Physics Journal Workshop
Physics Journal Workshop PHY 250
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Date Created: 10/21/15
w 4 w 4 n B An S e N S rl m e w e m In 0 t n d I 0 n 0 U a n S r e m a 05 V n e 0 e 0 W e I a e 0 9m 5 n L i m e t V I R t m g HD M b m M A MWM H r l w e e a m m B Y I B T V 3 quot 39 1 ilN F39L39A39T39lNVIGV BALLOON is a good analogy for understandingthe expansion ofthe universe The galaxies on the surface ofthe balloon i 39 are effectively at rest and getas the universe expands the distance between any two galaxies increases The galaxies themselVes do notincrea39sein size 39 wwwsciamcom 39 39 SCIENTIFIC AMERICAN 3 The expansion ofthe universe may be the most important fact we have ever discovered about our origins You39would nOt be reading this article if the universe had not eXpanded Human beings would not exist Cold molecular things such as life forms and terrestrial planets could not haVe Come into exis tence unless the universe starting from a quothot big bang had expanded and cooled The formation of all the structures in the universe from galaxies and stars to planets and Scienti c American articles has depended on the expansion Forty years ago this July scientists announced the discov ery of definitive evidence for the expansion 39of the universe from a hotter quotdenser primordial state They had found the cool afterglow of thebig bang the cosmic microwave back ground radiation Since this discovery the expansion and cooling of the universe has been the unifying theme of cos mology much as Darwinian evolutionis the unifying theme of biology Like Darwinian evOlution COSmic expansion pro vides the context within which simple structures form and develop over time into Complex structures Without evolution and expansion modern biology and cosmology make little sense 39 V V The expansion of the universe is like Darwinian evolution in another curious way most scientists think they understand it but few agree on what itquot really means A century and a half after On the Origin of Speciesbit39logists still debate the mechanisms and implications though not the reality of Dar winism while much of the public still flounders in preDar winian cluelessness Similarly 75 years after its initial discov ery the expansion of the universe is still widely misunder 38 SCIENTIFIC AMERICAN stood A prominent cosmologist involved in the interpretation of the cosmic microwave background James Peebles of Prince ton University wrote in 1993 The full extent and richness of this picture the hot big bang model is not as well understood as I think it ought to be even among those making some of the most stimulating contributions to the ow of ideas RenOWned physicists authors of astronomy textbooks and prominent popularizers of science have made incorrect misleading or easily misinterpreted statements about the ex pansion of the universe Because expansion is the basis of the big bang model these misunderstandings are fundamental Expansion is a beguilingly simple idea but what exactly does it mean to say the universe is expanding What does it ex pand into Is Earth expanding too To add to the befuddle merit the expansion of the universe now seems to be acceler ating a39process with truly mind stretching consequences What Is ExpansionAngway WHEN SOME FAMILIAR OBJECT expands such as a sprained ankle or the Roman Empire or a bomb it gets bigger by expanding into the space around it Ankles empires and bombs have centers and edges Outside the edges there is room to expand into The universe does not seem to have an edge or a center or an outside So how can it expand A good analogy is to imagine that you are an ant living on the surface of an inflating balloon Your world is two dimen sional the only directions you know are left right forward and backward You have no idea what up and down mean One day you realize that your walk to milk your aphids is taking lOnger than it used to ve minutes one day six min utes the next day seVen minutes the next The time it takes to walk to other familiar places is also increasing You are sure that you are not walking more slowly and39that theaphids are milling around randomly in groups not systematically crawl 39 ing away from you This is the important point the distances to the aphids are increasing even though the aphids are not walking away They are just standing there at rest with respect to the rubber of the balloon yet the distances to them and between them are increasing Noticing these facts you conclude that the ground beneath your feet is expanding That is very strange because you have walked around your world and found no edge or outside for it to expand into The expansion of our universe is much like the in ation of a balloon The distances to remote galaxies are increasing Astronomers casually say that distant galaxies are receding or moving away from us but the galaxies are not traveling through space away from us They are not fragments of a big bang bomb Instead the space between the galaxies and us is expanding Individual galaxies move around at random with in clusters but the clusters of galaxies are essentially at