discover magazine - einstein in a nutshell

8/14/2019 Discover Magazine - Einstein in a Nutshell

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Einstein [In a Nutshell]By Michio KakuDesigned and Illustrated by Nigel Holmes

DISCOVER Vol. 25 No. 09 | September 2004 | Astronomy & Physics

Relativity and quantum mechanics rank among the greatest achievements of 20th-

century science, constituting the sum of all fundamental physical knowledge. Theformer describes the world of the very large, including black holes and the expandinguniverse. The latter explains the world of the very small, the microscopic realm ofatoms and subatomic particles. One manAlbert Einsteinwas the undisputed fatherof the first theory and the godfather of the second.

What was the secret of Einsteins success? He once said that if a physical theorycannot be explained to a child, it is probably worthless. In other words, he thought interms of simple physical pictures. His greatness lay in his ability to use such picturesto solve fundamental problems, such as the conflict between Isaac Newtons theory of

mechanics and James Clerk Maxwells theory of light.

The Newtonian system was based on common sensethat a second on Earth is thesame as a second throughout the solar system. We could synchronize our watchesanywhere in the universe because time beats uniformly. Likewise, a foot or a poundon Earth is the same as a foot or a pound in every other location.

Using mental images of clocks and trains, light beams and speeding bicycles, Einsteinrealized that Newtons system could not be right because it contradicted Maxwellstheory of light. Einstein showed that the speed of light must be constant, no matterhow fast you move. For that to be true, time must get slower the faster you move.


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Stranger still, lengths contract and masses must increase as you approach the speed oflight. Space and time became relative in his new theory. This pivotal insightoverthrew 250 years of Newtonian physics.

Ten years later, Einstein resolved yet another contradiction in physics. According toNewton, gravity traveled instantly throughout the universe. But according to thetheory of relativity, nothing can go faster than light. To overcome these incompatibleviews, Einstein introduced another, even grander theory in which space and time are

not empty but are instead like a fabric that can be curved and stretched. This newpicturein which gravity originates from the bending of sheets of space-timerevolutionized cosmology and gave us the most compelling theory of creation, the BigBang.

Thus, pictures even a child could understand would change the course of history andtransform our understanding of the universe.

SPECIAL RELATIVITYSpecial relativity unlocked the secrets of the stars and revealed the fantastic quantitiesof energy stored deep inside the atom. But the seed of relativity was planted whenEinstein was only 16 years old and asked himself a childlike question: What would abeam of light look like if you could race alongside it? According to Newton, youcould catch up to any speeding object if you moved quickly enough. If you could

catch up to a light wave, Einstein realized, it would look like a wave frozen in time.But even as a teenager, he knew that no one had ever seen a frozen light wave before.In fact, such a wave makes no physical sense.

When Einstein studied Maxwells theory of light, he found something that othersmissedthat the speed of light always appears the same, no matter how quickly you

move. Einstein then boldly formulated the principle of special relativity: The speed of

light is a constant in all inertial frames (frames that move at constant velocity).No longer were space and time absolutes, as Newton thought. Space compresses andclocks tick at different speeds throughout the universe.

Previously, physicists believed in the ether, a mysterious substance thatpervaded the universe and provided the absolute reference frame for all

motions. But experiments to measure the ether wind blowing past Earthfound nothing. Even if Earth were by chance motionless at one moment, thereshould be a discernible ether.


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The Speed of Light Is Constant

In desperation to save Newtonian physics, some scientists suggested that theether wind had physically compressed the meter sticks in their experiments,

thus explaining the null result. Einstein showed that the ether theory wasunnecessary and that space itself contracts and time slows down as you movenear the speed of light.


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Timeis Relative

Imagine putting one twin on a rocket ship that blasts off at a speed near that

of light while the other twin remains back on Earth.Through a telescope, the Earth twin sees that his rocket twin appears youngerthan himself.When the rocket twin comes back to Earth,the Earth twin has aged more; the

rocket twin is much younger.A Relativity ParadoxFrom the vantage point of the rocket twin as he took off from Earth, it

appeared as if he were at rest and that the Earth moved away from him. Thus,to him it is the Earth twin who has traveled at great speed and become youngerwhile the rocket twin has aged. So who really is younger?


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Mass is Energy

Resolution of the twin paradox

The rocket twin, not the Earth twin, reversed directions during his journey.Since the rocket twin didnt travel with constant velocity, the two viewpointsare not the same. Hence, you can tell who is younger: the rocket twin.

In Newtons world, ameter stick has the same length anywhere in theuniverse. In Einsteins world, meter sticks get shorter the faster they move.Absolute spaceand distance do not exist.If space and time become distorted, then everything you measure with metersand clocks also becomes distorted, including all forms of mass and energy.It requires only a few lines to calculate how much mass and energy get

distorted. This led Einstein to E = mc2, the most celebrated equation in all of

science. It expresses the relationship between energy (E) and mass (m), linked

by the speed of light (c).

