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Deriving e=mc^2
We begin with the definition of relativistic mass:
We can now define relativistic momentum as: Since force is defined as we can define force in the relativistic context analogously: In classical physics work is defined as We can reduce this to a problem in a single dimension for simplicity, and recall that the kinetic energy added to a body is equal to the work done on the body by an external force: From here we can say: Applying the definition of relativistic mass, the last expression becomes: [ Integrating through, we have The term on the left, The kinetic energy can be expressed more clearly, in my opinion, as And there you have it. Mass is energy! |
Latex isn't working entirely properly. But you should get the gist of it.
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I have fixed it for now, but certain things aren't rendering correctly.
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I'm glad I know this now. Or rather that I've read it.
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Well, at least now I know HOW e = mc^2
I'd heard it used to many times in cartoons, it was in my head before teachers ever got around too it (infact, I've probably learned more from cartoons than text books), but at least now I know how it fits together. |
Well, I'm glad it helped someone, and was not an exercise in LaTeX. If there is anything I can clear up, let me know.
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