Why Does Energy = Mass Times the Speed of Light Squared?
Why Does E = MC2?
Kinetic energy, the energy of motion, is proportional to an object’s mass and to one-half of its velocity squared. This is expressed as:
KINETIC ENERGY = M x 1/2 V2.
According to the Special Theory of Relativity, as an object gets faster, i.e., as its velocity gets closer to the speed of light (“C”), the object shrinks in the direction of its motion, time slows down for the object, and its energy and mass increase.
According to the mathematics of Special Relativity, the amount by which an object shrinks and time slows down for it, can be calculated using the formula:
{1- V2/C2}1/2.
For ease of computation, this formula is approximated as:
1-1/2 V2/C2.
At very low velocities (normal speeds which we are used to) the formula generates very little shrinkage and slowdown in time. At rest (0 velocity) there is no shrinkage or slowdown.
As noted, instead of shrinking, as an object speeds up, its mass and energy increase. This increase can be calculated by using the reciprocal of the above shrinking factor:
1/1-1/2 V2/C2.
And, of course, as an object slows down, its mass and energy shrink by the same shrinking factor applicable to its size and time passage as it speeds up:
1-1/2 V2/C2.
Based on the fact that mass and energy both expanded and shrank by an identical factor, Einstein concluded that they are indistinguishable and interchangeable. They are the same thing.
So, if an object slows down, its mass decreases by an amount given by the shrinking factor:
1-1/2 V2/C2.
Mathematically, this means that the amount that an object’s mass decreases is determined by multiplying its mass before it slows down by 1/2 V2/C2. That is:
Mass Lost = M x 1/2 V2/C2.
Einstein realized that the first part of that formula i.e., M x 1/2 V2, is the formula for kinetic energy. This meant that mass lost is equal to kinetic energy divided by the speed of light squared:
Mass Lost = KINETIC ENERGY/C2, or, more simply, M = E/C2.
M = E/C2 can be re-written as:
E = MC2