# Non-Minimal Lorentz Violation in Macroscopic Matter

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Hamiltonian

#### 2.2. Equations of Motion

#### 2.3. Lorentz Transformations

## 3. Applications

#### 3.1. Tests of the Equivalence Principle

#### 3.2. Orbits

#### 3.3. Acoustic Resonators

## 4. Summary

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Table 1.**Limits on isotropic Standard-Model Extension (SME) coefficients from tests of the equivalence principle. The first column gives the coefficient combinations. The second column contains the combined constraints from ground-based free-fall experiments. The third column lists constraints from the space-based MICROSCOPE experiment. The last column gives the combined constraints from torsion-pendulum experiments.

Coefficients | Free Fall | MICROSCOPE | Torsion Pendulum |
---|---|---|---|

${{c}_{npe}}_{200}^{\left(4\right)}+{\textstyle \frac{1}{2}}{{c}_{npe}}_{000}^{\left(4\right)}$ | $(-5\pm 12)\times {10}^{-9}$ | $(3\pm 27\pm 27)\times {10}^{-14}$ | $(3\pm 7)\times {10}^{-12}\phantom{\rule{4.pt}{0ex}}\mathrm{GeV}$ |

${{a}_{npe}}_{200}^{\left(5\right)}+{{a}_{npe}}_{000}^{\left(5\right)}$ | $(5\pm 13)\times {10}^{-9}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-1}$ | $(-3\pm 29\pm 29)\times {10}^{-14}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-1}$ | $(3\pm 8)\times {10}^{-12}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-1}$ |

${{c}_{npe}}_{200}^{\left(6\right)}+{\textstyle \frac{3}{2}}{{c}_{npe}}_{000}^{\left(6\right)}$ | $(-6\pm 13)\times {10}^{-9}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-2}$ | $(3\pm 30\pm 30)\times {10}^{-14}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-2}$ | $(3\pm 8)\times {10}^{-12}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-2}$ |

${{a}_{npe}}_{200}^{\left(7\right)}+2{{a}_{npe}}_{000}^{\left(7\right)}$ | $(6\pm 14)\times {10}^{-9}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-3}$ | $(-4\pm 32\pm 32)\times {10}^{-14}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-3}$ | $(4\pm 9)\times {10}^{-12}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-3}$ |

${{c}_{npe}}_{200}^{\left(8\right)}+{\textstyle \frac{5}{2}}{{c}_{npe}}_{000}^{\left(8\right)}$ | $(-6\pm 15)\times {10}^{-9}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-4}$ | $(4\pm 34\pm 34)\times {10}^{-14}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-4}$ | $(4\pm 10)\times {10}^{-12}\phantom{\rule{4.pt}{0ex}}{\mathrm{GeV}}^{-4}$ |

**Table 2.**Euler angles of the planets [91].

Merc. | Ven. | Earth | Mars | Jup. | Sat. | Ur. | Nept. | |
---|---|---|---|---|---|---|---|---|

$\alpha $ | ${11.1}^{\circ}$ | ${8.0}^{\circ}$ | ${0}^{\circ}$ | ${3.4}^{\circ}$ | ${3.3}^{\circ}$ | ${6.0}^{\circ}$ | ${1.8}^{\circ}$ | ${3.5}^{\circ}$ |

$\eta $ | ${28.5}^{\circ}$ | ${24.4}^{\circ}$ | ${23.4}^{\circ}$ | ${24.7}^{\circ}$ | ${23.2}^{\circ}$ | ${22.6}^{\circ}$ | ${23.7}^{\circ}$ | ${22.3}^{\circ}$ |

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Non-Minimal Lorentz Violation in Macroscopic Matter. *Symmetry* **2020**, *12*, 2026.
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Non-Minimal Lorentz Violation in Macroscopic Matter. *Symmetry*. 2020; 12(12):2026.
https://doi.org/10.3390/sym12122026

**Chicago/Turabian Style**

Mewes, Matthew.
2020. "Non-Minimal Lorentz Violation in Macroscopic Matter" *Symmetry* 12, no. 12: 2026.
https://doi.org/10.3390/sym12122026