What happened? Aren't there any scientists here who could make this simple, high-school-level calculation? Who is the GR expert here on this forum?

Ok, here is one question for both GR expert, and some expert for one, or more, of (too) many overlapped and interrelated theories of micro-_{(nano-pico-femto-atto-zepto-yocto)}-cosmos (i.e. QM, QED, QCD, P-branes, D-branes, M-theory, string, superstring, gamma-gamma physics, Higgs-mechanism, any combination(s) of all that, etc.).

Let us imagine the following scenario (am I allowed to call it "gedanken experiment"?): We are in a small spaceship, far away in space, in the middle of some huge intergalactic void (that is, there where the general-relativity-effects are not measurable). Our spaceship has the lab equipped to accurately measure the mass of electron, of positron, as well as the energies of gamma-photons. We have measured the masses of electron and positron. And then, we setup the collision of one very slow electron and one very slow positron (hence, there are no measurable special-relativity-effects), and we measure the energies of two gamma-photons, which are the result of that collision. If we then divide the total measured energy of gamma-photons E with the sum of masses of electron and positron m, we will get that E/m = c^{2}. Hence, shouldn't this be the obvious proof that the equation E = mc^{2} is the fundamental, elementary, quantum-level equation, and not the consequence of relativity? Shouldn't this equation be the origin of relativity, and not the consequence? And, the origin-equations, that is, the cause-equations, that is, the fundamental equations, can be deduced from consequences (i.e. that is how the Planck's quantum equation was derived, that is how the Maxwell's equation for EM propagation velocity was derived). In other words, bricks are not the physical consequence of the brick-house, but opposite: the brick-house is the consequence of superpostion of bricks. Or I suffer from too much reason and common sense, which are "proved as unreliable qualities" if someone wants to deal with "real science"?

[tex]F = m \cdot a, F = \frac{dE}{dl}, a = \frac{dv}{dt} \Rightarrow[/tex] [tex]dE = m \cdot \frac{dv}{dt} \cdot dl = m \cdot \frac{dl}{dt} \cdot dv = m \cdot v \cdot dv[/tex] ; [tex]dE = dm \cdot c^2[/tex]

[tex]dm \cdot c^2 = m \cdot v \cdot dv \Rightarrow[/tex] [tex]\displaystyle \int_{m(v_{=0})}^{m(v)} \frac{dm}{m} = \frac{1}{c^2} \displaystyle \int_{v_{=0}}^{v} vdv[/tex] [tex]\Rightarrow[/tex] [tex]\ln \frac{m(v)}{m(v_{=0})} = \frac{1}{2} \cdot \frac{v^2}{c^2}[/tex] [tex]\Rightarrow[/tex] [tex]m=m_0 \cdot e^{\frac{1}{2} \cdot \frac{v^2}{c^2}}[/tex] [tex]\Leftrightarrow[/tex] [tex]E = E_0 \cdot e^{\frac{1}{2} \cdot \frac{v^2}{c^2}}[/tex]

This simple derivation is physically justified in the most essential way possible, and it is also experimentally confirmed: if positron and electron have higher kinetic energy before their „annihilation“, then the photons which are the result of the positron-electron „annihilation“ have higher energies, too. Hence, each infinitesimal increase of their kinetic energy [tex]dE = m \cdot v \cdot dv[/tex], is converted into appropriate energy increase [tex]dE = dm \cdot c^2[/tex] during "annihilation" - all in accordance with the energy conservation principle.

In order to get Einstein's equation, we have to add the part which is not physically explainable:

[tex]dm \cdot c^2 = m \cdot v \cdot dv + dm \cdot v^2[/tex]

[tex]dm \cdot (c^2 - v^2) = m \cdot v \cdot dv[/tex]

[tex]\frac{dm}{m} = - \frac{1}{2} \cdot \frac{d(1 - \frac{v^2}{c^2})}{1 - \frac{v^2}{c^2}}[/tex]

[tex]\displaystyle m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]