As we all know energy and mass are equivalent. When I burn wood a small amount of mass is converted to energy. In theory, I could convert energy to mass. This is not practically possible, but, if I understand it correctly, mathematically they are equivalent ($E=mc^2$). Mass, however, can be expressed in different ways. I can have a kg of iron or a kg of gold and they have the same mass. Mathematically, they can be converted to the same energy and then back to the same mass. So, mathematically, a kg of gold can be converted to a kg of iron. But iron and gold are not the same, so I should need energy to make the transformation. So, where is this extra energy coming from?
Addendum: Let me explain more, there are other questions (e.g. Why can't I do this to get infinite energy?) in this forum that go like this: if I can have a space station and I shoot energy to the space station, and in the space station they convert the energy back to mass and drop it on Earth, and somehow we could use that kinetic energy, then when the mass is on earth, we convert it to energy again and keep doing it, therefore we have unlimited energy (the kinetic energy). The problem, in that reasoning, is that when we send the mass up the space station the wave is also affected by gravity (decrease frequency).
What is the issue in my description?