Delta2 said:
This holds only if you view mass as something different from energy and maybe that holds in the classical or relativity point of view, but according to the QFT point of view, isn't everything corresponding to energy in some type of (oscillating) field? (We might need an expert with the Higgs field here...).
I am inspired for this by the typical example of QFT with photons, a photon is the quanta of EM field that carries energy ##E=hf##. Ok probably mass of a particle isn't exactly the quanta of the Higgs field, which is the Higgs boson but my guess is that somehow is related to the energy of the Higgs field.
You can convert one form of energy into other forms of energy, thus the total energy is constant. But the idea that you can convert mass into energy is simply wrong, for the reason I stated.
In relativity energy and momentum form a four vector called the four-momentum ##(E/c,\vec p)##. Mass is the invariant norm of the four momentum ##m^2 c^2= E^2/c^2-p^2##. For a system at rest ##\vec p=0## and we get the famous ##E=mc^2##. So the famous equation is a special case of the general relation and describes a system with 0 momentum. Such a system still has energy, and that energy is proportional to its mass. For a system with nonzero momentum the energy ##E=c\sqrt{m^2 c^2+p^2}## is no longer proportional to the mass. This is why a single photon can have non-zero energy with zero mass.
The four-momentum is conserved so energy is conserved and each component of momentum is conserved. Since the invariant mass is a function only of conserved quantities it is also a conserved quantity. Mass is therefore particularly important being both conserved and invariant. Energy is conserved but not invariant, so mass (in the standard usage of the term) is in fact different from energy.
However, mass is not additive as energy and momentum are. Suppose you have a system composed of an electron and a positron at rest. In units where ##c=1## and both mass and energy are measured in ##\mathrm{keV}## then the system has a four-momentum of ##(511,\vec 0)+(511,\vec 0)=(1022,\vec 0)## and therefore a mass of ##1022 \mathrm{\ keV}##. When the electron and positron annihilate two photons are produced with opposite momentum as ##(511,511,0,0)+(511,-511,0,0)=(1022,\vec 0)##. The post annihilation system has the same conserved four momentum and the same mass as the pre annihilation system. The resultant photons are each individually massless but the system composed of both of them together has the same mass as the original system of the electron and positron.
A nuclear reaction does not convert mass into energy. It converts a system of particles with low KE into a system of particles with high KE. The invariant mass of the system is unchanged, but sum of the masses of the resulting particles is less than the sum of the masses of the original particles.