Lorenz transform equations (LTEs) are invoked to preserve the principle of relativity by resolving paradoxes arising therefrom due to the invariance of light-speed in all frames of reference. Said resolution of those paradoxes manifests itself as the framework of Special Relativity (length contraction, time dilation and relativity of simultaniety). Accordingly, LTEs fail to explain the reason for the invariance of light-speed or the reason the set speed is a certain value.
Mathematics is a necessary tool to prove the accuracy of hypotheses. But we must always return to the original source of any given hypothesis, once proven, in order to appreciate, intuitively, what we have learned. That source is through the lens of everyday human experiences, experiences stored in the brain's memory bank (particularly visual) where our imagination allows us to manipulate them every which way to hopefully attain fuller understandings of how our newfound hypothesis relates to them. It is by such means where we access meaning and value to things. So, mathematics is simply a tool to get us where we want to be. Some who study physics are satisfied in resorting to a compendium of mathematical equations to answer questions without fully understanding the subject matter in an intuitive way. I am not satisfied with mathematical explanations alone; I need to understand the bases for them. So, please explain your answer in the same verbal (non mathematical) context which I am about to present the problem (below).
At the outset, my question does not concern a relationship between a given "stationary" frame and the corresponding "moving" frame. Instead, it concerns only a "stationary" frame. Now, to begin, here is my preliminary question. What precise factors come into play to make the "stationary" observer record the same speed of light whether the light is approaching them or receding from them?
If the recorded speed (distance per unit time) is invariant for this "stationary" observer, then as the light approaches, the space between it and the observer would have to be stretching by just enough to offset the decreasing distance in order to maintain the recorded light-speed ("c"). And, as the light is receding, the space between it and the observer would have to be shrinking by just enough to offset the increasing distance in order to, once again, maintain the recorded light-speed ("c").
But said stretching and shrinking of space would not apply for the "stationary" frame because observed effects of length contraction of space in SR would only apply to the "moving" frame's perspective (which in this case would be the light itself as opposed to a "moving" mass). Time dilation and relativity of simultaniety also wouldn't apply here because, again, we are concerned with only the elapsed time recorded on the "stationary" observer's clock.
The following is, I think, a plausible explanation for this seeming conundrum. Unlike a moving mass which has already gained its momentum before being subjected to a force which accelerated it to its subsequent greater speed (the latter speed which, by analogy, we would be measuring), light is not a mass subject to Newtonian mechanics but is, instead, a form of energy created at the very moment it is emitted from the moving mass. The light could have no history of motion before it was created. So, its speed is independent of the speed of the moving mass.
So, we are always measuring the speed of light, not a "moving" mass from which the light was emitted. All that said, my argument might explain why a "stationary" observer will record the same speed of light whether it is approaching or receding from them, but now my ultimate question which is why is light-speed invariant in the first place and why is this invariant speed 299,792,458 meters per second (as opposed to any other speed)?
