Conservation of mass
In chemistry it has long been agreed that the mass is preserved in chemical processes. It's different in physics. There is no general conservation law for the mass. The extermination of couples is taken as a counterexample. Here an electron and a positron are converted into so-called pure energy, ie into a pair of photons. Since one assumes, according to Einstein, that photons have a rest mass of 0, one assumes that mass is lost during this process.
It is a teaching of life that if one gets stuck on a path, try to approach the problem the other way around in order to shed light on it. In the history of physics it is assumed that photons not only have the rest mass 0, but also have the mass 0. Accordingly, it is concluded that there is no conservation of the masses.
Let's do it the other way around and take a step back. E = mc²: Einstein set up this equation, and it made him famous. Nowadays it is often assumed that this equation only applies in extreme cases and is not universally valid. That is of course wrong. The equivalence of space and time from an absolute point of view also means that E = mc² always applies in an absolute point of view. The speed is always c, thus equal to speed of light. Now we see that there is the Conservation of Energy in physics. In the closed system the energy is constant. This can be summarized in an equation: E = const. If we summarize the two equations described, we get m * c² = const. in a closed system. Since the speed of light c is always constant, we divide an arbitrary but certain number const. by a number. The result is of course any number, but a specific one. Clearly explained: The energy in the closed system would be 4. According to the unit system, c = 1 can be set. 4/1 is always 4. Since the energy does not change, the equivalent mass also remains the same. The following applies: m = const / 1² = const.
So the law of conservation of mass 'm = const.' Applies in a closed system.
Let us now go back to the pair annihilation of electron and positron, in which one or more photon pairs arise. We see that at the beginning of the reaction the two starting particles have mass. Since the mass must be preserved in this process, it follows from this: Photons have a mass. You can read more about this under Mass and momentum of a photon. Einstein deliberately left this question open and only said that photons have no rest mass.
Conservation of the rest mass
Today in 2013 it became clear to me that the rest mass would be retained. It's easy again. It is about the connection between energy and momentum according to Einstein. The formula for this is: E² = E (0) ² + c²p², where E is the energy, E (0) the rest energy, p the momentum and c the speed of light. The experienced reader of my wiki should already know what it's getting at. We consider the whole for the closed system and set constant all quantities that we know will be preserved. According to the law of conservation of energy E is constant in the closed system, according to the law of conservation of momentum p is constant in the closed system. So it results:
const² = E (0) ² + c² * const²
If an expression is constant, the square is also constant, because the square of any given number is also any given number. Then with the constancy of speed of light c the following results:
const. = E (0) ² + const.
So it arises
E (0) ² = const. - const.
The difference between two arbitrary but specific numbers is also any arbitrary, but specific number. In the same way, the root of any, but certain number, also any, but certain number, even if there are plus and minus values. But these are firmly defined.
E (0) ² = const.
E (0) = constant
This is the law of conservation of rest energies.
But since E (0) = m (0) * c² applies, or m (0) = E (0) / c², then m (0) = const. / c². However, since an arbitrary but certain number is in turn any arbitrary but certain number through a constant, the following applies:
m (0) = constant
This is the law of conservation of rest masses in a closed system. Today, the rest mass is often referred to as the actual mass on the Internet. That is wrong: rest mass is the mass that a particle assumes when it is at absolute rest. Since, according to Einstein, nothing occurs in absolute calm, it is a theoretical term. But the rest mass is also preserved, so that nothing stands in the way of accepting the law of conservation of mass, not even small exchanges of mass and rest mass.
Ratio of mass to rest energy
On Wikipedia it is assumed that the mass only contributes to the rest energy. But since radioactive radiation, more precisely gamma radiation, can convert rest energy into kinetic energy, as the Wikipedians believe, there can be no general law of conservation of mass.
That is wrong for two reasons. On the one hand, we have just proven the conservation of rest mass and also the law of conservation of rest energies. So it is not so easy to convert rest energy into kinetic energy, and certainly not in a closed system. You have to imagine it differently. Binding energy is released. The photons or gamma rays, a type of radioactive radiation, are already present as binding particles in the substance. Since it is unstable, the binding particles are gradually released. Additional kinetic energy is not released, the photons usually have the speed of light c both as binding particles and as free energy. Since these particles were already inherent in the substance, as said, no rest mass is lost, which would also contradict the law of conservation.
Further consideration may explain the error on Wikipedia. Ultimately, the faster a particle becomes, the lighter it becomes. The photon has less eV than the electron which in turn has less eV than the proton, etc ... But if the particle now becomes faster and loses rest energy, e.g. in the case of pair annihilation, the proportion of kinetic energy naturally increases. Not only that, but the ratio between kinetic energy and resting energy is getting higher and higher. Therefore, the absolute theory for the electron - positron annihilation also predicts another particle that is heavier than an electron and is neutrally charged as far as foreseeable. This particle then probably decays again, so that it has not yet been observed. Nevertheless, the sum of the rest masses of the photons + x must correspond to the rest masses of the electron and positron. And since the aces is retained and photons are faster than electron and positron as far as we know, the resulting particle must also be slower, because the average of the velocities on both sides of the reaction equation must remain the same. So v (electron) + v (positron) / 2 = v (photon) + v (x) / number of photons + number x.