I guess I must do it for those who asked the questions.
Computing for the unprimed in the 1-d Galilean transformation, we have the equations x=x'/(1-v/c) or t=t'/(1-v/c), or simply t=t'. Since the classical scientists consider space and time as non-transforming absolutes and since they consider the motion or velocity transformations, the space or time variables are replaced with the velocity variables u' and u that represent the differing velocities as viewed in the primed and unprimed frames of reference. The u' is the initial velocity that is equal to the velocity c - which is any velocity considered; and v is the added velocity.
The c variable basically represents the reference value for the velocity transformation; the c variable is the common denominator for the velocity addition according to the transformation factor (1-v/c), which is (c/c-v/c). And so, as suggested by the Galilean transformation factor, the c variable is any velocity considered and that becomes the reference for the velocity transformation on account of the added velocity v.
In the 2-d Lorentz transformation, the c variable represents the velocity of light - not just any velocity. And according to Maxwell the velocity of light c remains the same in all frames of reference. So, in the Lorentz transformations the Galilean idea of velocity transformations is no longer valid. The u' and u variables that are respectively used to represent the initial and resultant velocities as accounted by the Galilean transformation are therefore no longer generally definitive.
Einstein apparently discovered that the mass variables m and m' may be admitted by substitution into the transformations equation, instead of the u and u' variables. The substitution indicated that other physical transformations occur instead of the velocity transformations. And, notably, a tacit premise is that space and time are not transformed as suggested by the fact that the space and time variables are removed and replaced by the mass variables. The equations show that the mass phenomenon and the electromagnetic phenomenon are involved in the transformations and not space or time.
We know that electromagnetic waves are forms of motion. And the transformation factor indicates that mass is clearly expressed in terms of c2/c2 which is an expression that involves the electromagnetic phenomenon. I have argued that both the mass phenomenon and the electromagnetic phenomenon are constructs of motion. This is why I argue that only the motion transformation is valid and that the arbitrary space and time transformations of Einstein's theory of relativity is invalid.
The special relativity theory is apparently alright because it is mainly about the motion transformations that involve the mass phenomenon and the electromagnetic phenomenon. But general relativity that purports the 'motion' and transformations of space and time is illogical.
The motion transformation is true in the case of the Galilean velocity transformations. The motion transformation is also true in the case of the Lorentz transformations by which we have special relativity as accorded by the 'relativistic' mass formula and Einstein's mass-energy relation expressed by the famed formula. So, we have two points of proof (the Galilei-Newton transformations and the Lorentz-Einstein transformations) for motion transformation.
However, Einstein's general relativity - i.e., the relativity of the purported motion of space, the relativity of the purported motion of time, and the relativity of the motion of motion - is one grand gift of confusion that Einstein left us with.
I think the valid formulations may all be interpreted in terms of the transformations of motion. If we morefully embrace the fact that in the first place the defining premise is that of the consideration for the motion transformations, which is why in the transformation equations the space and time variables are removed and replaced with the variables (e.g., u, u', m, m', E, E') that represent motion constructs, I am convinced that we will find that it is all about motion transformations. I am convinced that we will find that our physics is all about motion transformations if we will seriously consider motion transformations in the strict sense.
I have detailed my explanations regarding the 1-d, 2-d, and 3-d transformations that occur in nature. You can find my explanations in my book/ebook, my website, and in my FQXi essay. However, a radical paradigm shift is necessary in order to allow the appropriate understanding of the new scientific views that I propone.
All that's needed is a formal appreciation of the idea of simply the motion transformations - the pure kinematic relativity.
I don't know if it will happen with the help of FQXi. I doubt if the reputable minds of FQXi (e.g., Tegmark, Aguirre, Hawking, Guth, Smolin, Weinberg, and etc.) ever had a glimpse of my work. It seems that they listen ONLY to what they themselves are saying.
It seems that only a few here read my book/ebook and the other things that I have written. But, I'm hoping for the best.
Regards.
castel/www.kinematicrelativity.com