Relativistic quantum econophysics - new paradigms in complex systems modelling

TL;DR

This paper introduces a relativistic quantum framework for econophysics, challenging classical and non-relativistic quantum paradigms by emphasizing the non-existence of definite system states and immediate values, leading to new modeling approaches for socio-economic systems.

Contribution

It proposes a relativistic quantum econophysics paradigm that redefines system states and measurement, offering a fundamentally different approach from classical and non-relativistic quantum models.

Findings

Relativistic quantum econophysics rejects the notion of definite system states.

System dynamics are discrete and approximate, with prediction limited by memory effects.

New paradigms shift focus to operators and probabilistic descriptions rather than precise states.

Abstract

This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system's state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondefinable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception, description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereffect i.e. the memory.