Eutrusca
30-09-2005, 17:05
COMMENTARY: Amazing that it's been 100 years since Einstein first formulated the famous equation. Also amazing how much impact such a concise statement of a physical principle can have on our lives. For those of you who question the value of science, here's an explanation that may open your eyes ( although I doubt it ). ;)
That Famous Equation and You (http://www.nytimes.com/2005/09/30/opinion/30greene.html?th&emc=th)
By BRIAN GREENE
Published: September 30, 2005
DURING the summer of 1905, while fulfilling his duties in the patent office in Bern, Switzerland, Albert Einstein was fiddling with a tantalizing outcome of the special theory of relativity he'd published in June. His new insight, at once simple and startling, led him to wonder whether "the Lord might be laughing ... and leading me around by the nose."
An object's mass is its resistance to being accelerated (to having its speed increased). According to E = mc2, an object's mass depends on its energy. This means that the faster an object goes, the harder one must push to increase its speed. (If an object's "rest mass" - called m0 - is the resistance it has to being sped up from a resting position, then Einstein's result can be written more explicitly as E = m0c2/ (1-v2/c2)½, so m = m0(1-v2/c2)-½, where v2 is the square of the object's speed. As the formula shows, when the object's speed approaches that of light, its mass grows infinitely large, which explains why, regardless of how hard it is pushed, it won't exceed light speed.)
But by September, confident in the result, Einstein wrote a three-page supplement to the June paper, publishing perhaps the most profound afterthought in the history of science. A hundred years ago this month, the final equation of his short article gave the world E = mc².
In the century since, E = mc² has become the most recognized icon of the modern scientific era. Yet for all its symbolic worth, the equation's intimate presence in everyday life goes largely unnoticed. There is nothing you can do, not a move you can make, not a thought you can have, that doesn't tap directly into E = mc². Einstein's equation is constantly at work, providing an unseen hand that shapes the world into its familiar form. It's an equation that tells of matter, energy and a remarkable bridge between them.
Before E = mc², scientists described matter using two distinct attributes: how much the matter weighed (its mass) and how much change the matter could exert on its environment (its energy). A 19th century physicist would say that a baseball resting on the ground has the same mass as a baseball speeding along at 100 miles per hour. The key difference between the two balls, the physicist would emphasize, is that the fast-moving baseball has more energy: if sent ricocheting through a china shop, for example, it would surely break more dishes than the ball at rest. And once the moving ball has done its damage and stopped, the 19th-century physicist would say that it has exhausted its capacity for exerting change and hence contains no energy.
After E = mc², scientists realized that this reasoning, however sensible it once seemed, was deeply flawed. Mass and energy are not distinct. They are the same basic stuff packaged in forms that make them appear different. Just as solid ice can melt into liquid water, Einstein showed, mass is a frozen form of energy that can be converted into the more familiar energy of motion. The amount of energy (E) produced by the conversion is given by his formula: multiply the amount of mass converted (m) by the speed of light squared (c²). Since the speed of light is a few hundred million meters per second (fast enough to travel around the earth seven times in a single second), c² , in these familiar units, is a huge number, about 100,000,000,000,000,000.
A little bit of mass can thus yield enormous energy. The destruction of Hiroshima and Nagasaki was fueled by converting less than an ounce of matter into energy; the energy consumed by New York City in a month is less than that contained in the newspaper you're holding. Far from having no energy, the baseball that has come to rest on the china shop's floor contains enough energy to keep an average car running continuously at 65 m.p.h. for about 5,000 years.
Before 1905, the common view of energy and matter thus resembled a man carrying around his money in a box of solid gold. After the man spends his last dollar, he thinks he's broke. But then someone alerts him to his miscalculation; a substantial part of his wealth is not what's in the box, but the box itself. Similarly, until Einstein's insight, everyone was aware that matter, by virtue of its motion or position, could possess energy. What everyone missed is the enormous energetic wealth contained in mass itself.
The standard illustrations of Einstein's equation - bombs and power stations - have perpetuated a belief that E = mc² has a special association with nuclear reactions and is thus removed from ordinary activity.
This isn't true. When you drive your car, E = mc² is at work. As the engine burns gasoline to produce energy in the form of motion, it does so by converting some of the gasoline's mass into energy, in accord with Einstein's formula. When you use your MP3 player, E = mc² is at work. As the player drains the battery to produce energy in the form of sound waves, it does so by converting some of the battery's mass into energy, as dictated by Einstein's formula. As you read this text, E = mc² is at work. The processes in the eye and brain, underlying perception and thought, rely on chemical reactions that interchange mass and energy, once again in accord with Einstein's formula.
