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<BLOCKQUOTE class=replbq style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #1010ff 2px solid"><TT>September 30, 2005<BR>That Famous Equation and You <BR>By BRIAN GREENE, NY Times<BR><BR>DURING the summer of 1905, while fulfilling his duties in the patent office in<BR>Bern, Switzerland, Albert Einstein was fiddling with a tantalizing outcome of<BR>the special theory of relativity he'd published in June. His new insight, at<BR>once simple and startling, led him to wonder whether "the Lord might be<BR>laughing ... and leading me around by the nose." <BR><BR>But by September, confident in the result, Einstein wrote a three-page<BR>supplement to the June paper, publishing perhaps the most profound afterthought<BR>in the history of science. A hundred years ago this month, the final equation<BR>of his short article gave the world E = mc². <BR><BR>In the century since, E = mc² has become the most recognized icon of the modern<BR>scientific era. Yet for all its symbolic worth, the
equation's intimate<BR>presence in everyday life goes largely unnoticed. There is nothing you can do,<BR>not a move you can make, not a thought you can have, that doesn't tap directly<BR>into E = mc². Einstein's equation is constantly at work, providing an unseen<BR>hand that shapes the world into its familiar form. It's an equation that tells<BR>of matter, energy and a remarkable bridge between them.<BR><BR>Before E = mc², scientists described matter using two distinct attributes: how<BR>much the matter weighed (its mass) and how much change the matter could exert<BR>on its environment (its energy). A 19th century physicist would say that a<BR>baseball resting on the ground has the same mass as a baseball speeding along<BR>at 100 miles per hour. The key difference between the two balls, the physicist<BR>would emphasize, is that the fast-moving baseball has more energy: if sent<BR>ricocheting through a china shop, for example, it would surely break more<BR>dishes than the ball at
rest. And once the moving ball has done its damage and<BR>stopped, the 19th-century physicist would say that it has exhausted its<BR>capacity for exerting change and hence contains no energy.<BR><BR>After E = mc², scientists realized that this reasoning, however sensible it<BR>once seemed, was deeply flawed. Mass and energy are not distinct. They are the<BR>same basic stuff packaged in forms that make them appear different. Just as<BR>solid ice can melt into liquid water, Einstein showed, mass is a frozen form of<BR>energy that can be converted into the more familiar energy of motion. The<BR>amount of energy (E) produced by the conversion is given by his formula:<BR>multiply the amount of mass converted (m) by the speed of light squared (c²).<BR>Since the speed of light is a few hundred million meters per second (fast<BR>enough to travel around the earth seven times in a single second), c² , in<BR>these familiar units, is a huge number, about 100,000,000,000,000,000. <BR><BR>A
little bit of mass can thus yield enormous energy. The destruction of<BR>Hiroshima and Nagasaki was fueled by converting less than an ounce of matter<BR>into energy; the energy consumed by New York City in a month is less than that<BR>contained in the newspaper you're holding. Far from having no energy, the<BR>baseball that has come to rest on the china shop's floor contains enough energy<BR>to keep an average car running continuously at 65 m.p.h. for about 5,000 years.<BR><BR>Before 1905, the common view of energy and matter thus resembled a man carrying<BR>around his money in a box of solid gold. After the man spends his last dollar,<BR>he thinks he's broke. But then someone alerts him to his miscalculation; a<BR>substantial part of his wealth is not what's in the box, but the box itself.<BR>Similarly, until Einstein's insight, everyone was aware that matter, by virtue<BR>of its motion or position, could possess energy. What everyone missed is the<BR>enormous energetic wealth
contained in mass itself.<BR><BR>The standard illustrations of Einstein's equation - bombs and power stations -<BR>have perpetuated a belief that E = mc² has a special association with nuclear<BR>reactions and is thus removed from ordinary activity. <BR><BR>This isn't true. When you drive your car, E = mc² is at work. As the engine<BR>burns gasoline to produce energy in the form of motion, it does so by<BR>converting some of the gasoline's mass into energy, in accord with Einstein's<BR>formula. When you use your MP3 player, E = mc² is at work. As the player drains<BR>the battery to produce energy in the form of sound waves, it does so by<BR>converting some of the battery's mass into energy, as dictated by Einstein's<BR>formula. As you read this text, E = mc² is at work. The processes in the eye<BR>and brain, underlying perception and thought, rely on chemical reactions that<BR>interchange mass and energy, once again in accord with Einstein's formula.<BR><BR>The point is that
