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E has units (SI) of kg m^{2}s^{-2}. m has units of kgTherefore you have to multiply m by a m^{2}s^{-2} to equate it to E or the units won't match, which is units of velocity ^{2}. If you raised it to any other power you'd have an equation that didn't make sense, units-wise.As for why it's c as opposed to another velocity, you can derive it from the equations of SR (Lorentz contractions). A hand-waving alternative to justify it is that for an object at rest (which is where that equation holds), you'd expect the only meaningful velocity in the theory to be the speed of light (or zero, but zero is trivial).

E has units (SI) of kg m^{2}s^{-2}.

you could work out a system using feet and ounces if you really wanted to.

It is very well known that E=mc².Why is it precisely c squared rather than c to the power 1.93, or some other power?Is it squared because of some sort of two dimensional relationship?

Quote from: JP on 26/05/2010 08:48:16E has units (SI) of kg m^{2}s^{-2}. the SI unit for energy is the Joule. What you've done there is to try to express it in terms of a combination of three other SI units i.e. mass (kg), size (m) and time (s).I have a pet speculation 'theory' that E= mc^{2} may represent the energy required to raise a two-dimensional order object to a three-dimensional order object (or conversely, the energy liberated by collapsing a three-dimensional order object down to a two-dimensional order object). Note that this is purely speculation though, and shouldn't be regarded as science; I only mention it here because it does seem to be along similar lines to what Geezer was thinking.