rest MARCH 2005 SLIM FILMS preceding pages SLlM FILMS preceding pages ALFRED T KAMAJIAN RIGHT It was an explosion of spaceitself WHA KIND OF EXPLOSION WAS THE BIG A NG WRONG The big bang was like a39bomb going off at a certain location in previously empty space quotIn this view the universecame into existence when matter exploded out from some particular location The pressure was highest at the center and lowest in the surrounding void this pressure difference pushed material outward The space we inhabit is itselfexpanding There was no centerto this explosion it happened everywhere The density and pressure were the same everywhere so there was no pressure difference to drive a conventional explosion The term at rest can bedde ned rigorously The microwave background radiation lls the universe and de nes a universal reference frame analogous to the rubber of the balloon with respect to which motion can be measured This balloon analogy should not be stretched too far From our point of view outside the balloon the expansion of the curved two dimensional rubber is possible only because it is embedded in threedimensional space Within the third dimension the balloon has a center and its surface expands into the surrounding air as it inflates One might conclude that the expansion of our three dimensional space requires the presence of a fourth dimension But in Einstein s general theory of relativity the foundation of modern cosmology space is dynamic It can expand shrink and curve without r being embedded in a higher dimensional space In this sense the universe is self contained It needs nei ther a center to expand away from nor empty space on the outside wherever that is to expand into When it expands it does not claim previously unoccupied space from its sur roundings Some newer theories such as string theory do pos tulate extra dimensions but as our threedimensional uni verse expands it does not need these extra dimensions to spread into Ubiquitous Cosmic Traffic Jam IN 0 U R U N I V E R s E as on the surface of the balloon every thing recedes from everything else Thus the big bang was wwwsciamcom not an explosion39in space it Was more like an explosion of space It did not go off at a particular location and spread out from there into some imagined preexisting void It occurred everywhere at once 39 If one imagines running the clock backward in time any given region of the universe shrinks and all galaxies in it get closer and closer until they smash together in a cosmic traf c jam the big bang This traf c jam analogy might imply local congestion that you could avoid if you listened to the traf c report on the radio But39 the big bang was an unavoidable traf c jam It was like having the surface of Earth and all its high ways shrink while cars remained the same size Eventually the cars will be bumper to bumper on every road No radio broad CHARLES H LINEWEAVER and TAMARA M DAVIS are astronomers at Mount Stromlo Observatory near Canberra Australia They work on a wide range ofquestions from cosmology to life in the universe Lineweaver While at the University of California Berkeley inthe early 19905was part ofthe Cosmic Background Explorerteam which discovered uctuations in the cosmic mi crowave background radiation He has degrees not just in as trophysics but also in history and English literature used to 39 play soccer semiprofessionally and is the father39oftwo young soccer stars Colleen and Deirdre Davis works on the Super novaAcceleration Probe a space observatory now39being de signedShe representsAustralia in the sport ofUltimate Frisbee and has competed in two world championships rHeAurHoRS39 SCIENTIFIC AMERICAN 39 WRONG chourse not Einstein s special theory of relativity forbids that Consider a patch ofspace containing some galaxies The galaxies move away from us the fartherthe galaxy the faSter itsvelbcity yellow arro39ws If light speed is the ultimate li mitthe galaxy velocity must eventually plateangraph quot 39 x r Distance 3 V 3 rsfie fflzlgfi V D g B u r us Allttlltl39sl v Q KEEGE quot a Galaxy velocity CAN GAAIES RECEDE FASTERTHAN LlHT RIGHT Sure they can Special relativity does not apply to recession velocity In expanding space recession velocity keeps increasing with distance Beyond a certain distance known as the Hubble distance it exceeds the speed of light This is not a violation of relativity be cause39recession velocity is caused not by motion through space but by the expansion ofspace x r Recession Velocity cast is going to help you around that kind of traf c jam The congestion is everywhere Similarly thequot big bang happened everywhere in the room in which you are reading this article in a spot just to the left of Alpha Centauri everyWhere It was not a bomb going off at a particular spot that we can identify as the center of the explosion Likewise in the balloon analogy there is no spe cial place on the surface of the balloon that is the center of the expansion 39 Thisvubiquity of the big bang holds no matter how big the universe is oreven whether it is nite or in nite in size Cos mologists sometimes state that the universe used to be the size