Brian Greene has an interesting article in Edge.org, entitled, 'That Famous Equation and You'.
Some excerpts [long, but interesting]:
'Here's a story for E = mc². Two equally strong and skilled jousters, riding identical horses and gripping identical (blunt) lances, head toward each other at an identical speed. As they pass, each thrusts his lance across his breastplate toward his opponent, slamming blunt end into blunt end. Because they're equally matched, neither lance pushes farther than the other, and so the referee calls it a draw.
'This story contains the essence of Einstein's discovery. Let me explain.
'Einstein's first relativity paper, the one in June 1905, shattered the idea that time elapses identically for everyone. Instead, Einstein showed that if from your perspective someone is moving, you will see time elapsing slower for him than it does for you. Everything he does - sipping his coffee, turning his head, blinking his eyes - will appear in slow motion.
'This is hard to grasp because at everyday speeds the slowing is less than one part in a trillion and is thus imperceptibly small. Even so, using extraordinarily precise atomic clocks, scientists have repeatedly confirmed that it happens just as Einstein predicted. If we lived in a world where things routinely traveled near the speed of light, the slowing of time would be obvious.
'Let's see what the slowing of time means for the joust. To do so, think about the story not from the perspective of the referee, but instead imagine you are one of the jousters. From your perspective, it is your opponent - getting ever closer - who is moving. Imagine that he is approaching at nearly the speed of light so the slowing of all his movements - readying his joust, tightening his face - is obvious. When he shoves his lance toward you in slow motion, you naturally think he's no match for your swifter thrust; you expect to win. Yet we already know the outcome. The referee calls it a draw and no matter how strange relativity is, it can't change a draw into a win.
'After the match, you naturally wonder how your opponent's slowly thrusted lance hit with the same force as your own. There's only one answer. The force with which something hits depends not only on its speed but also on its mass. That's why you don't fear getting hit by a fast-moving Ping-Pong ball (tiny mass) but you do fear getting hit by a fast-moving Mack truck (big mass). Thus, the only explanation for how the slowly thrust lance hit with the same force as your own is that it's more massive.
'This is astonishing. The lances are identically constructed. Yet you conclude that one of them - the one that from your point of view is in motion, being carried toward you by your opponent on his galloping horse - is more massive than the other. That's the essence of Einstein's discovery. Energy of motion contributes to an object's mass.
'As with the slowing of time, this is unfamiliar because at everyday speeds the effect is imperceptibly tiny. But if, from your viewpoint, your opponent were to approach at 99.99999999 percent of the speed of light, his lance would be about 70,000 times more massive than yours. Luckily, his thrusting speed would be 70,000 times slower than yours, and so the resulting force would equal your own.
'Once Einstein realized that mass and energy were convertible, getting the exact formula relating them - E = mc² - was a fairly basic exercise, requiring nothing more than high school algebra. His genius was not in the math; it was in his ability to see beyond centuries of misunderstanding and recognize that there was a connection between mass and energy at all.
'A little known fact about Einstein's September 1905 paper is that he didn't actually write E = mc²; he wrote the mathematically equivalent (though less euphonious) m = E/c², placing greater emphasis on creating mass from energy (as in the joust) than on creating energy from mass (as in nuclear weapons and power stations).
'Over the last couple of decades, this less familiar reading of Einstein's equation has helped physicists explain why everything ever encountered has the mass that it does. Experiments have shown that the subatomic particles making up matter have almost no mass of their own. But because of their motions and interactions inside of atoms, these particles contain substantial energy - and it's this energy that gives matter its heft. Take away Einstein's equation, and matter loses its mass. You can't get much more pervasive than that ...' [emphasis added]
[Image credit: Wikimedia Commons]
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