[IP] Brian Greene: That Famous Equation and You
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From: Dewayne Hendricks <dewayne@xxxxxxxxxxxxx>
Date: September 30, 2005 11:21:37 AM EDT
To: Dewayne-Net Technology List <dewayne-net@xxxxxxxxxxxxx>
Subject: [Dewayne-Net] Brian Greene: That Famous Equation and You
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[Note: This item comes from reader John McMullen. DLH]
From: "John F. McMullen" <observer@xxxxxxxxxxx>
Date: September 30, 2005 6:26:58 AM PDT
To: "johnmac's living room" <johnmacsgroup@xxxxxxxxxxxxxxx>
Cc: Inwood2001 <inwood2001@xxxxxxxxxxxxxxx>, Dewayne Hendricks
<dewayne@xxxxxxxxxxxxx>
Subject: Brian Greene: That Famous Equation and You
(johnmac -- One of my students (say "hello", Caywell) asked last
night why we still quote Einstein when he lived so long ago --
surely there are newer theories that have surpassed his. --
Hopefully, I straighened that out :) -- and, if I didn't, this
article should )
From the New York Times -- <http://www.nytimes.com/2005/09/30/
opinion/30greene.html?
ex=1285732800&en=75072acd6902749d&ei=5090&partner=rssuserland&emc=rss>
Op-Ed Contributor
That Famous Equation and You
By BRIAN GREENE
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."
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 = mc.
In the century since, E = mc 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 = mc.
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 = mc, 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 = mc, 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 (c). 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), c , 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 = mc has a special
association with nuclear reactions and is thus removed from
ordinary activity.
This isn't true. When you drive your car, E = mc 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 =
mc 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 = mc 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.
The point is that although E=mc expresses the interchangeability of
mass and energy, it doesn't single out any particular reaction for
executing the conversion. The distinguishing feature of nuclear
reactions, compared with the chemical reactions involved in burning
gasoline or running a battery, is that they generate less waste and
thus produce more energy - by a factor of roughly a million. And
when it comes to energy, a factor of a million justifiably commands
attention. But don't let the spectacle of E=mc in nuclear reactions
inure you to its calmer but thoroughly pervasive incarnations in
everyday life.
That's the content of Einstein's discovery. Why is it true?
Einstein's derivation of E = mc was wholly mathematical. I know his
derivation, as does just about anyone who has taken a course in
modern physics. Nevertheless, I consider my understanding of a
result incomplete if I rely solely on the math. Instead, I've found
that thorough understanding requires a mental image - an analogy or
a story - that may sacrifice some precision but captures the
essence of the result.
Here's a story for E = mc. 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 = mc - 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 = mc; he wrote the mathematically
equivalent (though less euphonious) m = E/c, 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.
[snip]
Weblog at: <http://weblog.warpspeed.com>
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