An Easy Derivation of E = mc²
One of the most fundamental things we know about the universe is that electromagnetic radiation (EMR) is always measured to move at the speed of light, regardless of the speed of the energy source or the observer. This means we can establish a frame of reference where one of these, matter or energy, is at rest within it and the other is always moving at the speed of light 'c' within it. Since all matter is moving away from the Big Bang event at the speed of light due to the expansion of the universe, it makes sense to see matter as moving at the speed of light and energy as being stationary within this 4D frame of reference centered on the Big Bang event. In this model the apparent movement of EMR at the speed of light is just a relative movement, like that of the movement of the sun across the sky each day.
If the matter of the universe is in motion it has kinetic energy, given by the equation E=½mv². Since the speed of the matter is the speed of light, 'c', its kinetic energy is E=½mc². This is the amount of energy that would be released if a particle of matter of mass 'm' were converted to EMR energy, which has zero speed. However, what could slow down this particle of matter from 'c' to zero speed? Newton’s first law of motion says:
This means that to stop a particle like this there must be an external force—it cannot just stop itself. But what could this external force be? The only obvious thing that could stop a fast moving particle in its tracks like that would be if it collided with a particle of the same mass going the opposite direction at the same speed, like two cars in a head-on collision. This would mean a particle of matter would have to collide with a particle of the same mass traveling in the opposite (backward) direction through time at the same speed, “c”.
In this situation, this head-on collision would release the kinetic energy in both particles, and reduce the speed of both particles to zero, the quantum state of electromagnetic energy, and so release the energy as electromagnetic radiation. The total energy released, in terms of the mass of the particle moving forward through time that we are aware of, which has mass “m”, would thus be:
E = ½mc² + ½mc²
And adding the two terms on the right, we get:
E = mc²
If the concept of backward-through-time particles seems weird to you, let me point out that the concept of collisions between normal matter and backward through time matter yeilding energy according to E = mc² is not entirely new. Stephen Hawking, in his article "The Quantum Mechanics of Black Holes" (Scientific American, January 1977), says that, in Quantum Theory, an antimatter particle can be seen as "being really a [normal] particle that is traveling backward in time." Hawking is referring to the "Feynman–Stueckelberg interpretation" of antimatter, an accepted part of Quantum Theory.
To read more about the Stationary Energy Theory, that this derivation comes from, please click here.