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Mathematical Principles of Natural Philosophy

will dramatically overshadow in both tempo and magnitude the triggering events—con- sequences such as an explosive deterioration in the quality of life for our grandchildren. Finally, "to fuse" means to combine, unite, join. The oneness or unity of nature has been a theme of poets and philosophers for millen- nia. The unity of the laws of nature has been a theme of science since Galileo. Physicists have demonstrated that the laws of motion hold true on spaceships and distant stars as well as in earth's laboratories. Biologists have taught us that the same DNA

the trip as measured by ground clocks approaches L/c, but the proper time approaches zero! If a spaceship travels to a distant star, the time of the trip as measured by clocks on the spaceship goes to zero as the ship's speed approaches e. This consequence of relativity forms the basis for much fanciful speculation about space travel. In principle, there is no limit to the distance one could travel in one's own lifetime. EXAMPLE. A spaceship travels from earth to Alpha Centauri at speed 0.8e. The distance between earth and Alpha Centauri is 4 light-years, mea- sured

the speed (relative to 5) of a frame in which E occurs at the same place as Eo. If E is in the elsewhere of Eo, find the speed of a frame in which it is simultaneous with Eo. 5.2. Refer to the three events E1 , E2 , and E3 of problem 5.1. For each pair of events, (1,2), (2,3), and (1,3), find the value of (~S)2 and characterize the interval between the events as spacelike, timelike, or lightlike. Which pairs of events could be causally related? 5.3. Consider problem 3.8, in which a light pulse catches up to a spaceship. (a) Construct the space-time diagram for the

America. Of course, contemporary shopping malls are far from the modest strip malls of my youth. “It’s like a giant spaceship,” is the way Oscar, the store P R E F A C E A N D A C K N O W L E D G M E N T S viii • P R E F A C E A N D A C K N O W L E D G M E N T S clerk who gave me a tour of Titan Shopping Mall in Bogotá, Colombia, explained it. He was referring to the enclosed, curvilinear architecture and futuristic feel of the mall, which gave the impression that a massive spaceship had landed from nowhere, an alien structure with little relation- ship to the


, Ecologo certified, and manufac- tured by BioGas energy. Hernandez, Migra! 1/11/10 1:12 PM Page iv For my mother because you taught me to write For my father because you inspire me to take on the world For my brother because you teach me that change is possible For my husband because you are beautiful For my children because I love you Hernandez, Migra! 1/11/10 1:12 PM Page v Hernandez, Migra! 1/11/10 1:12 PM Page vi [Spoken] It’s a bird! It’s a plane! No man, it’s a wetback. [Sung] He came from the sky, but he is not a plane. He came in his spaceship from Krypton, And

? (c) What is the spatial distance between the points at which the pulses were emitted? (d) How much time elapsed between the emission of the first pulse and the meeting of the two pulses? (e) Did the pulses meet at the midpoint of the car? How could this answer have been predicted? 4.5. Spaceship A passes earth at earth time t = 0 at speed O.Be in the direction of the star Xerxes. At the same time (according to earth frame clocks) spaceship B passes Xerxes at speed 0.625e in the direction of earth. Assume that earth and Xerxes are at rest relative to one another and


xi When I was growing up, my parents often accused me of living more in my imagination than in the real world. And I’m not sure they were wrong. My nose always stuck in a book, my head in the clouds, as it were, I fought monsters, cast magic spells, flew spaceships, and saved the day in every story. Well, almost every story. Take, for example, my first attempt at being a superhero. It was—as it was, I imagine, for many others—short-lived. I was about five years old, and my growing comic book collection had convinced me that I understood exactly how Super


windup Popeyes and racist “Alabama Coon Jiggers,” outsourced production to Japan. After World War II, Japan became an exporter of robots and space toys made of tin cans to an American market eager for science-fiction and space themes: Japanese spaceships looked like hastily recycled tanks and other war toys, and the toy figures looked alien to Westerners because Japanese toy makers could not afford to license images of movie and TV icons like Flash Gordon and Space Cadet. By the late 1960s, however, Japan was producing quality Datsuns and other cars for export, and it