what a man - einstein

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GENERAL

RELATIVITYPedro Ferreira

INSTANTEXPERT

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In 1905, at the age of 26, Albert Einstein proposedhis special theory of relativity. The theory reconciledthe physics of moving bodies developed by GalileoGalilei and Newton with the laws of electromagnetic

radiation. It posits that the speed of light is alwaysthe same, irrespective of the motion of the personwho measures it. Special relativity implies thatspace and time are intertwined to a degree neverpreviously imagined.

Starting in 1907, Einstein began trying tobroaden special relativity to include gravity. His firstbreakthrough came when he was working in a patentoffice in Bern, Switzerland. “Suddenly a thought struckme,” he recalled. “If a man falls freely, he would notfeel his weight… This simple thought experiment…led me to the theory of gravity.” He realised that thereis a deep relationship between systems affected bygravity and ones that are accelerating.

The next big step forward came when Einstein wasintroduced to the mathematics of geometry developedby the 19th-century German mathematicians CarlFriedrich Gauss and Bernhard Riemann. Einsteinapplied their work to write down the equations thatrelate the geometry of space-time to the amount of

EINSTEIN’S INSIGHT”Space tells matter howto move and matter tells

space how to curve” John Archibald Wheeler

energy that it contains. Now knownas the Einstein field equations, andpublished in 1916, they supplantedNewton’s law of universal gravitation

and are still used today, nearly acentury later.

Using general relativity, Einsteinmade a series of predictions. Heshowed, for example, how his theorywould lead to the observed drift inMercury’s orbit. He also predictedthat a massive object, such as thesun, should distort the path taken bylight passing close to it: in effect, thegeometry of space should act as a lensand focus the light (see diagram).

Einstein also argued that thewavelength of light emitted close to

a massive body should be stretched,or red-shifted, as it climbs out of thewarped space-time near the massiveobject. These three predictions arenow called the three classical testsof general relativity.

Einstein suggested that light rays skimming past the sunwould be bent by its gravity. To test the idea, ArthurEddington rst photographed the Hyades stars at night.He then needed to photograph them when they wereon the far side of the sun. For this picture, it only becamepossible to see the starlight when the glare of the sunwas eliminated by a total solar eclipse. His imagescon rmed Einstein’s prediction

The mass of the sun bendsspace-time, so bright rays fromthe Hyades cluster bend too.Viewed from Earth, the starsappear to have shifted

SUN

EARTH

APPARENTPOSITION

ACTUALPOSITIONS

APPARENTPOSITION

HYADES STAR CLUSTER,150 LIGHT YEARS AWAY

According to generalrelativity, space-time canbe viewed as a smooth,

exible sheet that bendsunder the in uence ofmassive objects

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Albert Einstein’s general theory of relativity is one of the toweringachievements of 20th-century physics. Published in 1916, it explainsthat what we perceive as the force of gravity in fact arises from thecurvature of space and time.

Einstein proposed that objects such as the sun and the Earth changethis geometry. In the presence of matter and energy it can evolve,stretch and warp, forming ridges, mountains and valleys that causebodies moving through it to zigzag and curve. So although Earthappears to be pulled towards the sun by gravity, there is no suchforce. It is simply the geometry of space-time around the sun tellingEarth how to move.

The general theory of relativity has far-reaching consequences.It not only explains the motion of the planets; it can also describe thehistory and expansion of the universe, the physics of black holes and

the bending of light from distant stars and galaxies.

In 1919, the English astronomer Arthur Eddingtontravelled to the island of Príncipe off the coast of westAfrica to see if he could detect the lensing of lightpredicted by general relativity. His plan was to observea bright cluster of stars called the Hyades as the sunpassed in front of them, as seen from Earth. To seethe starlight, Eddington needed a total solar eclipseto blot out the glare of the sun.

If Einstein’s theory was correct, the positionsof the stars in the Hyades would appear to shift

by about 1/2000th of a degree.To pinpoint the position of the

Hyades in the sky, Eddington firsttook a picture at night from Oxford.Then, on 29 May 1919, hephotographed the Hyades as theylay almost directly behind the sunduring the total eclipse that Príncipeexperienced that day. Comparingthe two measurements, Eddingtonwas able to show that the shift wasas Einstein had predicted and too largeto be explained by Newton’s theory.

Following the eclipse expedition,

PHYSICIST, SUPERSTAR

In 1686, Isaac Newton proposed an

incredibly powerful theory of motion.At its core was the law of universalgravitation, which states that theforce of gravity between two objectsis proportional to each of their massesand inversely proportional to thesquare of their distance apart.Newton’s law is universal because itcan be applied to any situation wheregravity is important: apples fallingfrom trees, planets orbiting the sun,and many, many more.

