# Born rule and Schr\"odinger equation from first principles

## TL;DR

This paper derives the Born rule and Schrödinger equation from fundamental principles using a formalized framework that unifies classical and quantum theories, emphasizing measurement, composition, and causality.

## Contribution

It provides a first-principles derivation of core quantum mechanics equations within a unified operational framework, highlighting the foundational basis of quantum theory.

## Key findings

- Derivation of Born rule from first principles
- Recovery of Schrödinger equation within the positive formalism
- Unified framework for classical and quantum theories

## Abstract

A concise review of the derivation of the Born rule and Schr\"odinger equation from first principles is provided. The starting point is a formalization of fundamental notions of measurement and composition, leading to a general framework for physical theories known as the positive formalism. Consecutively adding notions of spacetime, locality, absolute time and causality recovers the well established convex operational framework for classical and quantum theory. Requiring the partially ordered vector space of states to be an anti-lattice one obtains quantum theory in its standard formulation. This includes Born rule and Schr\"odinger equation.