Three Meanings of E=mc²
E=mc^2 is surely one of the most misunderstood equations in physics.<p>The best interpretation is as part of the full momentum-energy equation (letting c=1): E^2 = p^2 + m^2. This simply says that the energy E of a system is a combination of energy due to movement (p) and energy due to mass (m). At rest (p=0) this reduces to E=m, or E=mc^2 if you kept track of units.<p>&gt; Even masses at rest have an energy inherent to them.<p>This is a real insight.<p>&gt; Mass can be converted into pure energy. This is the second meaning of the equation, where E = mc² tells us exactly how much energy you get from converting mass<p>This is a pop-sci explanation, but it falls apart when you dig a bit. Does F=ma tell you that &quot;force can be converted into acceleration?&quot; Of course not; it tells you that force implies acceleration, and vice versa.<p>Or: if mass can be converted into energy, then you would have more energy and less mass, so E=mc^2 would no longer hold. It can&#x27;t be both an equivalence and an exchange ratio.<p>&gt; If you take a photon and and electron and smash them together, you get a photon and an electron out. But if you smash them together with enough energy, you’ll get a photon, and electron, and a new matter-antimatter pair of particles out. In other words, you will have created two new massive particles.<p>Later we learn that mass is determined by energy and momentum, both of which are conserved, so mass must be conserved too.