It is well known that the equation E = mc² is related to Einstein and his theory of relativity. But hardly anyone knows that there is also a simple proof for this relation which Einstein himself derived from the laws of classical physics.
Let us see what Max Born says about this topic.
In his work “Einstein’s Theory of Relativity“, Born writes:
“Einstein’s equation E = mc², which determines the proportionality of energy and inertial mass, has often been called the most important result of the theory of relativity. We therefore want to give another simple proof of this, which comes from Einstein himself and makes no use of the mathematical formalism of the theory of relativity.”
It can be seen that the equation E = mc² is a simple consequence of the relation p=E/c, which represents the momentum of electromagnetic radiation. This relationship was already known in 1884, around 20 years before the theory of relativity was born.
But why is it so important to derive the energy-mass equivalence from classical physics? One could ask.
The answer is: because if E=mc² is derived from classical physics, then this formula is the first step on a direct path to the theory of relativity and represents the link between Newtonian and relativistic mechanics.
The fact is that Newton’s Second Law of Motion in connection with E = mc² gives the relativistic velocity-dependent mass formula.
The relativistic mass formula contains the Lorenz factor. Derived from the Second Law of Motion, this formula does not require the constancy of the speed of light, nor the Lorenz transformations with the elusive concepts of length contraction and time dilation.
From the mass formula using the laws of conservation of energy and momentum, all other relevant relativistic relations can be derived, up to the constancy of the speed of light.