A new approach to characterize the violation of Lorentz invariance

In this paper we introduced a parameter n to characterize the variation of the speed of light between different inertial systems. In order to satisfy the well-known fundamental principle and not violate some reliable experiments’ results, we should impose some necessary constraints on n. Firstly and importantly, the introduction of n should be in agree with the following three principles: (1)we can define the time in the whole space with a prescribed clock synchronization, (2)the time-space is uniform and the space is isotropic and (3)all the inertial systems are equivalent, which are the inheritance of the special relativity (SR). With some constraints on n, we construct a general coordinate transformation to meet the symmetry of inertial systems.

In recent years, many theories have shown the interest in the breakdown of the Lorentz invariance at ultrahigh energy scale, such as the quantum gravity, which imply that the energy of particle has a limited value (called the “Planck energy”) rather than be infinite derived from the Lorentz model. So we construct an expression for n to characterize the violation of Lorentz model. And further, by comparing with the well-known rainbow model, we found that the "maximum energy" derived in our paper is somewhat related to the "maximum energy" assumed in the rainbow model.