AN IDIOT'S 4-STEP DERIVATION

OF

E=MC²

PROBLEM DEF: If mass and energy are equivalent, what is the transformation equation?

Classical Variables We Will Use:

Distance x Time t Velocity v Speed of light c Mass m Work W Energy E

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Assume a particle at rest in our inertial frame and having a rest mass 'm'.

1) Now imagine that the rest mass is entirely converted to pure radiation energy during some time interval 't' and measured at distance 'x' from where the particle was first observed. We will use these facts to compute the apparent Newtonian energy exchange from an 'at-rest potential' mass m to an 'in-motion kinetic speed-of-light' energy E.

2) Classical speed or average velocity as measured over time 't' is given by v = x/t. Therefore the speed of light as measured over x and t is c = x/t.

Acceleration 'a' is defined similarily as the average time rate of change in velocity. Velocity goes from zero to c in time t.

Therefore we have acceleration a = c/t

3) Newton's Law of mass acceleration says that a constant force 'f' acting over a time 't' and distance 'x' on a mass 'm' will produce an acceleration 'a' such that the relation f = ma holds to be true.

and since a = c/t, we have force f = ma = m(c/t) = mc/t

f = mc/t

4) Now given this computed force f, we can compute the amount of theoretical work produced in moving over distance x. The classical equation for work is W = fx. The total energy exchange from rest mass to free kinetic energy 'E' is given by this value.

E = W = fx

Subsituting mc/t for f we have,

E = fx = (mc/t)x = mc(x/t)

but x/t = c

therefore: E = mc^2

Duh ?!