On the Nature of $a^{*}_{k}a_{k}$ and the Emergence of the Born's Rule

TL;DR

This paper explores how revising the concept of game theoretical utility in quantum systems can lead to the emergence of Born's rule, connecting utility measures with quantum measurement outcomes.

Contribution

It introduces a novel approach linking game theory and quantum mechanics to derive Born's rule from utility considerations within an isolated system.

Findings

Revised utility concept leads to Born's rule emergence

Game measure aligns with quantum measurement probabilities

Provides a new perspective on quantum measurement foundations

Abstract

This paper is intended to show that a review in the concept of the game theoretical utility, the revised utility to be applied to the definition of the utility of a wave function representing an object subsystem relative to its observer subsystem, both within an isolated system, leads to the emergence of the Max Born's rule as a profit under a von Neumann's good measure game.