# Can you create mass with $E=mc^2$?

If you use the equation $E=mc^2$ could you make matter by dividing the $c^2$? I'm sorry if this is a really stupid sounding question or if it shouldn't be asked here.

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If you're asking "can matter be created from energy" the answer is yes; this is done all the time in particle accelerators, though only in extremely tiny quantities. Consider the production of antimatter for instance. –  Nathan Reed Mar 21 at 3:19
It's not a stupid question, that's exactly the kind of "what if" question that should always be asked when discovering a new formula. Indeed, if very energetic light (gamma rays) hits atoms, the light particle can be converted into an electron and a positron pair. –  Lagerbaer Mar 21 at 3:22
You can't create anything with a formula. I'm kind of confused about what you're asking here... –  David Z Mar 21 at 6:14

As noted by someone else, energy can be "converted" into mass e.g. via pair production. However, there is another example of this that you may be interested in:

The mass of the matter you come into contact with on an everyday basis is almost entirely from protons and neutrons, which are roughly 2000x more massive than electrons. The proton, for example, is comprised of two up quarks and one down quark. The combined rest mass of these quarks is about 10 MeV/c$^2$. However, the proton mass is about 100x larger, i.e. roughly 1000 MeV/c$^2$.

Thus about 99 percent of the mass of a proton (and indeed, the mass of everything you interact with) does not arise from the rest mass of elementary particles (e.g. quarks) but rather from their binding energy. Note that this does not come from the rest mass of e.g. gluons, which are massless. Details here.

So is it possible for energy to be converted into "matter"? In the above sense, not only is it possible, but almost all the mass you interact with is due to binding energy. To put it cutely: It's the glue.

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Yes. Matter (assuming it has mass) can be created from energy using the mass-energy equivalence. And, hence this principle got its name. For instance, take pair production where an energetic photon can create an electron-positron pair.

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