Because c2 is a fantastically large number (34,701,000,000 mi.2/ sec.2 ), a

small amount of mass can be converted into an enormous amount of energy.When an atom of uranium-235 is split, it loses about 0.1 percent of its mass;that tiny amount is enough to produce the vast energy of an atomic bomb.


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GENERAL RELATIVITY

Special relativity was incomplete because it made no mention of acceleration orgravity. Einstein then made the next key observation: Motion under gravity andmotion in an accelerated frame are indistinguishable. Since a light beam will bend in arocket that is accelerating, a light beam must also bend under gravity.

To show this, Einstein introduced the concept of curved space. In this interpretation,planets move around the sun not because of a gravitational pull but because the sunhas warped the space around it, and space itself pushes the planets. Gravity does notpull you into a chair; space pushes on you, creating the feeling of weight. Space-timehas been replaced by a fabric that can stretch and bend.

General relativity can describe the extreme warping of space caused by the gravity of

a massive dead stara black hole. When we apply general relativity to the universe asa whole, one solution naturally describes an expanding cosmos that originated in afiery big bang .

If the sun were to disappear suddenly, what would happen? Newton would saythat the entire universe would instantly feel the loss of the suns gravity.Einstein recognized that nothingnot even gravitycan travel faster than light.

Since sunlight takes eight minutes to travel from the sun to Earth, Einsteinbelieved that it would likewise take eight minutes for Earth to respond to thesuns disappearance.


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One key to Einsteins thinking is to analyze a spinning disk. Since the rim of thedisk travels faster than the center of the disk, the theory of relativity statesthat the rim is compressed more than the center. If so, the disk must be

distorted (its circumference is no longer pi times its diameter). The surface ofthe disk is, in fact, curved.Einstein showed that space itself could be similarly curved and that curvedspace could explain gravity.Put a bowling ball on a bedsheet and shoot a marble past it. The marble willmove in a curved line. A Newtonian physicist would say that the bowling ballexerts a force that pulls on the marble, making it move in a curved line. Arelativist would say that the ball curves the bedsheet and that the bedsheet

pushes against the marble.Now replace the bowling ball with the sun and the marble with Earth. Byanalogy, gravity does not pull Earth around the sun. Rather, the sun bendsspacearound it, and curved spacepushes Earth so thatit moves around thesun.This effect will also bend starlight.In 1919, during an eclipse of the sun, two expeditions actually measured thebending of starlight as it passed by the sun, shifting the apparentposition ofthe stars. Thissealed Einsteins fame.(If we remove the bowling ball, the fabric springs back to its normal shape and

releases a wave that spreads out. If the sun disappeared, it would take eightminutes for theanalogous gravity wavesto reach Earth.)As itpassesby the sun,starlight is bentby the suns distortionof space. As aresult,the stars appear to move.


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The Big BangThe entire universe can be regarded as a by-product of curved space and time.

Curved space-time is analogous to the surface of a balloon. If you blew up aballoon covered with dots, each dot would appear to be speeding away from

the other dots. We seem to live on the surface of a four-dimensional balloonthat is expanding in a similar manner. Our telescopes show galaxies speedingaway from us in all directions.

Black Holes

If a star grows enormously dense, either through collapse or by accumulatingmatter, its gravity creates a rip in space-time. The result: a black hole, anobject from which even light cannot escape. Hundreds of black holes have beendetected, many lurking in the centers of galaxies.WormholesEinstein and Nathan Rosen introduced the concept of a bridge that might linkto a location on the other side of a black hole. Einstein did not believe a personcould pass through this bridge, since the gravitational forces would be lethal.


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EINSTEINS LEGACY

Three of the seminal papers Einstein wrote in his miracle year of 1905 probablydeserved the Nobel Prize. In one paper, he showed that light has a dual naturethatis, it exhibits both wavelike and particle-like qualities. Einsteins quantum theory oflight is essential to modern electronics, including television, solar cells, lasers, andfiber optics.

He was also the first to give solid justification for the existence of atoms. By

analyzing how the random impact of atoms can distort the motion of tiny dustparticles, creating a continuous zigzag motion, he showed a practical way to calculatethe size of atoms.

Einsteins 1905 paper on special relativity paved the way for a four-dimensionaldescription of the world. These formulations provide a framework that may ultimatelysolve his greatest quest: the search for a theory of everything that can unify all the

laws of nature.

Some fault Einstein for opposing quantum mechanics because he believed that Goddoes not play dice. In reality, he did not dispute the undeniable successes of quantummechanics. Instead, his true goal was to swallow up quantum mechanics with hisunified field theory.

The Photoelectric Effect

Einsteins theory gave rise to quantum physics

(Since then, solutions have been found in which travel through a wormholemight be possible, although this is still controversial.)


