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[MadMojoMonkey]

Why is the value that mass and energy are relative to one another related to the speed of light?

Damn, that's a good one.

After a couple hours of searching, that's not an easy question to answer. The closest I have now is an explanation of the fact that Einstein took 11 more years to work out GR once he worked out Special Relativity. It wasn't a single flash of insight that he fully understood all at once. It was slowly developed on the back of experimental data showing that the speed of light is constant in all directions, regardless of the speed of the observer. It was developed in the knowledge that light is an electromagnetic wave, which obeys Maxwell's Laws. The speed of light can be derived from Maxwell's Laws and 2 measured values:

1) The electrical permittivity of free space, ε_0
2) The magnetic permeability of free space, μ_0

such that c = 1/SQRT(ε_0*μ_0)


The motivation for Einstein's Relativity was that the previous hypothesis said that space was not "empty", but made of "aether". This hypothesis implies that the speed of light would be like any other speed: If you are moving in the same direction of a moving object, then that object's speed relative to you appears less than it would appear to a stationary observer. (This is known as Galilean Relativity today, but was the only relativity theory at the time.) However, many experiments, culminating in the Michelson-Morley Experiment were collecting data which showed that the speed of light is the same in all directions, regardless of the speed of the observer.

The Earth is spinning on its axis, as well as orbiting the sun, so the "actual" speed of a single spot on Earth's surface varies between night and day, and with the seasons. No matter where on Earth or when the experiment was performed, the speed of light was always the same. Experiments on Earth measuring the speed of light always show the same value, regardless of whether it's day or night, or summer or winter.

The motivation behind Einstein's Theory was to explain observations about light, so the speed of light being an integral part seems obvious.

This is not a coincidence, surely?

It's not a coincidence, and stop calling me Shirley.

Does it [...] imply that not only are matter and energy different aspects of the same thing, but also different aspects of space and time too?

I think so. Mass/energy warps space-time, so they're intrinsically linked in an inter-active way. As I understand it, there is no other source of space-time warping.

If that's true, then all of these descriptions are equivalent. Mass = energy = warp in space-time.

If that doesn't make any sense, maybe it's clearer to ask... why c squared?

Great question, ong!

This may take some time. Everything I've read seems so excited that E = mc^2, that it's not too concerned about where the c^2 came from.

***
Interesting side note: E = mc^2 has very little to do with fission physics. The popular link between E = mc^2 and atomic bombs is erroneous. Fission reactions result in almost no conversion of mass into energy. The energy comes from the breaking of inter-nuclear bonds, not mass-to-energy conversion.

Mostly what we observe in this mass-energy equivalence is the very tiny change in mass of a substance when it absorbs or emits photons... or changes temperature.

[chemist]

Interesting side note: E = mc^2 has very little to do with fission physics. The popular link between E = mc^2 and atomic bombs is erroneous. Fission reactions result in almost no conversion of mass into energy. The energy comes from the breaking of inter-nuclear bonds, not mass-to-energy conversion.

The reason Einstein's equation is important to atomic bombs or nuclear power funnily enough is the C, because the resulting energy releases at the speed of light.

Which makes the energy a very big number
if c=299792458 m/s
then c^2 = 8.98755179×10^16
So a small mass can make a lot of energy.

[MadMojoMonkey]

The reason Einstein's equation is important to atomic bombs or nuclear power funnily enough is the C, because the resulting energy releases at the speed of light.

Which makes the energy a very big number
if c=299792458 m/s
then c^2 = 8.98755179×10^16
So a small mass can make a lot of energy.

"Somehow the popular notion took hold long ago that Einstein's theory of relativity, in particular his famous equation E = mc2, plays some essential role in the theory of fission. Albert Einstein had a part in alerting the United States government to the possibility of building an atomic bomb, but his theory of relativity is not required in discussing fission. The theory of fission is what physicists call a non-relativistic theory, meaning that relativistic effects are too small to affect the dynamics of the fission process significantly."
-Robert Serber of the Manhattan Project

"While Serber's view of the strict lack of need to use mass–energy equivalence in designing the atomic bomb is correct, it does not take into account the pivotal role which this relationship played in making the fundamental leap to the initial hypothesis that large atoms were energetically allowed to split into approximately equal parts (before this energy was in fact measured)."

-Wiki