My physics teacher claimed to derive $E=mc^2$ by manipulating the equation for the speed of a standing wave on a string. A commonly known fact about the string wave equation is that speed can be calculated by $c^2=\frac{T}{\mu}$ where $\mu$ is the mass per unit length of the string. "Since Fds is energy we can work out $E = mc^2$". I feel like this is cheating. In fact, I know this is cheating but still, why does it work so well in terms of the units for energy? Isn't this just a funny coincidence?
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Here c is not the speed of light so the equation obtained is not the same as Einstein's equation. The fact that energy has dimensions of mass times some velocity squared is trivial and you can get it by dimensional analysis. Or just look at definition of kinetic energy.
nasu
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If the relation is correct then it will be dimensionally correct too u can manipulate it to get any dimensionally correct relation
eg.
user41111
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