Quantum mechanics: last stop for reductionism

TL;DR

This paper explores how the foundational assumptions about a body's reducibility influence the mathematical frameworks of classical and quantum mechanics, highlighting the transition from real to complex vector spaces.

Contribution

It demonstrates that the assumption of irreducibility naturally leads to the complex vector space structure of quantum mechanics, offering a conceptual basis for the quantum formalism.

Findings

Infinitesimal reducibility results in a real vector space for classical mechanics.

Irreducibility assumption leads to a complex vector space in quantum mechanics.

Provides a conceptual link between physical assumptions and mathematical structures.

Abstract

The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a complex vector space, used in quantum mechanics.