1) In your last post you have \(\displaystyle x = \dfrac{X}{X4}\). Previously I had thought X4 was some kind of component of a 4 dimensional vector. Apparently that isn't what you are talking about. One major element of my confusion is that X4 has no units? Even in projective geometry X4 should have a unit. Also, as far as notation is concerned, X4 is a numerical factor in all equations, such as \(\displaystyle v = \dfrac{V}{X4}\). It seems to be some kind of ratio (as you mentioned earlier) but you haven't yet defined what that ratio actually is. If I'm understanding what you are trying to say X4 is nothing more than a scale factor, which doesn't have any analogue in Physics. So physically speaking just what is X4?

2) In an earlier post you gave a set of equations that were explained in Chinese. I have been unable to translate those. My best guess is this: You are working in a system where \(\displaystyle \infty\) is a real number. To be precise: \(\displaystyle \dfrac{1}{0} = \infty\). This is not true for the real numbers as \(\displaystyle \infty\) is not an actual number.

If my guess is correct you are trying to discuss X4 in terms of a type of number system called the hyperreal numbers. Hyperreal numbers have two major features not belonging to the real number system. First, they include \(\displaystyle \pm \infty\) as actual numbers. Second, they also include infinitesimals, but you don't seem to need that feature. The hyperreal and real numbers have some similarities but you need to have some care in using them: the topology of the hyperreals and reals are not the same.

Depending on your answers I'm going to tackle

tomorrow.I have to make an analogy here and refer to SR temporarily. What render 3D space contracted? It’s movement or in my own way, the increase of mass.

-Dan