons the pursuit of a single, determinate optimum and embraces endogenous uncertainty; policymakers cease to be omniscient system engineers and become prudent stewards of consensus and designers of measurement bases. This volume establishes the unified bedrock for the whole quantum economics series and calls for a new, more honest and realistic economics embedded within the economic process itself.
One of the long-standing conundrums of science is the exact mathematical relationship of quantum mechanics to Newtonian physics, as well as to relativistic physics. Herein it is shown to be possible to use the Planck constant as represented by the quantum formula for photon energy, E=hc/λ , where h is the Planck constant, and using an approach similar to Bohr’s classical mechanical solution for the atom, to construct equations that show the mathematical relationship among all three in fundamental terms. This has the possibility of showing how relativity applied to Newtonian physics produces a quantum mechanical result, and may lead to a better understanding of quantum mechanics from a non-statistical approach, as well as possibly allowing a direct calculation of quantum gravity.