# Is the Notion of Time Really Fundamental?

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Time and Gravity

## 2. Is the Notion of Time Really Fundamental?

## 3. A Toy-Model

#### 3.1. Description of the Toy-Model

#### 3.2. Emerging the Lorentzian Signature

#### 3.3. Emerging a Diffeomorphisms Invariant Space-Time Dynamics

## 4. Discussion: Dynamical Space-Time from a Timeless Non-Dynamical Space

## References

- Barbour, J. The Discovery of Dynamics; Oxford University Press: New York, NY, USA, 2001. [Google Scholar]
- Wald, R. General Relativity; University Of Chicago Press: Chicago, IL, USA, 1984. [Google Scholar]
- Ellis, G.F.R. Physics in the real universe: Time and spacetime. Gen. Rel. Grav.
**2006**, 38, 1797–1824. [Google Scholar] [CrossRef] - Visser, M. Lorentzian Wormholes: From Einstein to Hawking; AIP: Woodbury, MN, USA, 1995. [Google Scholar]
- Kay, B.S.; Radzikowski, M.J.; Wald, R.M. Quantum field theory on spacetimes with a compactly generated Cauchy horizon. Commun. Math. Phys.
**1997**, 183, 533–556. [Google Scholar] [CrossRef] - Nordström, G. Zur theorie der gravitation vom standpunkt des relativitsprinzip. Ann. Phys.
**1913**, 42, 53354. [Google Scholar] - Will, C.M. The confrontation between general relativity and experiment. Living Rev. Relat.
**2005**, 9, 3. [Google Scholar] [CrossRef] [PubMed] - Gardiner, C.W. A Particle number conserving Bogolyubov method which demonstrates the validity of the time dependent Gross-Pitaevskii equation for a highly condensed Bose gas. Phys. Rev. A
**1997**, 56, 1414–1423. [Google Scholar] [CrossRef] - Markopoulou, F.; Smolin, L. Quantum theory from quantum gravity. Phys. Rev. D
**2004**, 70, 124029. [Google Scholar] [CrossRef] - Barcelo, C.; Liberati, S.; Visser, M. Analogue gravity. Living Rev. Relat.
**2005**, 8, 12. [Google Scholar] [CrossRef] - Girelli, F.; Liberati, S.; Sindoni, L. Gravitational dynamics in Bose Einstein condensates. Phys. Rev. D
**2008**, 78, 084013. [Google Scholar] [CrossRef] - Jacobson, T. Thermodynamics of space-time: The Einstein equation of state. Phys. Rev. Lett.
**1995**, 75, 1260–1263. [Google Scholar] [CrossRef] - Conrady, F.; Freidel, L. On the semiclassical limit of 4d spin foam models. Phys. Rev. D
**2008**, 78, 104023. [Google Scholar] [CrossRef] - Oriti, D. Group field theory as the microscopic description of the quantum spacetime fluid: A new perspective on the continuum in quantum gravity. Available as arXiv:0710.3276. (Accessed on 29 June 2011).
- Girelli, F.; Liberati, S.; Sindoni, L. Emergence of Lorentzian signature and scalar gravity. Phys. Rev. D
**2009**, 79, 044019. [Google Scholar] [CrossRef] - Liberati, S.; Sonego, S.; Visser, M. Faster-than-c signals, special relativity, and causality. Ann. Phys.
**2002**, 298, 167–185. [Google Scholar] [CrossRef] - Pictures taken from. http://www.bris.ac.uk/Depts/Chemistry/MOTM/diamond/diamond.htm (Accessed on 29 June 2011).
- Einstein, A.; Fokker, A.D. Nordström’s theory of gravitation from the point of view of the absolute differential calculus. Ann. Phys.
**1914**, 44, 321–328. [Google Scholar] [CrossRef] - Westman, H.; Sonego, S. Coordinates, observables and symmetry in relativity. Ann. Phys.
**2009**, 324, 1585–1611. [Google Scholar] [CrossRef] - Weinberg, S.; Witten, E. Limits On massless particles. Phys. Lett. B
**1980**, 96, 59–62. [Google Scholar] [CrossRef] - Jenkins, A. Topics in Particle Physics and Cosmology beyond the Standard Model. Ph.D. Thesis, California Institute of Technology, Pasadena, CA, USA, 26 May 2006. [Google Scholar]

**Figure 1.**On the left, the graphite lattice has a preferred slicing, contrary to the diamond lattice on the right [17].

© 2011 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 license (http://creativecommons.org/licenses/by/3.0/.)

## Share and Cite

**MDPI and ACS Style**

Girelli, F.; Liberati, S.; Sindoni, L.
Is the Notion of Time Really Fundamental? *Symmetry* **2011**, *3*, 389-401.
https://doi.org/10.3390/sym3030389

**AMA Style**

Girelli F, Liberati S, Sindoni L.
Is the Notion of Time Really Fundamental? *Symmetry*. 2011; 3(3):389-401.
https://doi.org/10.3390/sym3030389

**Chicago/Turabian Style**

Girelli, Florian, Stefano Liberati, and Lorenzo Sindoni.
2011. "Is the Notion of Time Really Fundamental?" *Symmetry* 3, no. 3: 389-401.
https://doi.org/10.3390/sym3030389