What does the #E# represent in Einstein's equation, #E=mc^2#?
2 Answers
The E represents the energy that released in the annihilation of a mass m, and vice-versa.
Explanation:
If you measure the mass of a lump of coal and then burn it. Is that mass annihilated? No . If you gather the ashes, all the smoke and gasses given off and determine the mass of all that, you will find that the mass you measured before and the total of the masses you measured after were equal.
In nuclear reactions, like those in the sun or in an atomic energy plant, mass is annihilated. If you could have measured the mass of the all the mass of the original atoms and all the atoms and perhaps some smaller particles that result, you would find that some mass has disappeared. Call that discrepancy
The thing is, there would also be a large amount of energy among the products of that nuclear reaction. That energy is the
Assume that you measured the amount of energy released and then converted that equation into
Now plug the speed of light and your measurement of the energy released into the revised version of Einstein's formula you would obtain a value for m. Compared that value of m to the discrepancy
So Einstein is telling us that mass and energy are equivalent and his formula is how to calculate the relationship. Note: only unusual situations allow mass to convert to energy, or energy to convert to mass.
I hope this helps,
Steve
Just adding a quick relativistic perspective to Steve's answer:
Where special relativity is considered, the quantity
The equation
The relativistic total energy is given as