Mass Defect vs Conservation of Mass

Here is the standard view connecting mass defect to $E=mc^2$.

Material bodies consist of matter formed by the elementary particles of protons and electrons, which do not ever decay and so express conservation of matter. The amount of matter is measured by the number of protons and electrons (and neutrons composed thereof). Matter is connected to gravitational mass manifested by free fall acceleration in a gravitational field scaling with the strength of the field, while being independent of the amount of matter/mass. As a result, all material bodies exhibit the same gravitational acceleration independent of composition. Conservation of matter translates to conservation of mass in the sense that mass does not change under gravitational free fall.

Assuming that inertial mass = gravitational mass, which is a cornerstone of both Newton's and Einstein's mechanics, it follows that all material bodies independent of composition react in the same way subject to gravitation or acceleration.

In particular, material bodies do not get ripped apart under gravitation, as the basic observation by Galileo. Further, a body in free gravitational fall will gain speed while loosing potential energy, while its mass will be conserved and not change. 

In chemical reactions the composition of molecules consisting of atoms consisting of protons and electrons change, but mass is conserved within measurement precision. So far so good. 

If we now bring in Einstein’s $E=mc^2$ as the golden apple of his Special Theory of Relativity SR, that is the idea that somehow mass $m$ is ”equivalent” to energy $E$ mediated by the factor $c^2$ with $c$ the speed of light, then things become strange. Einstein thus claims that in an exothermic chemical reaction releasing heat energy, there must be a corresponding mass defect with a loss of mass although the number of protons and electrons is the same after as before. However, this defect is too small to be measured, but in principle according to Einstein it is there, even if it cannot measured. This sounds like ghost science claiming ghosts to exist even if they cannot be detected.

But Einstein comes back in the case of nuclear reactions, claiming that the enormous release of energy in a nuclear explosion exactly corresponds to a mass defect according to $E=mc^2$, exactly. This is still under conservation of number of protons and electrons, since like in a chemical reaction only the composition (now of the nucleus) changes. And since the energy release is so big the mass defect is now measurable and then turns out to exactly match $E=mc^2$. Can anyone question this? In particular since the match is so precise! Exact!

Now the mass concept of SR is mysterious since it is supposed to change with velocity vs different observers using different reference frames moving with different velocities, and so be observer dependent, which appears to conflict with conservation of mass. If mass/matter is number of protons and electrons and this number does not change, then how can it be that different observers have different conceptions of mass? Are they not able to count?

This is a question which a child can pose, but it seems that physicists have no better answer than: Yes that is strange, but this is the way it is. Just accept it!

But it is easy for a suspicion to grow that in SR mass defect is computed from $E=mc^2$ to exactly fit with observed heat energy release. The mass defect would then not be the result of a measurement, which would be viewed to be superfluous, since anyway it is to be computed from $E=mc^2$. In other words, A = mass defect is claimed to be a consequence of B = $E=mc^2$. That is, B implies A or assuming B we obtain A. 

Now there is a lot confusion concerning the logic of implications, since often A implies B is viewed to be the same or at least a consequence of B implies A. But this is not correct logic. Nevertheless this incorrect logic is often used as argument to support that indeed $E=mc^2$ must be correct, since there is so much energy released in a nuclear explosion. But there is nothing in a nuclear reaction that has anything to do with the speed of light. 

Another thing to remember is that the mass-corrections from SR only become significant for speeds comparable to the speed of light. In the atom or the nucleus nothing is moving att such speeds and som the relevance of SR for atoms and nuclei is hard to motivate. You find as Many-Minds Relativity and analysis different from SR of measurements/perceptions of mass at velocities comparable to the speed of light. 

The net result is that conservation of mass and mass defect appear to be contradictory, and since there appears to be very good arguments for conservation of mass, we are led to conclude that mass defect is an illusion created by assuming $E=mc^2$ and computing mass defect from observing energy release. In particular, the argument that the existence of nuclear explosions proves $E=mc^2$, can be seriously questioned, even if modern physicists view it like undeniable evidence. 

Recall that $E=mc^2$ is derived from an assumption that all observers measure the same speed of light independent of inertial motion, which however is not an assumption (which can be wrong) but an agreement or definition (which cannot be wrong), since the unit of length (meter) is nowadays agreed to be measured in terms of the distance traveled by light over a certain length of time determined by the same atomic clock for all observers. This gives support to our  suspicion that $E=mc^2$ is also an agreement/definition from which mass defects are agreed to be computed in a certain way. The fact that computed mass defects exactly agree with $E=mc^2$ is a sign that we face an agreement/definition rather than physical fact.