It is a feature of the way the world is made that two protons together have less mass than two protons separately. This is a startling but indisputable fact. Weigh two protons separately, then weigh them together: the numbers don't match. The numbers differ by about 1 percent. This curious difference is not to be explained by some law of nature; it is a law of nature, as basic to the way the world works as any fact in our possession. The mass discrepancy is equivalent to an amount of energy given by Albert Einstein's formula E = mc^2, where c is the velocity of light. The velocity of light IS a big number; squared, an even bigger number. A tiny mass difference is equivalent to a huge amount of energy. Make protons stick together and you have access to this energy. There's a catch, however. Protons have positive electrical charge, and like charges repel. To make two protons stick, you must overcome the electrical repulsion that drives them apart. You must get the protons close enough together so that a short-range but powerful nuclear force comes into play. The nuclear force is the glue that holds protons together.
Nowhere on Earth is there sufficient force to overcome the electrical repulsion of protons and make them stick together, except a few hugely expensive particle accelerators and fusion reactors —and in the fury of atomic bomb explosions. However, protons are easily squeezed together at the centers of stars: all that huge weight pushing down. Protons fuse at the center of the sun and 1 percent of their mass is turned into energy. There is a famous line by the poet Dylan Thomas: "The force that through the green fuse drives the flower" Thomas was more right than he realized. That word: fuse. Fusion is the force that drives the sun and sunlight drives the flow^er. The energy of proton fusion at the sun's core flow^s upward, through half a million miles of the sun's bulk. It percolates through the sun's seething interior, absorbed and reradiated again and again. As the energy approaches the solar surface, it is carried along by the churning mass of the sun itself, m huge convective loops of hot gas. At last, at the furiously roiling surface, the energy is hurled into space as heat and light. Every second at the sun's core 700 million tons of protons—the nuclei of hydrogen—are fused together Every second five million tons of proton mass disappear from the universe, replaced by an amount of energy equal to the missing mass times the speed of light squared. Every second the sun throws five million tons of its own substance into space as radiant energy. The sun never misses so tiny a fraction of its bulk. The sun has been burning steadily for more than four billion years, and in all of that time it has used up less than a thousandth of its mass.
Every second, five million tons worth of energy is thrown into space by the sun. Eight minutes later, one two-billionths of that energy is intercepted by Earth. That's five pounds worth of the sun's vanished mass that falls every second upon the Earth. About a billionth of an ounce's worth of that energy falls upon my three-quarter-acre plot of land on the island of Exuma, where it is absorbed by palms, palmettos, coco plums, sea grapes, sea oats, b grass, beach grass, and beach morning glories. The plants photosynthesize, building carbohydrates. Moths sup and die. Ants devour moths. Frogs eat ants. Humans eat coco plums. Sand flies eat humans. The energy is shared around. Our little community of flora and fauna sucks up every last drop of that billionth of an ounce of the sun's missing mass. that "force that through the green fuse drives the flower" Dylan Thomas and Albert Einstein were contemporaries. They died within a few years of each other in the mid1950s. Poet and scientist, they perceived the essential unity of matter and energy. They recognized m nature a force that drives all things, creative and destructive, holy and terrible. Its source is the sun.
Moving back to the sub-light-speed world: We are not through with Einstein yet. His famous relation between mass and energy, E=mc 2 , which is a consequence of special relativity, presents a further challenge to space travel at impulse speeds. As I have described it in chapter 1, a rocket is a device that propels material backward in order to move forward. As you might imagine, the faster the material is propelled backward, the larger will be the forward impulse the rocket will receive. Material cannot be propelled backward any faster than the speed of light. Even propelling it at light speed is not so easy: the only way to get propellant moving backward at light speed is to make the fuel out of matter and antimatter, which (as I describe in a later chapter) can completely annihilate to produce pure radiation moving at the speed of light.
However, while the warp drive aboard the Enterprise uses such fuel, the impulse drive does not. It is powered instead by nuclear fusionthe same nuclear reaction that powers the Sun by turning hydrogen into helium. In fusion reactions, about 1 percent of the available mass is converted into energy. With this much available energy, the helium atoms that are produced can come streaming out the back of the rocket at about an eighth of the speed of light. Using this exhaust velocity for the propellant, we then can calculate the amount of fuel the Enterprise needs in order to accelerate to, say, half the speed of light. The calculation is not difficult, but I will just give the answer here. It may surprise you. Each time the Enterprise accelerates to half the speed of light, it must burn 81 TIMES ITS ENTIRE MASS in hydrogen fuel. Given that a Galaxy Class starship such as Picard's Enterprise-D would weigh in excess of 4 million metric tons, 3 this means that over 300 million metric tons of fuel would need to be used each time the impulse drive is used to accelerate the ship to half light speed! If one used a matter-antimatter propulsion system for the impulse drive, things would be a little better. In this case, one would have to burn merely twice the entire mass of the Enterprise in fuel for each such acceleration.