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E=mc² is only conditionally valid. While mass can turn into energies, an energy alone may not be equivalent to a mass.
Although E=mc² has been accepted as unconditional since the atomic bomb, investigation shows that this formula is only conditional according to general relativity. The book E = mc² by David Bodanis (Walker, 2000) discusses only cases of where mass converts to energy. Many failed to notice that the mass would convert to a combination of energies. Therefore, a single type of energy may not be converted into mass. It is surprising that the scientific community almost missed this. The investigation started from a conclusion that there are no dynamic solutions for the Einstein field equation unless the coupling constants for energy-stress tensors can have different signs. This leads to questioning the general validity of this formula. In fact, there is a conflict from electromagnetism because the trace of an electromagnetic energy tensor is traceless. Also Einstein failed to extend the proof of the formula beyond the case of photons. (Photons actually include non-electromagnetic energy.) The invalidity of E = mc2 has been demonstrated experimentally by a reduction in weight of a charged metal ball (2005). However, E=mc² would predict an increase in weight, as Einstein would assert. This can be explained with a new repulsive force between charge and mass for a static case in general relativity. Moreover, weight reduction is observed when a capacitor is charged (1960) or when a piece of metal is heated up (2010). However, these cannot be explained with a four-dimensional theory, but can be explained in term of a five-dimensional relativity that has an additional general charge-mass interaction. Thus, mass can be converted to energy according to E = mc², but energy may not be converted to mass in terms of m = E/c². Now, energy is conserved in a closed system, but mass may not be. For example, although the photons have no mass, they can increase the mass of a matter, after it absorbs them. These findings have been published in the professional journals and the internet.