A while ago, I mentioned some stuff about relativity; thinking about the weird and counterintuitive sciences is something I do occasionally. Read up a bit on Einstein's theories of relativity and the energy mass conversion formula if you aren't particularly familiar with them.
Now here's my thought experiment, which rather resembles one of the Greek paradoxes: Say that we have a spaceship which propels itself by converting matter directly to energy, which is converted directly to propulsion. (Actually, even the simplest chemical reactions, in addition to nuclear fission and fusion, involve the conversion of matter into energy; it's just that in chemical reactions, the amounts are almost undetectably small, and energy can essentially be converted back into matter by other reactions. This makes the theoretical grounds here less irrelevant than you'd think.) We set the ship to accelerate at a given rate.
When the ship starts approaching the speed of light c (and in the vacuum of space, if there aren't any big objects nearby, nothing will stop it from doing so), relativity says that its mass will start to perceptibly increase. Now, as a result of this, or so scientists say, it will progressively take more and more energy to push towards c, thus making it harder and harder to perform additional acceleration.
But as the ship's mass increases, so does the mass of its fuel... and since the mass of the fuel is increasing, the amount of energy that the ship's engines can create with that fuel increases by c squared, which you should be aware is a very large value indeed.
Is this one of those things that time dilation is supposed to account for, or is it something that nobody's addressed? I've read Hawking's A Brief History of Time and Michio Kaku's Hyperspace, and skimmed other books on the subject; none of them mention this at all.
Is it something that's been explained somewhere and I just haven't heard, or what?
-Signing off.
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