Theory of relativity - mass and energy

The formula now looks like this: Eₒ = mc². Which means: rest energy corresponds to mass, that is, only some internal energy.

See online calculator - Einstein Energy Calculator.

However, if by m we mean the relativistic mass, then it is also true E = mc² - for the total energy. This is an outdated approach.

So all the same: does mass correspond to energy?
It corresponds only to the energy of rest, that is, internal. For example, the mass of a body brought into rotation will become larger - according to the increase in its energy.

By the way, the formula was known before Einstein. At the turn of the century, the best minds huddled on this site.

Indeed, electrodynamics gave an expression for the impulse of the wave: p = E / c (E is energy). And considering that p = mv = mc, they came to the famous: E = mc². Since there was no doubt that mass is additive, Einstein made a seemingly logical conclusion: a body emitting light loses mass along with energy. It turned out that the formula expresses a universal property of any matter: energy corresponds to mass, and mass corresponds to energy.

Einstein was wrong? No, if by m we mean the mass arising from the relation p = mv. But it turns out to be a banality: relativistic mass is just another name for energy.

Can mass be converted into energy?
It sounds strange: mass is energy (rest) - up to a coefficient.

But what about the mass defect, nuclear energy, the source of which is said to be a decrease in mass? Annihilation? Let's figure it out.

When the nucleus decays, the total energy of the system does not change at all (the law of conservation of energy!) The total mass does not change either.

Energy is redistributed: part of the energy (and mass!) Of the nucleus is transferred to particles emitted during fission, including quanta of electromagnetic energy. Accordingly, the fragments into which the original nucleus disintegrated have a lower total mass.

It turns out that the fraction of the initial mass of the nucleus, as it were, "turned into energy." In fact, some of the rest energy (along with the mass) was simply released. During annihilation, all the rest energy (and mass) is completely transformed into another form - into the rest energy (and mass) of a set of quanta - photons.

How can photons have mass?
It seems to be known that the mass of a photon is zero ... Yes, for a single photon. But the set of photons moving in different directions already has a nonzero mass.

Let's give an illustration. For example, the system consists of two identical bodies moving oppositely at equal speeds. In general, it is at rest (the total momentum is zero). Then the kinetic energies of the two bodies are included in the internal energy of the system. Which, as you know, is equivalent to mass. The mass of the system turns out to be greater than the sum of the masses!

In place of bodies, there may be scattering photons, it doesn't matter. It is important that if the total momentum of the system is equal to zero, all its total energy turns out to be rest energy ... that is, mass.