of a grapefruit but what they mean is that the part of the universe we can now see our observable universe used to be the size of a grapefruit Observers living in the Andromeda galaxy and beyond have their own observable universes that are different from but overlap with ours Andromedans can see galaxies we cannot simply by virtue of being slightly closer to them and vice versa Their observable universe also used to be the size of a grape fruit Thus we can conceive of the early universe as a pile of overlapping grapefruits that stretches in nitely in all direc 40 SCIENTIFIC AMERlCA39N tions Correspondingly the idea that the big bang was small is misleading The totality of space could be in nite Shrink an in nite space by an arbitrary amount and it is still in nite Receding Faster Than Light ANOTHER SET OFMISCONCEPTIONS involves the quan titative description of expansion The rate at which the dis tance between galaxies increases follows a distinctive pattern discovered by American astronomer Edwin Hubble in 1929 the recession velocity of a galaxy away from us 1 is directly proportional to its distance from us d or v Hd The pro portionality constant H is known as the Hubble constant and quanti eshowfast space is stretching not just around us but around any observer in the universe Some people get confused by the fact that some galaxies do not obey Hubble s law Andromeda our nearest large ga lactic neighbor is actually moving toward us not away Such exceptions arise beCause Hubble s law describes only the aver age behavior of galaxies Galaxies can also have modestlocal motions as they mill aroundand gravitationally pull on one another as the Milky Way and Andromeda are doing Dis tant galaxies also have small local velocities but from our MARCH 2005 ALFRED T KAMAJlAN ALFRED T KAMAJIAN P CHALLIS Centerfar AstrophysicsSTSclNASA perspective at large values of d these random velocities are swamped by large recession velocities v Thus for those galaxies Hubble s law holds with good precision Notice that according to Hubble s law the universe does not expand at a single speed Some galaxies recede from us at 1000 kilometers per second others those twice as distant at 2000 kms and so on In fact Hubble s law predicts that galaxies beyond a certain distance known as the Hubble dis tance recede faster than the speed of light For the measured value of the Hubble constant this distance is about 14 billion lightyears Does this prediction of faster than light galaxies mean that Hubble s law is wrong Doesn t Einstein s special theory of relativity say that nothing can have a velocity exceeding that of light This question has confused generations of stu dents The solution is that special relativity applies only to normal velocities motion through space The velocity in Hubbles law is a recession Velocity caused by the expansion of space not a motion through space It is a general relativis tic effect and is not bound by the special relativistic limit Having a recession velocity greater than the speed of light does not Violate special relativity It is still true that nothing ever overtakes a light beam Stretching and Cooling THE PRIMARY 0 B S ERVAT I ON that the universe is expand ing emerged between 1910 and 1930 Atoms emit and absorb light of specific wavelengths as measured in laboratory ex periments The same patterns showup in the light from dis tant galaxies except that the patterns have been shifted to longer wavelengths Astronomers say that the galactic light has been redshifted The explanation is straightforward As space expands light waves get stretched If the universe dou bles in size during the waves journey their wavelengths dou ble and their energy is halved This process can be described in terms of temperature The photons emitted by a body collectively have a temperature a certain distribution of energy that re ects how hot the body is As the photons travel through expanding space they lose en ergy andtheir temperature decreases In this way the universe cools asi t expands much as compressed air in a scuba tank cools when it is released and allowed to expand For example the microwave background radiation currently has a tempera ture of about three kelvins whereas the process that released the radiation occurred at a temperature of about 3000 kelvins Since the time of the emission of this radiation the universe has increased in size by a factor of 1000 so the temperature of the photons has decreased by the same factor By observing the gas in distant galaxies astronomers have directly measured the temperature of the radiation in the distant past These measure ments con rm that the universe has been cooling with time Misunderstandings about the relation between redshift and velocity39abound The redshift caused by the expansion is often confused with the more familiar redshift generated by the Doppler effect The normal Doppler effect causes sound o WWWSCIamC0m SCIENTIFIC AMERICAN 41 waves to get longer if the source of the sound is moving away for39example a receding ambulance siren Thesame principle also applies to light waves which get longer if the sOurce of the light