although E=mc² expresses the interchangeability of mass and<BR>energy, it doesn't single out any particular reaction for executing the<BR>conversion. The distinguishing feature of nuclear reactions, compared with the<BR>chemical reactions involved in burning gasoline or running a battery, is that<BR>they generate less waste and thus produce more energy - by a factor of roughly<BR>a million. And when it comes to energy, a factor of a million justifiably<BR>commands attention. But don't let the spectacle of E=mc² in nuclear reactions<BR>inure you to its calmer but thoroughly pervasive incarnations in everyday life.<BR><BR>That's the content of Einstein's discovery. Why is it true? <BR><BR>Einstein's derivation of E = mc² was wholly mathematical. I know his<BR>derivation, as does just about anyone who has taken a course in modern physics.<BR>Nevertheless, I consider my understanding of a result incomplete if I rely<BR>solely on the math. Instead, I've found that thorough understanding
requires a<BR>mental image - an analogy or a story - that may sacrifice some precision but<BR>captures the essence of the result.<BR><BR>Here's a story for E = mc². Two equally strong and skilled jousters, riding<BR>identical horses and gripping identical (blunt) lances, head toward each other<BR>at an identical speed. As they pass, each thrusts his lance across his<BR>breastplate toward his opponent, slamming blunt end into blunt end. Because<BR>they're equally matched, neither lance pushes farther than the other, and so<BR>the referee calls it a draw.<BR><BR>This story contains the essence of Einstein's discovery. Let me explain.<BR><BR>Einstein's first relativity paper, the one in June 1905, shattered the idea<BR>that time elapses identically for everyone. Instead, Einstein showed that if<BR>from your perspective someone is moving, you will see time elapsing slower for<BR>him than it does for you. Everything he does - sipping his coffee, turning his<BR>head, blinking his eyes -
will appear in slow motion. <BR><BR>This is hard to grasp because at everyday speeds the slowing is less than one<BR>part in a trillion and is thus imperceptibly small. Even so, using<BR>extraordinarily precise atomic clocks, scientists have repeatedly confirmed<BR>that it happens just as Einstein predicted. If we lived in a world where things<BR>routinely traveled near the speed of light, the slowing of time would be<BR>obvious.<BR><BR>Let's see what the slowing of time means for the joust. To do so, think about<BR>the story not from the perspective of the referee, but instead imagine you are<BR>one of the jousters. From your perspective, it is your opponent - getting ever<BR>closer - who is moving. Imagine that he is approaching at nearly the speed of<BR>light so the slowing of all his movements - readying his joust, tightening his<BR>face - is obvious. When he shoves his lance toward you in slow motion, you<BR>naturally think he's no match for your swifter thrust; you expect to
win. Yet<BR>we already know the outcome. The referee calls it a draw and no matter how<BR>strange relativity is, it can't change a draw into a win. <BR><BR>After the match, you naturally wonder how your opponent's slowly thrusted lance<BR>hit with the same force as your own. There's only one answer. The force with<BR>which something hits depends not only on its speed but also on its mass. That's<BR>why you don't fear getting hit by a fast-moving Ping-Pong ball (tiny mass) but<BR>you do fear getting hit by a fast-moving Mack truck (big mass). Thus, the only<BR>explanation for how the slowly thrust lance hit with the same force as your own<BR>is that it's more massive.<BR><BR>This is astonishing. The lances are identically constructed. Yet you conclude<BR>that one of them - the one that from your point of view is in motion, being<BR>carried toward you by your opponent on his galloping horse - is more massive<BR>than the other. That's the essence of Einstein's discovery. Energy of
motion<BR>contributes to an object's mass. <BR><BR>AS with the slowing of time, this is unfamiliar because at everyday speeds the<BR>effect is imperceptibly tiny. But if, from your viewpoint, your opponent were<BR>to approach at 99.99999999 percent of the speed of light, his lance would be<BR>about 70,000 times more massive than yours. Luckily, his thrusting speed would<BR>be 70,000 times slower than yours, and so the resulting force would equal your<BR>own.<BR><BR>Once Einstein realized that mass and energy were convertible, getting the exact<BR>formula relating them - E = mc² - was a fairly basic exercise, requiring<BR>nothing more than high school algebra. His genius was not in the math; it was<BR>in his ability to see beyond centuries of misunderstanding and recognize that<BR>there was a connection between mass and energy at all. <BR><BR>A little known fact about Einstein's September 1905 paper is that he didn't<BR>actually write E = mc²; he wrote the mathematically equivalent
