# Observers and Their Notion of Spacetime beyond Special Relativity

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Beyond the Framework of Special Relativity

#### 1.2. Modified Conservation Laws and Locality

#### 1.3. Phenomenology in LIV and DSR

## 2. Spacetime through Local Interactions

#### 2.1. Relative Locality and a First Attempt to Recover Absolute Locality in a New Spacetime

#### 2.2. A Second Attempt to Define Spacetime in the Two-Particle System

#### 2.3. Application to $\kappa $-Poincaré

#### 2.4. More than Two Particles

## 3. Phenomenology in the Relative Locality Framework

#### 3.1. Two Notions of Spacetime

#### 3.2. Photon Time Delays in a DSR Theory: A First Possibility

#### 3.3. Photon Time Delays in a DSR Theory: A Second Possibility

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SR | Special Relativity |

GR | General Relativity |

LIV | Lorentz Invariant Violation |

DSR | Deformed Special Relativity |

MCL | Modified Composition Law |

EFT | Effective Field Theory |

MDR | Modified Dispersion Relation |

## References

- Oriti, D. (Ed.) Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]
- Kallosh, R.; Linde, A.D.; Linde, D.A.; Susskind, L. Gravity and global symmetries. Phys. Rev.
**1995**, D52, 912–935. [Google Scholar] [CrossRef] - Smolin, L. What are we missing in our search for quantum gravity? In Foundations of Mathematics and Physics One Century After Hilbert; Springer: Cham, Switzerland, 2018; pp. 287–304. [Google Scholar] [CrossRef]
- Colladay, D.; Kostelecky, V.A. Lorentz violating extension of the standard model. Phys. Rev.
**1998**, D58, 116002. [Google Scholar] [CrossRef] - Amelino-Camelia, G. Quantum-Spacetime Phenomenology. Living Rev. Relativ.
**2013**, 16, 5. [Google Scholar] [CrossRef] [PubMed] - Hossenfelder, S. Bounds on an energy-dependent and observer-independent speed of light from violations of locality. Phys. Rev. Lett.
**2010**, 104, 140402. [Google Scholar] [CrossRef] [PubMed] - Amelino-Camelia, G.; Matassa, M.; Mercati, F.; Rosati, G. Taming Nonlocality in Theories with Planck-Scale Deformed Lorentz Symmetry. Phys. Rev. Lett.
**2011**, 106, 071301. [Google Scholar] [CrossRef] [PubMed] - Amelino-Camelia, G.; Freidel, L.; Kowalski-Glikman, J.; Smolin, L. The principle of relative locality. Phys. Rev.
**2011**, D84, 084010. [Google Scholar] [CrossRef] - Carmona, J.M.; Cortés, J.L.; Romeo, B. Nonuniversal relativistic kinematics. Phys. Rev.
**2015**, D91, 085036. [Google Scholar] [CrossRef] - Carmona, J.M.; Cortes, J.L.; Relancio, J.J. Spacetime from locality of interactions in deformations of special relativity: The example of κ-Poincaré Hopf algebra. Phys. Rev.
**2018**, D97, 064025. [Google Scholar] [CrossRef] - Carmona, J.M.; Cortes, J.L.; Relancio, J.J. Does a modification of special relativity imply energy dependent photon time delays? Class. Quant. Grav.
**2018**, 35, 025014. [Google Scholar] [CrossRef] - Kowalski-Glikman, J.; Nowak, S. Noncommutative space-time of doubly special relativity theories. Int. J. Mod. Phys.
**2003**, D12, 299–316. [Google Scholar] [CrossRef] - Kosinski, P.; Maslanka, P. The Kappa-Weyl group and its algebra. In From Field Theory to Quantum Groups; World Scientific: Singapore, 2012; pp. 41–51. [Google Scholar] [CrossRef]

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Carmona, J.M.; Cortés, J.L.; Relancio, J.J.
Observers and Their Notion of Spacetime beyond Special Relativity. *Symmetry* **2018**, *10*, 231.
https://doi.org/10.3390/sym10070231

**AMA Style**

Carmona JM, Cortés JL, Relancio JJ.
Observers and Their Notion of Spacetime beyond Special Relativity. *Symmetry*. 2018; 10(7):231.
https://doi.org/10.3390/sym10070231

**Chicago/Turabian Style**

Carmona, José Manuel, José Luis Cortés, and José Javier Relancio.
2018. "Observers and Their Notion of Spacetime beyond Special Relativity" *Symmetry* 10, no. 7: 231.
https://doi.org/10.3390/sym10070231