For more than 200 years, Newton’stheory of gravity was successfullyused to predict the motions ofcelestial bodies and accuratelydescribe the orbits of the planets inthe solar system. Such was its powerthat in 1846 the French astronomerUrbain Le Verrier was able to use itto predict the existence of Neptune.

There was, however, one casewhere Newton’s theory didn’t seemto give the correct answer. Le Verriermeasured Mercury’s orbit withexquisite precision and found that itdrifted by a tiny amount – less than

one-hundredth of a degree overa century – relative to what wouldbe expected from Newton’s theory.The discrepancy between Newton’stheory and Mercury’s orbit was stillunresolved at the beginning of the20th century.

GRAVITYBEFOREEINSTEIN

HISTORY OF GENERAL RELATIVITY

there was some controversy thatEddington’s analysis had been biasedtowards general relativity. Matterswere put to rest in the late 1970swhen the photographic plates wereanalysed again and Eddington’sanalysis was shown to be correct.

Eddington’s result turned Einsteininto an international superstar:“Einstein’s theory triumphs” was

the headline of The Times of London.From then on, as more consequencesof his theory have been discovered,general relativity has becomeentrenched in the popularimagination, with its descriptions ofexpanding universes and black holes.

In 1959, the American physicistsRobert Pound and Glen Rebkameasured the gravitational red-shifting of light in their laboratoryat Harvard University, therebyconfirming the last of the threeclassical tests of general relativity.

By 1930, AlbertEinstein andArthur Eddingtonwere famous fortheir work ongeneral relativity

Images of the 1919solar eclipse proved thatgravity bends starlight R

O Y A L A S T R O N O M I C A L S O C I E T Y / S P L

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”No black holes have beenseen directly yet, thoughthere is overwhelmingevidence that they exist”

Shortly after Einstein proposed his general theory ofrelativity, a German physicist called Karl Schwarzschildfound one of the first and most important solutionsto Einstein’s field equations. Now known as theSchwarzschild solution, it describes the geometryof space-time around extremely dense stars – andit has some very strange features.

For a start, right at the centre of such bodies, thecurvature of space-time becomes infinite – forming afeature called a singularity. An even stranger featureis an invisible spherical surface, known as the eventhorizon, surrounding the singularity. Nothing, noteven light, can escape the event horizon. You can

almost think of the Schwarzschild singularity as ahole in the fabric of space-time.

In the 1960s, the New Zealand mathematicianRoy Kerr discovered a more general class of solutionsto Einstein’s field equations. These describe denseobjects that are spinning, and they are even morebizarre than Schwarzschild’s solution.

The objects that Schwarzschild and Kerr’s solutionsdescribe are known as black holes. Although no blackholes have been seen directly, there is overwhelmingevidence that they exist. They are normally detectedthrough the effect they have on nearby astrophysicalbodies such as stars or gas.

The smallest black holes can be found paired up

BLACK HOLESwith normal stars. As a star orbitsthe black hole, it slowly sheds someof its material and emits X-rays. Thefirst such black hole to be observedwas Cygnus X-1, and there are nowa number of well-measured X-raybinaries with black holes of about10 times the mass of the sun.

Evidence for much larger blackholes came in the 1960s when anumber of very bright and distantobjects were observed in the sky.Known as quasars, they arise from

the havoc black holes seem to createat the cores of galaxies. Gas at thecentre of a galaxy forms a swirlingdisc as it is sucked into the blackhole. Such is the strength of theblack hole’s pull that the swirlinggas emits copious amounts ofenergy that can be seen manybillions of light years away. Currentestimates place these black holesat between a million and a billiontimes the mass of the sun. As aresult, they are called supermassiveblack holes.

The evidence now points to therebeing a supermassive black hole atthe centre of every galaxy, includingour own. Indeed, observations of theorbits of stars near the centre of theMilky Way show that they are movingin very tightly bound orbits. These canbe understood if the space-time theylive in is deeply distorted by thepresence of a supermassive black holewith more than 4 million times themass of the sun.

Despite their names, British

physicist Stephen Hawking haspointed out that black holes may notbe completely black. He argues that,near the event horizon, the quantumcreation of particles and antiparticlesmay lead to a very faint glow. Thisglow, which has become known asHawking radiation, has not beendetected yet because it is so faint.Yet, over time, Hawking radiationwould be enough to remove all theenergy and mass from a black hole,causing all black holes to eventuallyevaporate and disappear.



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Einstein’s general theory of relativity has revealed that the universeis an extreme place. We now know it was hot and dense and has beenexpanding for the past 13.7 billion years. It is also populated withincredibly warped regions of space-time called black holes that trap

anything falling within their clutches.

HOW GENERAL RELATIVITY SHAPES OUR UNIVERSE

One of general relativity’s most

striking predictions arises if weconsider what happens to theuniverse as a whole.

