By the way, I remember that string theory is Lorentz invariant to all energies and all distances. f

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John Wheeler proposed that spacetime at the Planck scale is a quantum foam. A quantum theory of gravity that describes this quantum foam should violate Lorentz's theory of relativity. To explore this quantum foam, Giovanni Amelino-Camelia and several colleagues foam dice proposed in 1998 to study the energy-momentum relation for a photon has traveled great distances, ie examine whether the speed of a photon in vacuum depends on its energy ( is not constant).
Thanks to gamma-ray space telescope Fermi LAT (Large Area Telescope) have studied the photons emitted by the intense foam dice gamma-ray burst GRB 090510. No notes that the quantum foam insert any random dependence of the rate of photons with energy to follow a normal distribution at least to an energy of 2.8 E 95% CL Pl (Pl 1.6 99% E). Remember that E Pl is the Planck energy E Pl ~ 1.22 October 19 GeV. Therefore, there is no evidence of the existence of quantum foam at the Planck scale, reminds L Pl ~ 1.62 x 10 -33 cm.
Agnieszka Jacholkowska tells us, "Quantum foam dice gravity: Spacetime fuzziness in focus," Nature Physics, AOP 16 Mar 2015, doi: 10.1038 / nphys3293; . Vlasios echoing Vasileiou becomes et al, "A limit on Planck-scale spacetime Lorentz invariance fuzziness and stochastic foam dice violation," Nature Physics, AOP 16 Mar 2015, doi: 10.1038 / nphys3270.
Every distance scale has an associated energy level; foam dice for example, L is linked to E Pl Pl. The quantum foam at a distance scale should introduce a random variation of the speed of photons in vacuum v (E) = c + .DELTA.V (E), where .DELTA.V (E) is a random variable that is normally distributed ( Gaussian). Therefore, the time of arrival (T) of photons emitted foam dice by a distant source should submit foam dice a T + t distribution (E), where DT (E) is also a random variable distributed normally.
As a result you can explore a quantum theory of gravity that predicts a quantum foam to certain energy scale studying photons emitted by intense outbreaks foam dice of gamma ray bursts foam dice (GRBs). One of the most intense is GRB090510 having redshift z = 0.903 0.001. Its duration was very short ~ 1 s, but produced very high energy photons (up to ~ 31 GeV) with a light curve showing a temporal fine structure with separate ~ 10 ms spikes.
316 photons were observed less energy E th = 300 MeV and 37 photons foam dice with greater energy. foam dice Comparing the light curve with computer simulations can estimate the quantity w (z) = DT (E) / E. The confidence interval is calculated using the method of Feldman-Cousins. This figure shows the measured value of the dispersion (w best) for each value of the theoretical foam dice dispersion (w). The result is best w <0.013 (0.023) s / GeV at 95% (99%). From this value the power limit Pl E 2.8 for the energy scale associated with quantum foam is obtained.
By the way, I remember that string theory is Lorentz invariant to all energies and all distances. foam dice With mirror symmetry foam dice (mirror symmetry) between Calabi-Yau, R> L Pl distances and 1 / R <L Pl are equivalent (when R = 1 is the Planck scale). The Lorentz invariance is met at all scales and no quantum foam affecting photons speed.
Therefore, the new limit restricts other quantum theories of gravity, such as loop quantum gravity (LQG) and theories that assume that spacetime is discrete. In these theories there is a quantum foam that violate Lorentz invariance (at least at the Planck scale). To prevent new experimental limit must be assumed that the dependence of the rate of photons with energy is superlinear (quadratic or cubic), while the linear dependence (several theories as LQG, you can adjust for it) suppressed.
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