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Einstein's Equation At 100

From: Diana Cammack <cammack.nul>
Date: Fri, 30 Sep 2005 13:25:37 +0200
Fwd Date: Sat, 01 Oct 2005 08:22:26 -0400
Subject: Einstein's Equation At 100

Source: The New York Times


September 30, 2005

NY Times, Op-Ed
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 =3D mc=B2.

In the century since, E =3D mc=B2 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 =3D mc=B2. 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 =3D mc=B2, 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 =3D mc=B2, 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=B2). 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=B2 , 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 =3D mc=B2 has a
special association with nuclear reactions and is thus removed
from ordinary activity.

This isn't true. When you drive your car, E =3D mc=B2 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 =3D mc=B2 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 =3D mc=B2
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=3Dmc=B2 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=3Dmc=B2 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 =3D mc=B2 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 =3D mc=B2. 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

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 =3D mc=B2 - 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 =3D mc=B2; he wrote the
mathematically equivalent (though less euphonious) m =3D E/c=B2,
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.

Its singular fame notwithstanding, E =3D mc=B2 fits into the pattern
of work and discovery that Einstein pursued with relentless
passion throughout his entire life. Einstein believed that deep
truths about the workings of the universe would always be "as
simple as possible, but no simpler." And in his view, simplicity
was epitomized by unifying concepts - like matter and energy -
previously deemed separate. In 1916, Einstein simplified our
understanding even further by combining gravity with space,
time, matter and energy in his General Theory of Relativity. For
my money, this is the most beautiful scientific synthesis ever

With these successes, Einstein's belief in unification grew ever
stronger. But the sword of his success was double-edged. It
allowed him to dream of a single theory encompassing all of
nature's laws, but led him to expect that the methods that had
worked so well for him in the past would continue to work for
him in the future.

It wasn't to be. For the better part of his last 30 years,
Einstein pursued the "unified theory," but it stubbornly
remained beyond his grasp. As the years passed, he became
increasingly isolated; mainstream physics was concerned with
prying apart the atom and paid little attention to Einstein's
grandiose quest. In a 1942 letter, Einstein described himself as
having become a "a lonely old man who is displayed now and then
as a curiosity because he doesn't wear socks."

Today, Einstein's quest for unification is no curiosity - it is
the driving force for many physicists of my generation. No one
knows how close we've gotten. Maybe the unified theory will
elude us just as it dodged Einstein last century. Or maybe the
new approaches being developed by contemporary physics will
finally prevail, giving us the ultimate explanation of the
cosmos. Without a unified theory it's hard to imagine we will
ever resolve the deepest of all mysteries - how the universe
began- so the stakes are high and the motivation strong.

But even if our science proves unable to determine the origin of
the universe, recent progress has already established beyond any
doubt that a fraction of a second after creation (however that
happened), the universe was filled with tremendous energy in the
form of wildly moving exotic particles and radiation. Within a
few minutes, this energy employed E =3D mc=B2 to transform itself
into more familiar matter - the simplest atoms - which, in the
course of about a billion years, clumped into planets and stars.

During the 13 billion years that have followed, stars have used
E =3D mc=B2 to transform their mass back into energy in the form of
heat and light; about five billion years ago, our closest star -
the sun - began to shine, and the heat and light generated was
essential to the formation of life on our planet. If prevailing
theory and observations are correct, the conversion of matter to
energy throughout the cosmos, mediated by stars, black holes and
various forms of radioactive decay, will continue unabated.

In the far, far future, essentially all matter will have
returned to energy. But because of the enormous expansion of
space, this energy will be spread so thinly that it will hardly
ever convert back to even the lightest particles of matter.
Instead, a faint mist of light will fall for eternity through an
ever colder and quieter cosmos.

The guiding hand of Einstein's E =3D mc=B2 will have finally come to

Brian Greene, a professor of physics and mathematics at
Columbia, is the author of The Elegant Universe and The
Fabric of the Cosmos.

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