  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.
