Posts Tagged ‘math’
Math is Pretty
Sunday, November 18th, 2007One point twenty-one gigawatts my ass!
Wednesday, March 7th, 2007Mathematically, you can certainly say something is traveling to the past, Liu said. “But it is not possible for you and me to travel backward in time,” he said.However, some scientists believe that traveling to the past is, in fact, theoretically possible, though impractical.
Maybe if there were a theory of everything, one could solve all of Einstein’s equations through a wormhole, and see whether time travel is really possible, Kaku said. “But that would require a technology far more advanced than anything we can muster,” he said. “Don’t expect any young inventor to announce tomorrow in a press release that he or she has invented a time machine in their basement.”
For now, the only definitive part of travel in the fourth dimension is that we’re stepping further into the future with each passing moment. So for those hoping to see Earth a million years from now, scientists have good news.
“If you want to know what the Earth is like one million years from now, I’ll tell you how to do that,” said Greene, a consultant for “Déjà Vu,” a recent movie that dealt with time travel. “Build a spaceship. Go near the speed of light for a length of time—that I could calculate. Come back to Earth, and when you step out of your ship you will have aged perhaps one year while the Earth would have aged one million years. You would have traveled to Earth’s future.”
Mathematics of Invisibility
Tuesday, December 26th, 2006The theorists who first created the mathematics that describe the behavior of the recently announced ‘invisibility cloak’ have revealed a new analysis that may extend the current cloak’s powers, enabling it to hide even actively radiating objects like a flashlight or cell phone.Allan Greenleaf, professor of mathematics at the University of Rochester, working with colleagues around the globe, has announced a mathematical theory that predicts some strange goings on inside the cloak—and that what happens inside is crucial to the cloak’s effectiveness.
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Their analysis also revealed another surprise: a person trying to look out of the cloak would effectively be faced with a mirror in every direction. If you can imagine Harry Potter’s own invisibility cloak working this way, and Harry turning on his flashlight to see, its light would shine right back at him, no matter where he pointed it.
Greenleaf’s team determined that a more complicated phenomenon arises when using Maxwell’s equations, leading to a “blow up” (an unexpected infinite behavior) of the electromagnetic fields. They determined that by inserting conductive linings, whose properties depend on the specific geometry of the cloak, this problem can be resolved. Alternatively, covering both the inside and outside surfaces of the cloaked region with carefully matched materials can also be used to bypass this problem.
“We should also keep in mind that, given the current technology, when we talk about invisibility, we’re talking only about being invisible at just a narrow range of wavelengths,” says Greenleaf. “For example, an object could be rendered invisible at just a specific wavelength of red; it would be visible in nearly every other color.”