[ This article is 3 pages long. To read the rest of the article, go here (http://www.nytimes.com/2005/09/30/opinion/30greene.html?pagewanted=2&th&emc=th). ]
That Famous Equation and You (http://www.nytimes.com/2005/09/30/opinion/30greene.html?th&emc=th)
By BRIAN GREENE
Published: September 30, 2005
DURING the summer of 1905, while fulfilling his duties in the patent office in Bern, Switzerland, Albert Einstein was fiddling with a tantalizing outcome of the special theory of relativity he'd published in June. His new insight, at once simple and startling, led him to wonder whether "the Lord might be laughing ... and leading me around by the nose."
An object's mass is its resistance to being accelerated (to having its speed increased). According to E = mc2, an object's mass depends on its energy. This means that the faster an object goes, the harder one must push to increase its speed. (If an object's "rest mass" - called m0 - is the resistance it has to being sped up from a resting position, then Einstein's result can be written more explicitly as E = m0c2/ (1-v2/c2)½, so m = m0(1-v2/c2)-½, where v2 is the square of the object's speed. As the formula shows, when the object's speed approaches that of light, its mass grows infinitely large, which explains why, regardless of how hard it is pushed, it won't exceed light speed.)
But by September, confident in the result, Einstein wrote a three-page supplement to the June paper, publishing perhaps the most profound afterthought in the history of science. A hundred years ago this month, the final equation of his short article gave the world E = mc².
In the century since, E = mc² has become the most recognized icon of the modern scientific era. Yet for all its symbolic worth, the equation's intimate presence in everyday life goes largely unnoticed. There is nothing you can do, not a move you can make, not a thought you can have, that doesn't tap directly into E = mc². Einstein's equation is constantly at work, providing an unseen hand that shapes the world into its familiar form. It's an equation that tells of matter, energy and a remarkable bridge between them.
Before E = mc², scientists described matter using two distinct attributes: how much the matter weighed (its mass) and how much change the matter could exert on its environment (its energy). A 19th century physicist would say that a baseball resting on the ground has the same mass as a baseball speeding along at 100 miles per hour. The key difference between the two balls, the physicist would emphasize, is that the fast-moving baseball has more energy: if sent ricocheting through a china shop, for example, it would surely break more dishes than the ball at rest. And once the moving ball has done its damage and stopped, the 19th-century physicist would say that it has exhausted its capacity for exerting change and hence contains no energy.
After E = mc², scientists realized that this reasoning, however sensible it once seemed, was deeply flawed. Mass and energy are not distinct. They are the same basic stuff packaged in forms that make them appear different. Just as solid ice can melt into liquid water, Einstein showed, mass is a frozen form of energy that can be converted into the more familiar energy of motion. The amount of energy (E) produced by the conversion is given by his formula: multiply the amount of mass converted (m) by the speed of light squared (c²). Since the speed of light is a few hundred million meters per second (fast enough to travel around the earth seven times in a single second), c² , in these familiar units, is a huge number, about 100,000,000,000,000,000.
A little bit of mass can thus yield enormous energy. The destruction of Hiroshima and Nagasaki was fueled by converting less than an ounce of matter into energy; the energy consumed by New York City in a month is less than that contained in the newspaper you're holding. Far from having no energy, the baseball that has come to rest on the china shop's floor contains enough energy to keep an average car running continuously at 65 m.p.h. for about 5,000 years.
Before 1905, the common view of energy and matter thus resembled a man carrying around his money in a box of solid gold. After the man spends his last dollar, he thinks he's broke. But then someone alerts him to his miscalculation; a substantial part of his wealth is not what's in the box, but the box itself. Similarly, until Einstein's insight, everyone was aware that matter, by virtue of its motion or position, could possess energy. What everyone missed is the enormous energetic wealth contained in mass itself.
The standard illustrations of Einstein's equation - bombs and power stations - have perpetuated a belief that E = mc² has a special association with nuclear reactions and is thus removed from ordinary activity.
This isn't true. When you drive your car, E = mc² is at work. As the engine burns gasoline to produce energy in the form of motion, it does so by converting some of the gasoline's mass into energy, in accord with Einstein's formula. When you use your MP3 player, E = mc² is at work. As the player drains the battery to produce energy in the form of sound waves, it does so by converting some of the battery's mass into energy, as dictated by Einstein's formula. As you read this text, E = mc² is at work. The processes in the eye and brain, underlying perception and thought, rely on chemical reactions that interchange mass and energy, once again in accord with Einstein's formula.
[ This article is 3 pages long. To read the rest of the article, go here (http://www.nytimes.com/2005/09/30/opinion/30greene.html?pagewanted=2&th&emc=th). ]