Ryan Hancock, of Kings High School, asks :-
How did Einstein come up with E = Mc^2
Rob Ballagh, a physicist at Otago University, responded.
This famous equation, E = Mc^2 is part of Einstein's theory of special relativity and he based this theory on two seemingly simple ideas. First, the speed of light is the same for every observer moving at a constant speed, regardless of what their speed is. Second, the equations of physics must have the same form for any such observer.
Actually these ideas weren't that obvious at the time, and he arrived at them, probably after a great deal of thought, with the aim of providing the simplest possible explanation for a number of puzzling experimental results that were known at the time. Although his ideas were revolutionary, he wanted to preserve some other ideas in physics that had proved very useful in the past. In particular he wanted the principle of conservation of momentum to be retained (the momentum of a particle is its mass times its velocity), he wanted to define the force on a particle as the rate of change of its momentum, and he also wanted to keep the existing definition of energy, which means that the rate at which the energy of an object increases is given by the force times velocity.
Einstein then expressed these ideas in a mathematical form, and found that the principle of momentum conservation required that the mass of an object must increase with its velocity. When this was included in the expression for the increase of energy of a particle (Force times velocity) this wonderful equation E = Mc^2 appeared.