Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment

The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy. In this paper, the Lorentz invariance violation (LIV) of the photon sector is investigated in the locally Minkowski spacetime. The locally Minkowski spacetime is a class of flat Finsler spacetime and refers a metric with the anisotropic departure from the Minkowski one. The LIV matrices used to fit the experimental data are represented in terms of these metric deviations. The GRAAL experiment constrains the spacetime anisotropy to be less than $10^{-14}$. In addition, we find that the simplest Finslerian photon sector could be viewed as a geometric representation of the photon sector in the minimal standard model extension (SME).Comment: 13 pages, 2 tables. Two typos are corrected in Table

Debye entropic force and modified Newtonian dynamics

Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature $T_D$. The modified entropic force returns to the Newton's law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics (MOND). The constant $a_0$ involved in MOND is linear in the Debye frequency $\omega_D$, which can be regarded as the largest frequency of the bits in screen. We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde's entropic force, if the holographic screen is taken to be bound of the Universe. The Debye frequency is linear in the Hubble constant $H_0$