(though less<BR>euphonious) m = E/c², placing greater emphasis on creating mass from energy (as<BR>in the joust) than on creating energy from mass (as in nuclear weapons and<BR>power stations).<BR><BR>Over the last couple of decades, this less familiar reading of Einstein's<BR>equation has helped physicists explain why everything ever encountered has the<BR>mass that it does. Experiments have shown that the subatomic particles making<BR>up matter have almost no mass of their own. But because of their motions and<BR>interactions inside of atoms, these particles contain substantial energy - and<BR>it's this energy that gives matter its heft. Take away Einstein's equation, and<BR>matter loses its mass. You can't get much more pervasive than that.<BR><BR>Its singular fame notwithstanding, E = mc² fits into the pattern of work and<BR>discovery that Einstein pursued with relentless passion throughout his entire<BR>life. Einstein believed that deep truths about the workings of the
universe<BR>would always be "as simple as possible, but no simpler." And in his view,<BR>simplicity was epitomized by unifying concepts - like matter and energy -<BR>previously deemed separate. In 1916, Einstein simplified our understanding even<BR>further by combining gravity with space, time, matter and energy in his General<BR>Theory of Relativity. For my money, this is the most beautiful scientific<BR>synthesis ever achieved.<BR><BR>With these successes, Einstein's belief in unification grew ever stronger. But<BR>the sword of his success was double-edged. It allowed him to dream of a single<BR>theory encompassing all of nature's laws, but led him to expect that the<BR>methods that had worked so well for him in the past would continue to work for<BR>him in the future. <BR><BR>It wasn't to be. For the better part of his last 30 years, Einstein pursued the<BR>"unified theory," but it stubbornly remained beyond his grasp. As the years<BR>passed, he became increasingly isolated;
mainstream physics was concerned with<BR>prying apart the atom and paid little attention to Einstein's grandiose quest.<BR>In a 1942 letter, Einstein described himself as having become a "a lonely old<BR>man who is displayed now and then as a curiosity because he doesn't wear<BR>socks." <BR><BR>Today, Einstein's quest for unification is no curiosity - it is the driving<BR>force for many physicists of my generation. No one knows how close we've<BR>gotten. Maybe the unified theory will elude us just as it dodged Einstein last<BR>century. Or maybe the new approaches being developed by contemporary physics<BR>will finally prevail, giving us the ultimate explanation of the cosmos. Without<BR>a unified theory it's hard to imagine we will ever resolve the deepest of all<BR>mysteries - how the universe began- so the stakes are high and the motivation<BR>strong. <BR><BR>But even if our science proves unable to determine the origin of the universe,<BR>recent progress has already established
beyond any doubt that a fraction of a<BR>second after creation (however that happened), the universe was filled with<BR>tremendous energy in the form of wildly moving exotic particles and radiation.<BR>Within a few minutes, this energy employed E = mc² to transform itself into<BR>more familiar matter - the simplest atoms - which, in the course of about a<BR>billion years, clumped into planets and stars. <BR><BR>During the 13 billion years that have followed, stars have used E = mc² to<BR>transform their mass back into energy in the form of heat and light; about five<BR>billion years ago, our closest star - the sun - began to shine, and the heat<BR>and light generated was essential to the formation of life on our planet. If<BR>prevailing theory and observations are correct, the conversion of matter to<BR>energy throughout the cosmos, mediated by stars, black holes and various forms<BR>of radioactive decay, will continue unabated. <BR><BR>In the far, far future, essentially all matter
will have returned to energy.<BR>But because of the enormous expansion of space, this energy will be spread so<BR>thinly that it will hardly ever convert back to even the lightest particles of<BR>matter. Instead, a faint mist of light will fall for eternity through an ever<BR>colder and quieter cosmos. <BR><BR>The guiding hand of Einstein's E = mc² will have finally come to rest. <BR><BR>Brian Greene, a professor of physics and mathematics at Columbia, is the author<BR>of "The Elegant Universe" and "The Fabric of the Cosmos."</TT></BLOCKQUOTE></DIV><BR><BR><DIV>
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<P>La vie est belle!<BR><BR>Yosé (<A href="http://www.cordeiro.org">www.cordeiro.org</A>)</P>
<P>Caracas, Venezuela, Americas, TerraNostra, Solar System, Milky Way, Multiverse</P></DIV></DIV>