I'm just a highschool student and thus not particularly knowledgeble about special relativity. However, I've always wanted to find a derivation of the famous equation E=MC^2. I could never find one in textbooks or on the web that didnt rely on oversimplifications or unexplained steps, so I tried to formulate one myself. I already knew the simple stuff, time dialation equations/relativistic mass stuff. That's easy to find. I figured it should be possible to derive E=MC^2 from that + classical mechanics stuff, so I went ahead and tried. To my astonishment, I think I may (emphasize may) have succeded. And so I was wondering if someone could take a look at my logic and tell me if it's valid:(adsbygoogle = window.adsbygoogle || []).push({});

I started with two equations, M2=M1[1/ √(1-V^2/C^2)] (relativistic mass equation) and KE=1/2(MV^2) (classical kinetic energy equation). I realized one could, by solving for V^2 in the first equation and plugging that into the latter (and recognizing that M2= M1+ΔM), obtain an equation for kinetic energy based on initial mass and the change in the mass due to the effects of relativity. This comes out to be 2KE= ΔMC^2(2+ ΔM/M1) after some algebraic manipulation. So what I then realized is that, because V^2=[1-(M1/{M1+ ΔM})^2] from the original equation, as M1 approaches infinity the energy imparted into an object results more and more solely in a relativistic mass increase because V approaches 0. Thus kinetic energy imparted into an object with "infinite" rest mass results in 0 change in velocity, meaning all that imparted energy results in a mass increase. This is what we want, a relation between mass and energy alone, regardless of velocity. So, if we take the limit of the equation formulated for KE based on M1 and ΔM as M1 approaches infinity, we get 2KE= ΔMC^2(2+0). This simplifies to KE= ΔMC^2, or more properly E=MC^2.

(Hopefully that made sense. I can elaborate on it a little more if isn't clear enough)

So, is that a valid "proof" or not? Thanks in advance for any replies.

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# E=mc^2 and it's derivation

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