Shortly after Einstein publishedhis theory, Russian meteorologist andmathematician Alexander Friedmannand Belgian priest Georges Lemaîtreshowed that it predicted that theuniverse should evolve in response toall the energy it contains. They arguedthat the universe should start offsmall and dense, and expand anddilute with time. As a result, galaxiesshould drift away from each other.

Einstein was initially sceptical ofFriedmann and Lemaître’s conclusion,favouring a static universe. But adiscovery by the American astronomerEdwin Hubble changed his mind.

Hubble analysed how galaxiesrecede from the Milky Way. He foundthat distant galaxies move awayfaster than those that are relativelynearby. Hubble’s observationsshowed that the universe was indeedexpanding. This model of the cosmoslater became known as the big bang.

Over the past 20 years, a plethoraof powerful observations by satellitesand large telescopes have furtherfirmed up the evidence for anexpanding and evolving universe.We have obtained an accurate measureof the expansion rate of the universeand of the temperature of the “relicradiation” left over from the big bang,and we have been able to observeyoung galaxies when the universewas in its infancy. It is now acceptedthat the universe is about 13.7 billionyears old.

THEEXPANDINGUNIVERSE

Images from the HubbleSpace Telescope (above)and Chandra X-rayObservatory have firmedup our relativity-basedideas about the universe

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According to general relativity, even empty space-time, devoid of stars and galaxies, can have a lifeof its own. Ripples known as gravitational wavescan propagate across space in much the same way

that ripples spread across the surface of a pond.One of the remaining tests of general relativity

is to measure gravitational waves directly. To thisend, experimental physicists have built the LaserInterferometer Gravitational-Wave Observatory (LIGO)at Hanford, Washington, and Livingston, Louisiana. Eachexperiment consists of laser beams that are reflectedbetween mirrors placed up to 4 kilometres apart. If agravitational wave passes through, it will slightly distortspace-time, leading to a shift in the laser beams. Bymonitoring time variations in the laser beams, it ispossible to search for the effects of gravitational waves.

No one has yet detected a gravitational wave directly,but we do have indirect evidence that they exist. When

pulsars orbit very dense stars, we expect them to emita steady stream of gravitational waves, losing energyin the process so that their orbits gradually becomesmaller. Measurement of the decay of binary pulsars’orbits has confirmed that they do indeed lose energyand the best explanation is that these pulsars arelosing energy in the form of gravitational waves.

Pulsars are not the only expected source ofgravitational waves. The big bang should have createdgravitational waves that still propagate through thecosmos as gentle ripples in space-time. These

GRAVITATIONAL WAVESprimordial gravitational waves aretoo faint to be detectable directly,but it should be possible to see theirimprint on the relic radiation from

the big bang – the cosmic microwavebackground. Experiments are nowunder way to search for thesesignatures.

Gravitational waves should alsobe emitted when two black holescollide. As they spiral in towards eachother, they should emit a burst ofgravitational waves with a particularsignature. Provided the collision issufficiently close and sufficientlyviolent, it may be possible to observethem with instruments on Earth.

A more ambitious project is the

Laser Interferometer Space Antenna(LISA), made up of a trio of satellitesthat will follow the Earth in its orbitaround the sun. They will emitprecisely calibrated laser beamstowards each other, much like LIGO.Any passing gravitational wave willslightly distort space-time and lead toa detectable shift in the laser beams.NASA and the European Space Agencyhope to launch LISA in the next decade.

Einstein’s theory allows for the intriguingpossibility of time travel. One suggested way ofachieving this involves the construction of tunnelscalled wormholes that link different parts ofspace at different times. It is possible to buildwormholes – in theory. But unfortunately theywould require matter with negative energy, andother unnatural physical circumstances, not onlyto open them up but also to allow them to betraversed. Another possibility is to create a largeregion of space that rotates, or use hypotheticalobjects called cosmic strings.

TIME TRAVELThe possibility of time travel

can lead to physical paradoxes,such as the grandfather paradox inwhich the time traveller goes back intime and kills her grandfather beforehe has met her grandmother. As aresult, one of her parents would nothave been conceived and the timetraveller herself would not exist. It hasbeen argued, however, that physicalparadoxes such as these are, inpractice, impossible to create.

”It is possible to buildtunnels linking differentparts of space anddifferent parts of time –in theory, at least”

The LIGO detectors(left) are looking forgravitational wavesringing through space



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General relativity predicts that the universe is full of exotic phenomena.Space-time can tremble like the surface of a pond and it seems to befull of a mysterious form of energy that is pushing it apart. It is alsoconceivable for space-time to be so warped that it becomes possible

to travel backwards in time.

