More precisely, they are most close to the real model of gravity, but of course they are not right theories (just a sets of rules, which whether well or bad work). However, today we have nothing better than they are.
In fact if you even somebody else try to measure a mass, then you even somebody else can obtain only a (rest) mass. In this sense a mass doesn't increase with velocity, nobody can to measure it because a (rest) mass is an invariant.
I like it. After Pauli's book everyone should termed the mass... kinda "Oh! yes, of course, I quite forgot (in Pauli's terms, not Einstein) the rest mass..."
Just say me, you really use those terms when you read or use the QFT??? There are no the relativistic or rest mass and total and rest...
Energy yes, mass no.
What is a relativistic and rest mass or total and rest energy? What for? Moreover with c=1. Energy and mass.
In general, I think, that we already have understood each other.
Of course, not. You’ve made mistake again p=mug, where
`````____
g=1/Ö1–b2,
b=u/c.
In Einstein's first paper he really does speak of transverse and longitudinal mass, but he obtain the following equation,
``````````______
W=mV2(1/Ö1–u2/V2–1)
where m – mass, V – speed of light.
And...
Once again, mass is an invariant concerning Lorentz and Poincare transformation groups. You can't defining mass by gravitation, because measure of attraction within dependence to both an energy and direction of moving. E.g. two photons with the same energy, but the perpendicular momentums will...
English is much easier than German, French and Chinese, last ones are much easier than Russian. But English is most useful for managing and mutual understanding, Russian is most useful for expression of emotions.
That's mass, you can call it the rest energy, but not rest mass.
You've made mistake. In general, E0=mc2, but total energy of particle E is equal to mc2 if and only if the particle's momentum p is equal to zero, because E=p2c2+E02=p2c2+m2c4
Let c=1, then
E=p2+E02=p2+m2.
The serious...
Because photon has both linear part of four-momentum, and helicity, therefore it needs the four-dimensional space. You can't describe a photon in space having smaller dimensionality. You can't conserve both momentum, and helicity, and spin, without four-dimensional space.