Lorentz, Edwards transformations and the principle of permutation   invariance
  The Lorentz transformation is derived without the postulate of the universal limiting speed, and the general Edwards transformation is obtained by using the principle of permutation invariance (covariance). It is shown that the existences of the one-way universal limiting speed (in the Lorentz transformation) and the constancy of the two-way average speed of light (in the Edwards transformation) are the necessary consequences of the principle of permutation invariance that is consistent with the postulate of relativity. The connection between the Edward transformation and the general coordinate transformation is discussed, and based on this, we find that the physical meaning of the Edward parameter, which indicates the anisotropy of the speed of light, is a gravitomagnetic potential of the spacetime. 
Jian Qi Shen