FRONTIERS OF GENERAL RELATIVITY

The expanding universe predicted by general relativityhas become firmly entrenched in modern science. Asour ability to observe distant galaxies and map out thecosmos has improved, our picture of the universe has

revealed some even more exotic features.For a start, astronomers have been able to

measure how fast distant spiral galaxies spin, and thisshows that the outskirts of galaxies are rotating fartoo quickly to be reined in by the mass of the stars andgas at their centres. More matter is needed in galaxiesto generate enough gravity to prevent galaxies fromflying apart.

The popular explanation is that galaxies containlarge quantities of other forms of matter – known as“dark matter” because it does not emit or reflect light.Dark matter is thought to clump around galaxies andclusters of galaxies in gigantic balls known as halos.Dark matter halos can be dense enough tosignificantly distort space-time and bend the pathof any light rays that pass close by. This gravitationallensing has been observed in a number of clusters ofgalaxies, and is one of the strongest pieces ofevidence for the existence of dark matter.

But that’s not all. Cosmologists have been able tofigure out how fast the universe expanded at differenttimes in its history. This is done by measuring thedistance to exploding stars called supernovae, andhow quickly they are receding due to the expansionof space-time. The ground-breaking results from these

THE DARK UNIVERSEobservations, which emerged just overa decade ago, is that the expansion ofthe universe seems to be speeding up.

One explanation for this

accelerating expansion is that theuniverse is permeated by an exoticform of energy, known as dark energy.Unlike ordinary matter and darkmatter, which bend space-time in away that draws masses together, darkenergy pushes space apart, making itexpand ever more quickly over time.

If we weigh up all the forms ofmatter and energy in the universe weend up with a striking conclusion: only4 per cent of the universe is in theform of the matter we are familiarwith. Around 24 per cent is darkmatter and 72 per cent is dark energy.

This result emerged from themarriage of the general theory ofrelativity and modern astronomyand it has become a prime focus ofphysics. Experimenters and theoristsare directing their efforts at tryingto answer the burning questions:what exactly are dark matter anddark energy? And why do they havesuch strange properties?

The group of galaxiesknown as the Bulletcluster provides goodevidence for darkmatter (added in blue)

H E N Z E / N A S A F A R L E F T : D

A V E B U L L O C K R I G H T : C X C / C F A / M

. M A R K E V I T C H E T A L

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Pedro Ferreira is professor ofastrophysics at the University ofOxford. He works on the originof large-scale structures in theuniverse, on the general theoryof relativity and on the nature ofdark matter and dark energy

Pedro Ferreira NEXTINSTANTEXPERT

THE BIG UNSOLVED PROBLEM QUANTUM GRAVITY

Ian WilmutCLONING

7 August

General relativity is only one of

the pillars of modern physics. Theother is quantum mechanics, whichdescribes what happens at the atomicand subatomic scale. Its modernincarnation, quantum eld theory,has been spectacularly successfulat describing and predicting thebehaviour of fundamental particlesand forces.

The main challenge now is tocombine the two ideas into oneoverarching theory, to be known asquantum gravity. Such a theory wouldbe crucial for explaining the rstmoments of the big bang, when theuniverse was dense, hot and small,or what happens near the singularityat the cores of black holes, wherethe e ects of quantum physicsmay compete with those ofgeneral relativity.

Although there is as yet no naltheory of quantum gravity, thereare several candidate theories beingactively explored. One is string theory,which describes the fundamentalconstituents of matter not as point-like particles but as microscopic

vibrating strings. Depending on

how they vibrate, the strings will beperceived as di erent particles –including the graviton, the particlethought to carry the gravitational force.

Another possibility is that space-time is not smooth but built up ofdiscrete building blocks that interactwith each other. As a result, if wewere able to peer at its ne structure,it might look like a frothy space-timefoam. In such theories, what weperceive as the space-time that bendsand warps smoothly in the presenceof matter is merely an emergentphenomenon masking more radicalbehaviour on small scales.

The quest for the theory ofquantum gravity is arguably thebiggest challenge facing modernphysics. One of the di culties isthat it only really manifests itself at

extremely high energies, well beyondour experimental reach. Physicistsnow face the task of devisingexperiments and astronomicalobservations that can test candidatetheories of quantum gravity in thereal world.

RECOMMENDED READINGThe State of the Universe byPedro G. Ferreira (Phoenix)Black Holes and Time Warps: Einstein’s Outrageous Legacy by Kip Thorne(Papermac)Gravity: An Introduction to Einstein’s General Theory of Relativity by JamesB. Hartle (Addison-Wesley)Time Travel in Einstein’s Universe by Richard Gott (Phoenix)Was Einstein Right? Putting General Relativity to the Test by Clifford Will(Basic Books)

Cover imageXMM-Newton/ESA/NASA

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