[dleviwing]

Nimit;
If you have read my posts, you know that I do not view mass as a quantitative measure of a physical substance. You should also know that I do not view time dilation as a change in "Absolute Time", but only a perceived slowing of the device used to measure time. (a clock)

Since mass is a function of inertia, it will increase in value as an object acquires uniform motion.
Length will contract only due to the condensing of the physical substance as its quantity of uniform motion increases.

Lorentz transformation is the mathematical solution to define the behavior of the motions of matter. To understand them and the concepts of Relativity (STR and GTR) you must understand the nature of motion and its affects on the nature and behavior of the fundamental substance of the universe.

Using mathematical gauge theories to interpret reality only make the interpretation as abstract as the math. You should not view these interpretations as true paradigms for real scientific philosophy. These theories only define the science of measure.

Until you achieve this understanding you will only believe you know or only know without understanding; like so many others do.

- David, do you really think that “relativistic mass” concept arise from GTR, if so how?

Relativistic Mass is the consequence of the equation for the mass of a particle. Since light is presumed to have zero "rest mass", the momentum function (p) of the equation is removed and thus you have relativistic mass as defined by E=mc^2. What I actually think, is that rest mass and relativistic mass are the result of the same phenomena; uniform motion. Rest mass is primarily uniform angular motion were as relativistic mass is produced by uniform motion in the form of linear velocity (in the case of EM it is "c")

Best wishes;
Dave

PS: You already have many of the solutions for a TOE, I believe you only need a better understanding of motion.