Error

I discovered a fatal flaw in my scheme to conquer the galaxy. My plan involved adapting a linear accelerator for use as a mass driver to provide propulsion for my spaceship. Using Taichowsky's rocket equation*, I calculated that if we could accelerate our reaction mass (iron filings) to 95% of the speed of light, we would only need 4 times as much reaction mass as a payload. That would make a round trip to Alpha Centauri possible. It would still require a large quantity of reaction mass**. Linear accelerators run on electricity, and we build nuclear power plants that generate electricity, so this should be easy.
     What I forgot was that the total amount of energy required to boost that much mass to that high a velocity. Remember our old friend E=mc^2? Well in this case it means we would need to convert an equal amount of mass to energy in order to accelerate our reaction mass. That would still be doable if we could get 100% conversion of mass to energy, but nuclear reactors are not nearly that efficient. Only about 1% of energy released by the radioactive fuel in a reactor is recovered in the form of heat, and only about 1/3 of that is turned into electricity. I'm pretty sure the amount of mass lost by nuclear fuel in the process of generating energy is negligible, so we would need an infinite (infinite is the inverse of negligible, right?) amount of nuclear fuel, which would up our reaction mass requirements to stratospheric heights.

* Yes, I know it's not Taichowsky's, but I can't figure out how to pronounce the real name, and without that I'm not even going to try and spell it.
** 625 times the payload. 4+1=5. 5^4=625. Initial mass of payload (1) plus 4 for the reaction mass gives you five. A round trip requires accelerating twice, and decelerating twice, for a total of four. So you need to multiple by 5 four times, which means 5 to the 4th power, or 5^4 in mathematical shorthand.