Dear Espritch:

Thank you for your comments. Perhaps the following can help to clarify what I have presented.

Some time before the Inquisition burnt him at the stake for his ideas, Giordano Bruno (1548–1600) stated “The center of the universe is everywhere, and the circumference nowhere.” That idea anticipated twentieth century cosmology with its centerless, unbounded universe. It is presently believed that all motion is relative. Therefore, like Bruno, we can choose any location as our center, origin, or reference point; it might as well be the Earth from which we make our observations.

The galaxy distances we measure and the galaxy velocities we calculate are all relative to the Earth. In this context, then, the Earth does not move away from a source of light; only the source moves away. To consider motions of the earth and a galaxy we must take a reference point distant from either of them. Of course if the Earth were viewed from galaxy M83, for example, the earth would seem to move rather than M83. But we observe from here. Thus the distance traveled by the light is the distance of the galaxy from Earth at the time the galaxy’s light was emitted. In the interim, relative to Earth, the Earth would have stayed put and the galaxy that would have moved away. The light travels no additional distance.

In your second paragraph you suggest that earlier, when galaxies were closer, their velocities were lower. That would imply that the further they separated the higher their velocities became. Accelerations of any kind, whether for a skateboard or a galaxy, require the input of energy. If the galaxies have continuously accelerated since the ‘big bang’, where has the energy for their acceleration come from? If you believe in the ‘big bang’, the galaxies (or their precursors) were set into motion at the beginning. Then, after radiation pressure had spent itself all galaxies (except our neighbor the Andromeda galaxy and a few others we see where one cannibalizes the other) began to coast apart at constant velocities. Mutual gravitational attraction, strangely, seems not to have entered the picture to any appreciable extent. Cosmologists do not know whether the universe will expand forever or eventually collapse.

In a universe undergoing unaccelerated expansion the distances between galaxies increase linearly with time, and since there is no acceleration the relative velocities of galaxies remain constant (i.e., independent of time). Thus, at any one time it is true that velocity = Hubble’s constant multiplied by distance (v= Hd). However, since relative velocities remain constant, it follows that since distances increase with time, the Hubble constant must decrease with time. Hubble’s law cannot be independent of time. Hubble’s law is flawed by the error of time confusion: the confusion of past times with each other and with the present time. See my recent post SPECTROGRAPHIC RED-SHIFT
IS NOT CAUSED BY RECESSION OF GALAXIES for more of this.

As for my duplex graph, once you get used to multiplex graphs they present no problems. They show the relationship of data in one graph to that in another and are a great convenience to the draftsman.