This post continues a series of posts. The previous one was here.
I’ve noted before that the one-way speed of light is a convention (see John A. Winnie, Philosophy of Science, v. 37, 1970). The two-way (round-trip) speed of light is known to equal c, but the one-way speed may vary between c/2 and infinity, as long as the two-way speed equals c. The isotropic convention is the “scientific” one because modern science prefers symmetry.
What do people ordinarily do? As I’ve mentioned before here, people act as though the light from stars is where it is seen, when it is seen. The light is viewed as if it traveled instantaneously. As long as the return trip is considered to travel at the speed of c/2 this is perfectly legitimate.
This is also the approach of Newtonian mechanics, which uses the Galilean transformation in which the time coordinates are universal. This implicitly uses an anisotropic convention for the speed of light. Because no time elapses between light coming from distant stars in this model, time can be universally identical.
As I’ve pointed out before here, there is a dual to this Galilean transformation:
Galilean transformation (3+1): r1´ = r1 – vt1,
Dual Galilean transformation (1+3): t1´ = t1 – r1/v,
where the other coordinates remain unchanged. The dual Galilean transformation implicitly uses the opposite convention: the return trip of light travels instantaneously. The isotropic convention leads to the Lorentz transformation or its dual, which was described here.
The scientific approach then should be to combine the Lorentz transformations into a 3+3 dimensional invariant interval, which I’ve presented here. The problem with all this is that it loses touch with the way people ordinarily live and speak. Science becomes more and more esoteric. Is there a way to be consistent with empirical knowledge and with ordinary life, too?
The answer is yes, but only by sacrificing the single, static answer that modern science so craves. We would have to use the Galilean transformation for observers/receivers and the dual Galilean transformation for transporters/transmitters. There would be a kind of dialectic of the two transformations to represent reality.
Instead of the isotropic center would be the anisotropic center, a dynamic center.