It turns out v_t overlaps the same line as v and v' and the slope of each overlapping line is dependent on what coordinates you assign to the ct' axis.

Let's look at the point labelled ct'=1.

The coordinates of the velocity line at this point are (1.25,.75) where v=x/ct =.6c and the slope of the line is 1/v = 5/3. The velocity is x-axis/ct-axis.

The coordinates of the v'=Yv line are (1,.75) where v'=x/ct' = .75c and the slope of the line is 1/v' = 4/3. v' is the x-axis/ct'-axis.

The coordinates of the v_t=ct'/ct = c/Y line are (1.25,1) where v_t=ct'/ct = .8 and the slope of the line is 1/v_t = 5/4. v_t is the ct'-axis/ct-axis.

Normal algebra would not have labelled that point as 1, it would have only labelled it with the cartesian coordinates of (1.25,.75). I'm adding a 3rd ct'-axis which not only allows all facets of the main equation to be seen on the diagram but it allows both perspective views to be seen on one diagram instead of 2. It also avoids the mistakes relativity makes when switching from one perspective to the other as I'll discuss in the next post.

But let's go back to basic normal algebra for now. The simplest equation is y=x (which comes from the equation for a line y=mx+y_0 ). This equation would define the speed of light c on a spacetime diagram. c has no coordinates in relativity because c is actually made up of overlapping lines due to a cheat Minkowski added to his diagrams to make c appear the same from all perspectives (which it is anyway). The cheat he used was to take a normal frame rotation and flip the x'-axis up over the x-axis to make it look like the ct'-axis and x'-axis were rotated independently towards each other. Mathematically perfectly acceptable in order to force all c lines from every frame to overlap each other and have the same 45 degree angle on the Minkowski diagram. Epstein could have done the same thing on his diagrams except all frames would have the slope of c at 0 degrees. Epstein diagrams reveal a lot about the underlying mathematical constructs of relativity that do not necessarily follow the philosophical conclusions the Minkowski diagrams advocate.

In algebra, the equation y=1/x defines a hyperbola. The main equation of relativity creates straight lines and hyperbolas shifted 45 degrees from the simple equations of basic algebra. (This is not set in stone as the Epstein sum of squares version of the main equation uses circles that do not shift the velocity lines at 45 degrees or have an overlapping c line at 45 degrees.) The hyperbolas in relativity intersect the velocity lines at the same proper time. These hyperbolas connect a true, unseen, universal present at a distance and are not to be confused with the fake perspective present that Einstein invented in his clock sync method. In "ralfativity", I replace the hyperbolic lines with straight lines of 1/v_h lines of proper simultaneity of the Loedel half speed perspective (my own term).

Ralfativity only cares about the slopes of key velocity lines (v, v', v_t ,v_h ,v_ht, ) and their reciprocals which are lines of simultaneity. It only considers velocities separated into their coordinates of time and space and perspectives at the end. All clocks beat at the same universal rate within a frame and while earth may measure a ship going at .6c using earth clocks, the guy in the ship measures his v' speed at .75c using his own clock. The lines of perspective simultaneity (also called in relativity as now slices and x'-axes), arising out of Einstein's clock sync method, are illusory curiosities. They do not define a perspective present because the distance between points negates the very definition of a shared present.