Danny Hillis: It doesn't matter whether the energy is electrical energy, chemical energy, or even atomic energy. It all weighs the same amount per unit of energy. In fact, the equation even works with something physicists called "kinetic" energy, that is, the energy something has when it is moving. For example, when I throw a baseball, I put energy into the baseball by pushing it with my arm. According to Einstein's equation, the baseball actually gets heavier when I throw it. (A physicist might get picky here and distinguish between something getting heavier and something gaining mass, but I'm not going to try. The point is that the ball becomes harder to throw.) The faster I throw the baseball, the heavier it gets. Using Einstein's equation, e = mc2, I calculate that if I could throw a baseball one hundred miles an hour (which I can't, but a good pitcher can), then the baseball actually gets heavier by 0.000000000002 grams — which is not much.
Now, let's go back to your starship. Let's assume that your engines are powered by tapping into some external energy source, so you don't have to worry about carrying fuel. As you get going faster and faster in your starship, you are putting more and more energy into the ship by speeding it up, so the ship keeps getting heavier. (Again, I should really be saying "massier" not "heavier" since there is no gravity in space.) By the time you reach 90 percent of the speed of light, the ship has so much energy in it that it actually has about twice the mass as the ship has at rest. It gets harder and harder to propel with the engines, because it's so heavy. As you get closer to the speed of light, you begin to get diminishing returns — the more energy the ship has, the heavier it gets, so the more energy that must be put into it to speed it up just a little bit, the heavier it gets, and so on.
The effect is even worse than you might think because of what is going on inside the ship. After all, everything inside the ship, including you, is speeding up, getting more and more energy, and getting heavier and heavier. In fact, you and all the machines on the ship are getting pretty sluggish. Your watch, for instance, which used to weigh about half an ounce, now weighs about forty tons. And the spring inside your watch really hasn't gotten any stronger, so the watch has slowed way down so that it only ticks once an hour. Not only has your watch slowed down, but the biological clock inside your head has also slowed down. You don't notice this because your neurons are getting heavier, and your thoughts are slowed down by exactly the same amount as the watch. As far as you are concerned, your watch is just ticking along at the same rate as before. (Physicists call this "relativistic time contraction.") The other thing that is slowed down is all of the machinery that is powering your engines (the dilithium crystals are getting heavier and slower, too). So your ship is getting heavier, your engines are getting sluggish, and the closer you get to the speed of light, the worse it gets. It just gets harder and harder and harder, and no matter how hard you try, you just can't quite get over the light barrier. And that's why you can't go faster than the speed of light.
(Excerpted from How Things Are: A Science Tool-Kit for the Mind , edited by John Brockman & Katinka Matson. William Morrow, 1996).