Can someone explain why the “c” is squared in Einstein’s relativity equation?
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Without getting into a proof which would be beyond the scope of ELI5, it’s to make sure that the units match up
Energy is measured in Joules, which is kg m^2 /s^2 and mass in measured in Kilograms (kg).
Mass at rest and energy are related, but they don’t have the same units of measurement. However if you multiply the mass by a velocity (m/s) squared you “force” the units to match up. It just turns out that the needed velocity is the speed of light.
Addendum:
in a slightly more general version of the equation (which accounts for movement) you have
E^2 = m^2 c^4 + p^2 c^2
Where p is momentum, measured in kg m/s. So in this case you would multiply momentum by only a single c rather then two because one copy of “m/s” is already accounted for.
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