# Origin of the Complex Structure of Quantum Mechanics

## TL;DR

This paper explores why quantum mechanics is formulated with complex numbers, suggesting that the complex structure naturally emerges from the linear dynamics of real quantum theory, and clarifies misconceptions about measurement and observables.

## Contribution

It provides a novel perspective on the origin of the complex structure in quantum mechanics by analyzing real quantum theory dynamics.

## Key findings

- Complex structure emerges from real quantum dynamics
- Clarifies misconceptions about measurement in quantum mechanics
- Highlights the role of linear dynamics in complex structure emergence

## Abstract

This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space hints at the emergence of a complex structure. A widespread misconception concerning the measurement process in quantum mechanics and the hermiticity of observables is briefly discussed.