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F.H. Stillinger, Axiomatic basis for spaces with noninteger dimension. J. Math. Phys. 18
1977
Earlier work this paper cites.
A. Schäfer, B. Müller, Bounds for the fractal dimension of space. J. Phys. A 19
1986
Earlier work this paper cites.
K. Svozil, Quantum field theory on fractal space-time. J. Phys. A 20
1987
Earlier work this paper cites.
G. Amelino-Camelia, J.R. Ellis, N.E. Mavromatos, D.V. Nanopoulos, Distance measurement and wave dispersion in a Liouville string approach to quantum gravity. Int. J. Mod. Phys. A 12
1997
Earlier work this paper cites.
D. Colladay, V.A. Kostelecký, Lorentz-violating extension of the standard model. Phys. Rev. D 58
1998
Earlier work this paper cites.
C.M. Will, Bounding the mass of the graviton using gravitational wave observations of inspiralling compact binaries. Phys. Rev. D 57
1998
Earlier work this paper cites.
T. Padmanabhan, Quantum structure of space-time and black hole entropy. Phys. Rev. Lett. 81
1998
Earlier work this paper cites.
T. Padmanabhan, Event horizon: magnifying glass for Planck length physics. Phys. Rev. D 59
1999
Earlier work this paper cites.
G. Amelino-Camelia, M. Arzano, A. Procaccini, Severe constraints on loop-quantum-gravity energy-momentum dispersion relation from black-hole area-entropy law. Phys. Rev. D 70
2004
Earlier work this paper cites.
J. Collins, A. Perez, D. Sudarsky, L. Urrutia, H. Vucetich, Lorentz invariance and quantum gravity: an additional fine-tuning problem? Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
J. Bolmont, J.-L. Atteia, A. Jacholkowska, F. Piron, G. Pizzichini, Study of time lags in HETE-2 Gamma-Ray Bursts with redshift: search for astrophysical effects and a quantum gravity signature. Astrophys. J. 676
2008
Earlier work this paper cites.
A.A. Abdo et al. [Fermi GBM/LAT Collaborations], A limit on the variation of the speed of light arising from quantum gravity effects. Nature 462
Original
2009
Earlier work this paper cites.

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2016

Lorentz violations in multifractal spacetimes

Calcagni, Gianluca

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Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance.

In the so-called multifractional theory with $q$-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski.
The energy at which multifractal effects should become apparent is $E_*>10^{14}\,{\rm GeV}$ (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value $1/2$.
We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned.

Built on

F.H. Stillinger, Axiomatic basis for spaces with noninteger dimension. J. Math. Phys. 18
1977
Earlier work this paper cites.
A. Schäfer, B. Müller, Bounds for the fractal dimension of space. J. Phys. A 19
1986
Earlier work this paper cites.
K. Svozil, Quantum field theory on fractal space-time. J. Phys. A 20
1987
Earlier work this paper cites.
G. Amelino-Camelia, J.R. Ellis, N.E. Mavromatos, D.V. Nanopoulos, Distance measurement and wave dispersion in a Liouville string approach to quantum gravity. Int. J. Mod. Phys. A 12
1997
Earlier work this paper cites.
D. Colladay, V.A. Kostelecký, Lorentz-violating extension of the standard model. Phys. Rev. D 58
1998
Earlier work this paper cites.
C.M. Will, Bounding the mass of the graviton using gravitational wave observations of inspiralling compact binaries. Phys. Rev. D 57
1998
Earlier work this paper cites.
T. Padmanabhan, Quantum structure of space-time and black hole entropy. Phys. Rev. Lett. 81
1998
Earlier work this paper cites.
T. Padmanabhan, Event horizon: magnifying glass for Planck length physics. Phys. Rev. D 59
1999
Earlier work this paper cites.
G. Amelino-Camelia, M. Arzano, A. Procaccini, Severe constraints on loop-quantum-gravity energy-momentum dispersion relation from black-hole area-entropy law. Phys. Rev. D 70
2004
Earlier work this paper cites.
J. Collins, A. Perez, D. Sudarsky, L. Urrutia, H. Vucetich, Lorentz invariance and quantum gravity: an additional fine-tuning problem? Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
J. Bolmont, J.-L. Atteia, A. Jacholkowska, F. Piron, G. Pizzichini, Study of time lags in HETE-2 Gamma-Ray Bursts with redshift: search for astrophysical effects and a quantum gravity signature. Astrophys. J. 676
2008
Earlier work this paper cites.
A.A. Abdo et al. [Fermi GBM/LAT Collaborations], A limit on the variation of the speed of light arising from quantum gravity effects. Nature 462
Original
2009
Earlier work this paper cites.