Wrong. According to your idea, a photon with total energy E and an electron with total energy E should have the same mass, but it's not.

No, you apply E=Mc^{2} to an individual particle system. Sure you can work out different values for mass, but for a photon, it does not even have a mass. But that's a whole different ball game involving more difficult field processes I doubt you could fully understand unless you sat down and learned this stuff.

But you would not have said what you did, if you had read my post and understood also what was said. I said E=Mc^{2} is non-relativistic, meaning it does not apply to particles travelling at or near light speed.

About the concept of mass, I have understood to be quite careful and to make very precise statements, despite its seeming simplicity. You wrote:

"Mass is a concentrated form of energy"

and I reply:

mass is not "a form of energy", mass "is" energy. But that statement is not complete, because we have to add: "fixed a system in space". If it moves, then it's not true anylonger.

examples:

1) I heat a piece of iron which is "not moving in the frame of reference I have chosen", giving it an amount of thermal energy equal to ΔE; its mass increases of an amount Δm. It comes out that Δm = ΔE/c

^{2}.

2) That piece of iron has the shape of a spring. I give it the energy ΔE as elastic potential energy by compressing it of the appropriate amount. Its mass increases of Δm.

3) I give it ΔE as any other form of energy. Its mass increases of Δm.

4) I choose to consider a void volume of space. Its mass is zero. Then a beam of light goes through it, for a brief instant. During that instant, the mass of the system increases of Δm = ΔE/c

^{2}, if ΔE is the average light beam's energy in that volume of space during that brief instant of time.

It doesn't matter what form of energy ΔE I give to the piece of iron,

It doesn't matter what form of energy ΔE I give to the fixed system I am considering, its mass increases of Δm.

Conclusion: mass is not "a form of energy", mass "is" energy, provided the piece of iron or the system I'm considering doesn't move in space.

So, you don't have to explain what mass is, you already have an explanation.

Just to precise your statement.