By the time Albert Einstein turned 26, it was obvious to him that there are conditions for which time can be slowed down. He explained this reasoning in a paper published in 1905. The resolution seemed absurd to too many critics.
Lets come to the main matter i.e. relationship of matter to energy.
The issue that Einstein struggled with is that momentum is a function of mass. Photons carry energy without mass. Momentum is equal to mass times velocity. How, then there could be a postive momentum for a particle with zero mass ?
Einstein's mind experiment consisted of a box floating in space. A photon is emitted inside the box from the left side. The total momentum of the system needs to be conserved, so the box would have to recoil to the left when the photon was emitted. After a certain amount of time, the photon collides with the right side of the box, transferring its momentum back to the box, so now the box stops moving.
Einstein's conclusion was that since the photon clearly has energy, and has momentum, it must also have a mass equivalent. The energy of the moving photon is entirely equivalent to a moving mass. We can compute the equivalence by recongnising that the centere of mass of the system must remain stationary druing the movement of the photon. Working out the math, Einstein showed that mass and energy are related by a simple constant. That constant turned out to be enormous. It was the square of the speed of light.
Hence, we get Einstein's famous formula E = mc^2. Thus one ounce(28 grams) of mass is equivalent to 600,000 tons of TNT. Einstein wrote a letter to President Roosevelt on Aug 2, 1939, about the possibility of an atomic bomb.
Now you might think, that this would have been obvious earlier through the nature of radioactive substances. But it was believed that the radioactive substances have some fuel burn, we just that didn't know that such fuel was mass.
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