# Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective

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## Abstract

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## 1. Introduction

## 2. From Relativity to Physical Spacetime and the Particle Phase Space

#### 2.1. The Coset Space Representation

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

#### 2.2. From the Poincaré Algebra to Minkowski Space

#### 2.3. The Phase Space for Particle Dynamics as a Coset Space

## 3. Special Relativity as a Theory of Hamiltonian Dynamics

#### 3.1. Dynamics as Symmetry Transformations

#### 3.2. Particle Dynamics of Special Relativity

#### 3.3. Hamiltonian Flows Generated by Elements of the Poincaré Symmetry

## 4. Contractions as Approximations of Physical Theories

#### 4.1. A Crash Course on Symmetry Contractions

#### 4.2. The Poincaré to Galilean Symmetry Contraction

#### 4.3. Retrieving Newtonian Space-Time from Minkowski Spacetime

#### 4.4. Hamiltonian Transformations and Particle Dynamics at the Newtonian Limit

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Deformations as Probes of More Fundamental Physics

## Appendix B. A Physicist’s Sketch of the Necessary Group Theory Background

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Kong, O.C.W.; Payne, J.
Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective. *Symmetry* **2021**, *13*, 1925.
https://doi.org/10.3390/sym13101925

**AMA Style**

Kong OCW, Payne J.
Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective. *Symmetry*. 2021; 13(10):1925.
https://doi.org/10.3390/sym13101925

**Chicago/Turabian Style**

Kong, Otto C. W., and Jason Payne.
2021. "Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective" *Symmetry* 13, no. 10: 1925.
https://doi.org/10.3390/sym13101925