Relativity Lite

Figure 1. A representation of the universe in two spatial dimensions as lying on the surface of a sphere whose radius grows larger with time. The yellow disks lying on the inner sphere represent galaxies whose diameters are extremely exaggerated in size relative to the circumference of the universe. As the universe doubles in size, the galaxies—now red to distinguish the two times—have moved outward on the outer surface and have been dragged apart by the expanding universe without the galaxies changing size. A yellow galaxy sits at about the three o’clock position on the edge of our view of the universe at its initial size, with a second galaxy just above it and a third just above that. As the universe doubles in size, the corresponding, now-red, galaxies move twice as far apart. The blue arrows adjacent to the yellow galaxies may be used to count the center-to-center distance between the first, second, and third galaxies as the universe expands. The green arrows add to the blues ones and represent the change in distance, which we divide by the time interval to get the recessional velocities. The distance from the first to the third galaxy has grown by two green arrows, while the distance from the first to the second galaxy has grown by only one green arrow, so the recessional velocity of the third from the first is twice that of the second galaxy from the first. This is the meaning of the Hubble–Lemaître law.