rpenner, like Minkowski, would like you to believe that absolute space and time still exists.
It is unwise to misunderstand the moderators of a forum so badly that you misstate their positions on that forum. Neither time nor space is absolute because the metric of space-time geometry is indefinite. That is the quantity $$ds^2 \equiv \sum \limits_{\rho} \sum \limits_{\sigma} g_{\rho \sigma} \, d x^{\rho} \, d x^{\sigma} $$ can be zero or have either sign in contrast to the equivalent concept from Euclidean geometry, $$d L^2 = \sum \limits_{\rho} \sum \limits_{\sigma} \delta_{\rho \sigma} \, d x^{\rho} \, d x^{\sigma} = \sum \limits_{\rho} \left( d x^{\rho} \right)^2 $$. So there is no such thing as the absolute value of a pure space or time interval in Minkowski geometry or the geometry of GR. Most of us haven't been traumatized by a physics course, so your misstatements are glaring and without reasoned support. Thus you present no persuasive argument that you even have similar definitions for common physics terms in use.
If the geometry to support that can't be done in static 3D Euclidean (Pythagorean) space, then his mathematical solution is to simply posit an extra fourth dimension of time mutually orthogonal to the other three, set time proportional to jct, and triangulate away with the usual simple right triangle geometric relationships.
False, as the text of his 1908 lecture shows. It was just a throwaway comment, not a postulate.
https://en.wikisource.org/wiki/Space_and_Time_(Saha)
And the justification for inertialess light travel time (space) in every direction being equivalent to a Euclidean geometric solid is….? Don't tell me it's because it still a Euclidean vector space, because we already understand, it isn't.
It's obviously not a Euclidean anything because now we have complex numbers, making the norm now indefinite.
Velocities don't add the way you think they do mainly because they are really the same thing as your math refers to as "time". This is a reality, not an equivocation. You compare the proportional velocity of the moving hand of a stopwatch to the velocity of a runner. Time is nothing more or less than that.
That would be one choice of coordinate time, but not a
preferred choice of coordinate time. A choice of coordinate time is the opposite of absolute time, and it leads to a rejection of absolute space. The embrace of a per-trajectory notion of proper time does not endorse any sort of universal absolute time, but it is required property of a universe in which people to build sensible clocks.
By failing to distinguish between choices of coordinate time and the physical quantity known as proper time, you lose a lot of the mental scaffolding required to properly understand relativistic physics. By failing to do the work yourself, you fail to understand the velocity composition law.
Citation required.
Any time interval measured in any inertial reference frame is a measurement of a proportional relative velocity.
False. You need more information than the time interval. Even if you know the ratio between coordinate time and proper time, the velocity is not proportional to that ratio. Indeed, when the ratio is unity, the relative velocity between object and choice of standard of rest is zero.
This proportional relative velocity is one that RUNS AT DIFFERENT RATES at each and every one of those points in Minkowski spacetime rpenner has labeled names like: "Spot", "Jeremy" and "Tichibowenwicz". Time proceeds at different rates at "Spot", "Spot1", "Spot2" etc.
I named events, not locations. In special relativity, even location has nothing to do with the "rate of time". The rate of coordinate time is always 1 second per second. The rate of proper time is always 1 second per second. The two are only compatible notions when the clock is in the same state of motion as the choice of standard of rest.
The speed of light will measure exactly the same at all of those points, but none of them will be able to agree on how fast or slow anyone is aging unless they are in the same inertial reference frame.
Again you misuse language. No one is "in a frame" because a frame is an imaginary, invented system of Cartesian coordinates established about choices of a coordinate origin, a standard of rest, and orientation of the three spatial axes. They are not points, they are events, with zero extent in space and zero extent in time, so they aren't positions where a person could take time to think, discuss and agree on anything because there wouldn't be the time required to do so.
None of them will be able to report where they are or how fast they are going with respect to anything other than ONE of the other spots in relative motion. There is no absolute motion. There is no absolute time. You cannot make it conform to your ideas of absolute time by selectively dealing only with events that you consider to be simultaneous, which amounts to the exactly the same idea as freezing time so that you can do your fancy geometry in a non-existent static universe.
You need to read your sources better. No one has introduced absolute time into this conversation but you, and you haven't conveyed what you mean by it. No one is dealing with events which are considered absolutely simultaneous, although in coordinate time some events will be considered simultaneous given that system's choice standard of rest, obviously. Special Relativity does not describe a static universe, but a universe filled with motion.
In the universe of energy transfer events, EVERY QUANTUM OF ENERGY is in motion, and time as we measure it is simply a relative velocity.
A velocity relative to OUR choice of a standard of rest. Someone else might make a different choice of standard of rest, but describe the same universe. Understanding relativity is the ability to put oneself intellectually into the shoes of another and working out the logical consequences. Thus all of it comes as a logical whole: Lorentz transforms, velocity composition laws, Thomas precession, Minkowski norms, proper time, etc.
See
The Relativity of Simultaneity, post #22
The fifth thing is one-to-one-ness. (example with polar coordinates, example with three coordinates) The sixth thing is usefulness. (introduce metric) The seventh thing is simpleness. (orthogonal basis, Cartesian verses polar, equation of a straight line) [Breakfast!]
Regretfully, I again ran out of time to finish this now.