Time, space, and velocity in our expanding Universe

Why does the relative velocity between two frames of reference cause the length and time variations predicted by the Lorentz transformations? We know that a mass causes length contraction and time dilation in its surrounding spacetime. Could gravity be the cause of the length and time variations due to velocity?

With thanks to NASAESA, G. Illingworth (University of California, Santa Cruz), and G. Bacon (STScI) for the Hubble Legacy Field – Zoom of the galaxies, and the Hubble telescope’s deep field pictures on the home page, and the other pages on this site.