Okay, so most people have seen Einstein's famous equation that showed us that mass is fundamentally the same thing as energy: \( E=mc^2 \). But, what is often ignored is the total energy of the massive object, this equation is only the energy of an object at rest, its rest energy. You see, an object has both the potential energy stored in its mass, but also some kinetic energy when it moves. Einstein also had an equation that represents the total energy of an object and this is given by:
\( E = \gamma mc^2 \)
or, is we write it out more fully it is given by:
E = \(mc^2 \over \sqrt{1-(v/c)^2} \)
Without getting into this too much, this shows how as an object moves faster it's energy goes up and as the object approaches the speed of light, it approaches infinite speed. (Check out the plot below. Note: I took the theorist habit and set the speed of light to "1".)
Since this isn't a physical possibility, we cannot travel that fast.
