For an object at rest (and let’s assume we don’t have to worry too much about gravity), E=mc2 is a correct equation, where E is the overall energy of the object, and m is its mass, and c is the speed of light. For an object that’s moving, it also has momentum (→p), and this momentum necessarily implies that the object will have some kinetic energy adding on to its total energy. Special relativity provides a more general version of this equation that is relevant for moving objects as well. Namely:
E2−(→pc)2=(mc2)2
This reduces to the original E=mc2 version if the object is not moving (→p=0). Another interesting special case is when m=0. This is the case with photons, for example, which are massless. Then the above reduces to:
E=c|→p|
So photons have energy proportional to their momentum. (Which turns out to be equivalent to saying that their frequency is inversely proportional to their wavelength. Which has to be true, since they travel at the speed of light.)
Note that in special relativity, energy is frame-dependent, and if you want to deal with quantities that are the same in every frame, you’ll want to use the “4-momentum”. So one other requirement for using this equation is to fix a frame where we’re talking about the energy in that frame.
Source: Physics undergrad degree, several courses covered various aspects of this material. Part of this was learning about the various experiments that were done to establish special relativity. Back in the day, the Michelson-Morley experiment was quite a big piece of evidence, as were the laws of electromagnetism themselves, which were already very-well pinned down by Einstein’s time. Now we have much more evidence, what with being able to accelerate particles very close to the speed of light in the LHC and other accelerators.
For an object at rest (and let’s assume we don’t have to worry too much about gravity), E=mc2 is a correct equation, where E is the overall energy of the object, and m is its mass, and c is the speed of light. For an object that’s moving, it also has momentum (→p), and this momentum necessarily implies that the object will have some kinetic energy adding on to its total energy. Special relativity provides a more general version of this equation that is relevant for moving objects as well. Namely:
E2−(→pc)2=(mc2)2
This reduces to the original E=mc2 version if the object is not moving (→p=0). Another interesting special case is when m=0. This is the case with photons, for example, which are massless. Then the above reduces to:
E=c|→p|
So photons have energy proportional to their momentum. (Which turns out to be equivalent to saying that their frequency is inversely proportional to their wavelength. Which has to be true, since they travel at the speed of light.)
Note that in special relativity, energy is frame-dependent, and if you want to deal with quantities that are the same in every frame, you’ll want to use the “4-momentum”. So one other requirement for using this equation is to fix a frame where we’re talking about the energy in that frame.
Source: Physics undergrad degree, several courses covered various aspects of this material. Part of this was learning about the various experiments that were done to establish special relativity. Back in the day, the Michelson-Morley experiment was quite a big piece of evidence, as were the laws of electromagnetism themselves, which were already very-well pinned down by Einstein’s time. Now we have much more evidence, what with being able to accelerate particles very close to the speed of light in the LHC and other accelerators.