E=mc^2: What is Mass & Matter?

[ebodet18]

Mass or Matter in E=mc^2 ??

I understand that m stands for mass but I thought matter was transformed into energy. Is matter what mass is made of? I just don't get it.

 

[bcrowell]

Matter has historically been a loosely defined term, and its definition has evolved gradually over time. Today, many people seem to use it to mean fermions as opposed to bosons, but that's not universally accepted or understood. It really depends on context. The m in E=mc^2 is for mass, regardless of what the mass is made of.

 

[nonequilibrium]

Today, many people seem to use it to mean fermions as opposed to bosons, but that's not universally accepted or understood.

I think you might mean fermions/Higgs boson as opposed to gauge bosons?
To clarify to the OP: this distinction corresponds to the fact that we need to put in the fermions and Higgs boson by hand in the standard model, but that we get the gauge bosons "automatically" as they are the particles mediating the fundamental forces. Naively, this usage is the generalization of calling the electron matter, and the photon not (again: because photons merely describe interaction between matter).

Your question is a good one, and as bcrowelln has answered: what E = mc^2 is telling is, is that the rest energy of an object is related to its mass in that way. That's it. What this formula suggests, however, is much more. One knew, for example, that light had energy in it (but they didn't know it had mass) and one knew that atoms have mass (but they didn't really know it had energy for just "existing") but in light of this new formula, the question easily popped up: can we not somehow convert atoms into light, as long as we conserve this energy? In other words: this formula implied that rest energy might be a new kind of potential energy that you could convert. And indeed, we now know that for example electrons and positrons ("matter") can combine into photons ("not matter"), and the photons will have at least energy E = mc^2.