An alternative formalism for modeling spin

TL;DR

This paper introduces a novel formalism for modeling spin using base-2 sequences and correlations, providing an information-theoretic perspective that derives quantum rules without assuming space-time structure.

Contribution

It develops a new formalism based on base-2 sequences to model spin, deriving quantum rules and probabilities from first principles without space-time assumptions.

Findings

Derives selection rules for spin interactions from first principles.

Provides a method to calculate quantum probabilities as squared Clebsch-Gordan coefficients.

Offers an information-theoretic interpretation of spin systems.

Abstract

We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2 sequences. Upon choosing a reference base-2 sequence, a relational system of numbers can be defined, which we interpret as quantum numbers. Based on the properties of these relational quantum numbers, the selection rules governing interacting spin systems are derived from first principles. A tool for calculating the associated probabilities, which are the squared Clebsch-Gordan coefficients in quantum mechanics, is also presented. The resulting model offers a vivid information theoretic picture of spin and interacting spin systems. Importantly, this model is developed without making any assumptions about the nature of space-time, which presents an interesting opportunity to study emergent space-time models.