On Invalidity of E = mc^2 and Related Errors by C. Y. Lo
Based on specially relativity, it is conjectured that mass can be equivalent to energy with the relation E = mc^2. This conversion is supported by fission and fusion in nuclear physics. In such a conversion the resulting energy is a combination of different types of energy.
On the other hand, there is no example that a single type of energy can be converted to mass. Einstein claimed that electromagnetic energy can be equivalent to mass because the photons can be converted to mass. However, this is actually due to that Einstein failed to see that photons actually consist of gravitational energy. This is natural after general relativity since a charged particle always has mass. Einstein tried to extend this relation to other types of energy for several years (1905-1909) but failed. Recently, experiments have shown that electromagnetic energy alone is not equivalent to mass.
However, some argued that one can define the mass of a particle with the formula F = ma. A problem is that such a mass may not be related to the energy of such a force. For instance, one can measure the electromagnetic force acting on a charge particle. However, this does not enable one to establish a relation between such a mass and the electromagnetic energy. Note that this is an error of Nobel Laureate G.‘t Hooft made in his 1999 Nobel speech.
Some theorists might argue to define m E = E/c2. For instance, some define an electromagnetic mass in such a way. However, one still does not have the relation between such different masses. Thus, in my opinion, this line of thinking does not seem to lead to any meaningful physics. It is probably a result of a failure in distinguishing mathematics from physics that must be additionally supported by experiments.
