The pair of co-existing symmetrical universes, referred to as our (or positive) universe and negative universe, isolated and shown to constitute a two-world background for the special theory of relativity (SR) in previous papers, encompasses another pair of symmetrical universes, referred to as positive time-universe and negative time-universe. The Euclidean 3-spaces (in the context of SR) of the positive time-universe and the negative time-universe constitute the time dimensions of our (or positive) universe and the negative universe respectively, relative to observers in the Euclidean 3-spaces of our universe and the negative universe and the Euclidean 3-spaces of or our universe and the negative universe constitute the time dimensions of the positive time-universe and the negative time-universe respectively, relative to observers in the Euclidean 3-spaces of the positive time-universe and the negative time-universe. Thus time is a secondary concept derived from the concept of space according to this paper. The one-dimensional particle or object in time dimension to every three-dimensional particle or object in 3-space in our universe is a three-dimensional particle or object in 3-space in the positive time-universe. Perfect symmetry of natural laws is established among the resulting four universes and two outstanding issues about the new spacetime/intrinsic spacetime geometrical representation of Lorentz transformation/intrinsic Lorentz transformation in the two-world picture, developed in the previous papers, are resolved within the larger four-world picture in this first part of this paper.