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Brownian Motion and Atoms

Einstein gave the first credible experimental evidence for atoms

One common instance of this effect occurs when light enters a television

camera and is focused onto a metal plate. When it hits the plate, the light caneject an electron. In this way, light is converted into electricity, which is thenused to reconstruct the image in front of the camera.To explain how light knocks electrons loose, Einstein assumed that light occursin packets of energy, now known as quanta.Thus Einstein not only developed relativity but also helped give birth toquantum physics, the other great theory of the 20th century. Many of his

predictions concerning quantum theory are still being verified.

We often forget that just a century ago many scientists, including famedAustrian physicist and philosopher Ernst Mach, refused to believe in theexistence of atoms. Einstein proved the doubters wrong by explaining


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The Fourth DimensionA major legacy of Einsteins theories is the concept of space-time. Space and time could no

longer be viewed in isolation, because each of them depends on the other.

Space and time were now inseparable.

Brownian motion, the random, jerky movement of microscopic particles.Einstein showed that the motion is caused by the impact of individual atoms.By interpreting this chaotic motion, Einstein calculated the size of the atom, aphysics tour de force. He also used his analysis to determine the number ofatoms in a given mass of an element, which reveals an atoms mass.

Since space has three dimensions (length, width, and height), time can beviewed as the fourth dimension. For example, to arrange a rendezvous with afriend in Manhattan, you need to give four coordinates: Meet me on thenortheast corner of 5th Avenue and 42nd Street, on the 30th floor, at oneoclock. Relativity introduced the concept of the fourth dimension.Imagine plotting your location on a graph, with time on the vertical axis andspace on the horizontal axis. The bottom of the graph represents the past, andthe top part represents the future. If you simply sit in one place and do notmove, you trace a vertical line. If you start to move, you trace a vertical line

that curves a bit.All motions in the universe can similarly be represented as vertical lines that


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Einsteins Critique of Quantum Theory

Although Einstein felt uncomfortable about the introduction of probability in physics, his

critiques of the quantum theory vastly improved and sharpened its foundations.

wobble a bit as they progress upward in this diagram of space-time.

If you travel at the speed of light, you trace out a diagonal line on a plot ofspace versus time. The set of all possible light paths forms a cone. All possiblepaths moving at less than light speed trace curves located inside the upperlight coneof future events.If you could go faster than light (which is impossible), then you would leave

the cone. This is purely amathematicalpossibility.If you could go fast enough, you could hypotheticallyreach the bottom cone,which represents the past.


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A Unified Field?

The greatest legacy of Einsteins work may be the unified field theory, which would weave

all the laws of nature into a single coherent theory. He spent the last30 years of his lifechasing after this theory of everything.

But because little was known about the nuclear force before Einsteins death,there was alarge missing piece to the jigsaw puzzle.Today the leading unifying candidate is stringtheory.

Physicist Erwin Schrdinger conceived a thought experiment in which aprobabilistic event (the decay of an atom) determines whether a cat in a sealedbox lives or dies. Quantum theory says that you do not know what state the cat

is in until you open the box. Before you open the box, the cat is described bythe sum of being alive and dead simultaneously, which Einstein thought wasabsurd. Although quantum theory has withstood every test, physicists stilldebate the fate of the famous Schrdingers cat, regarded as being dead andalive at the same time.

The two great pillars of modern physics, relativity and quantum theory, mayeventually be combined into a single unified field theory, which wouldsummarize all known physics. Einstein believed that it would allow us to read

the mind of God.


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Relativity and You

Textbooks sometimes state that Einsteins theories do not affect our everyday life, because

we never travel anywhere close to the speed of light. But imagine for a moment what

would happen if we could somehow turn off relativity

First, our technology would fail. The Global Positioning System (which locatesour positionon Earth to within 50 feet or less)would malfunction, becausetheclock on the satellitedoes not tick at the samespeed as Earth clocks.Moreover,sincerelativity governsthe properties ofelectricity andmagnetism, allmodern electronicswould come to a halt,including generators,computers, radios, and TV.Without correcting for the effects of relativity, the GPS signals would haveerrors of several parts per billion, enough to make them useless.


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Second, Earth would be uninhabitable. The nuclear furnace that drives the sun

and the stars would shut down without relativity. If there were no E = mc2, the

universe would suddenly become black and cold, making life impossible.Without relativity, Earth would freeze solid.

Third, the atoms in our bodies would collapse. Relativity requires that allparticles spin like tops. This spin prevents multiple electrons from occupying thesame energy state in the atom. Without spin, electrons circling the nucleuswould all fall into the lowest energy state. This means that atoms would nolonger form molecules, and physical reality as we know it would dissolve.Without relativity, our bodies molecules would fall apart.

Michio Kaku, a theoretical physicist at the City University of New York, is the author ofEinsteins Cosmos and the forthcoming Parallel Worlds.

Nigel Holmes is a graphic designer in Westport, Connecticut,

who has finally learned to understand relativity.

discover magazine - einstein in a nutshell

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