# The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down

## Abstract

**:**

## 1. Preliminaries: Understanding Spinors and a New Approach to Quantum Mechanics

#### 1.1. Clifford Algebra

#### 1.2. Use of the Clifford Algebra to Derive the Dirac Equation from Scratch

#### 1.3. Consequences

#### 1.4. Breakdown of the Standard Dirac Formalism in the Case of Precession

## 2. The Stern–Gerlach Experiment: Confusion Reigns

#### 2.1. Preamble

#### 2.2. Total Absence of Theory

#### 2.3. Total Absence of Intuition

## 3. Tabula Rasa Approach Based on Spinors

## 4. More Traditional Formulation in Terms of a Differential Equation

## 5. The Pauli Exclusion Principle Remains Valid

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. The Missing Link: the Geometrical Meaning of the Spin-Up and Spin-Down States

## Appendix B. The Dirac Equation Does not Describe a Single Electron but a Superposition State that Must Be Interpreted as Corresponding to a Statistical Ensemble

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**MDPI and ACS Style**

Coddens, G.
The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down. *Symmetry* **2021**, *13*, 134.
https://doi.org/10.3390/sym13010134

**AMA Style**

Coddens G.
The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down. *Symmetry*. 2021; 13(1):134.
https://doi.org/10.3390/sym13010134

**Chicago/Turabian Style**

Coddens, Gerrit.
2021. "The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down" *Symmetry* 13, no. 1: 134.
https://doi.org/10.3390/sym13010134