kevin,
if we can create a device that has an energy output of infity with a finitve mass then we have no problem working with E=mc2, but right now we can't get to the higher speeds becasue we do not have enough energy to run the requird machines
Let's substitute the terms in the problem, as you define them, and evaluate it.
Let c=1
Let m=infinity
E=mc^2
E=m * 1^2 = infinity
E = infinity
You still end up with a situation where you need an infinite mass to end up with infinite energy.
You can't do this instantaneously. It takes time to convert mass to energy (or energy to mass) so you have:
E(m) = lim_t-->infinity d(mc^2)/dt
Translated it means that energy is a function of mass. Infinite mass can be converted to infinite energy as the limit of time as it approaches infinity.
In other words it takes forever to convert infinite mass to infinite energy.
And you still have to consider the Lorentz Transformation when you add into the basic problem relativistic changes in velocity (acceleration).
In that case the problem is no longer simply stated as E = mc^2. The relativistic statement of the problem becomes:
E = mc^2/sqrt(1-v^2/c^2)
As you can see in the divisor, as "v" increases ever closer to "c" v^2/c^2 begins to approach unity, i.e. v^2/c^2 = ~1. As that happens your transformation starts to look like this:
E = (mc^2)/sqrt(~1-1). "E" tends to infinity because the divisor is tending to zero. And energy is mass.
Mass is defined as the property of matter that resists a change in momentum. The more massive an object the harder it is to change its momentum (Harder to change its velocity. An imprecise statement for the purist but close enough.).
This is the reason why "c" becomes a limit that cannot be attained. You have to have increasingly larger units of energy to eck out even the slighest change in velocity as you cloesly approach the speed of light. Those units of energy input begin to look like "infinity" the closer you get to the light of speed.
This can't be stated precisely as an algebra problem. To fully appreciate the issue it has to be stated in terms of differential calculus. But the simplified math is close enough for our purposes. /ttiforum/images/graemlins/smile.gif