is39moving through space away fromus This issimilar but not identical to what39happens to the light from distant galaxies The cosmological redshift is not gt a normal Doppler shift Astronomers frequently refer to it as such and in doing so they have done their students a serious disserviCe The Doppler redshift and the cosmological red shift are governed by two distinct formulas The rst comes frOm sp ecial39relatiVity which does not take into account the expansion of space and the second comes from general rela tivity Which does The two fOrmulas are nearly the same for I nearby galaxies but diverge fOr distant galaxies According to the usual Doppler formula objects whose velocitythrough Space apprOaches light speed have redshifts that approachinfinity Their wavelengths become too long to V observe If that were true for galaxies the mOSt distant visible objeCts in the Skywould be receding at velocities just shy of the speed of light But the cosmological redshift formula leads toja different Conclusion In the current Standard model of cosmology galaxies With a redshift ofabout 3915 that is Whoselight has alwavelength 150 percent longer than the laboratory reference valueare receding at the speed of light Astrono39mer s39have observed about 1000 galaXies with red shifts larger than 15 That is they haveobserVed about 1000 objects receding from usyfaster than the speed of light Equiv alently we are receding from those galaXies faster than the speed of light Theradiation of the cosmic microwave back ground hasztraVeled even farther and has a redshift Of about 1000 the hot plasma of the early universe emitted the 39WRONQOfcoursegnot Light fromthfose galaxiefs never 4requota ch esUS 39 39 p I a DAVgalaxy fa r therthanthe HUbble 1 quot i distance sphere recedes from s quotus fastefrthanliglht lt emits a l Photeh alydlowsquigglelAs39 3P3C9399XPandsjthe photon is drfagse deWaHliKeSdmeone 39 v tryingto39swim39again stithei CurrentThe phjmonnever I radiation we now see it Was receding from our location atquot about 50 times the speed of light 39 Running to StagpStill T H E 39I D E A o F s E E I N G faster thanlight galaxies may sound mystical but it is made possible by changes in the expansion rate Imagine a light beam that is farther than the Hubble distance of 14 billion lightyears and trying to travel in our direction It is moving toward39us at the speed of light with respect to its local space but its local space is receding from us faster than the speed of light Although the light beam is traveling toWard us at the maximum speed possible it cannot keep up with the stretching of space It is abit like a child try ing to run the wrong way on a moving sidewalk Photons at the Hubble distance are like the Red Queen and Alice run ning as fast aSthey can just to Stay in the same place One might conclude39that the light beyond the Hubble dis tance would neVer reach us and that its source would be for ever undetectable But the Hubble distance is not xed be cause the Hubble constant on which it depends changes with time In particular the constant is proportional 39to the rate of increase inthedistance between two galaxies divided by that distance Any two galaxies can be used for this calculation In models of the universe that t the observational data the denominator increases faster than the numerator so the Hub ble constant decreases In this way the Hubble distancegets larger As it does light thatwas initially just outside the Hub ble distance and receding frOm us can come withinthe Hubble distance The photons then nd thems elves in a region of space that is receding slower than the speed of light Thereaf ter they can approach us 39 1 CEDIG FAE HN39 LIGHT i 39 RIGHT Sure wecan because the expansion rate changes overtime 39 i 39 39 The39photon39initiallg is39u39nable to approach us But the Hubble 39distan39ce39is not constant it 39 is increasing and can grow to encompass the photon Once that happens the photon approaches us and eventually reaches us 42 SCIENTlFIC AMERICAN 1 MARCH 2005 ALFRED T KAMAJIAN 39A LFREDT KAMAJIAN ALFRED T KAMAJIAN WRONG Because receding galaxies are moving through space and exhibit a Doppler shift inthe Doppler effect a galaxy s 39 movement aWay from the observer stretches the light waves makingthem redder top The wavelength of I light then stays the same during itsjourney through space middle The observer detects the light measures its Doppler redshift and computesthe galaxy velocity 1 bottom WHY IS THERE A COSMIC REDSHIFT RIGHT Because expanding space stretches all light waves as they propagate 39 Galaxies hardly movethrough space so they emit light with nearly the same wavelength in all directions top The39wavelength gets longer during thejourney because space is expanding Thus the light gradually reddens middle and bottom The amountof redshift differs from what a Doppler shift would prOduCe The galaxy they came from though may continue to re cede superluminally Thus we Can observe light from galaxies that have alWays been and will always be receding faster than the speed of light Another way to put it is that thequot Hubble distance is not xed and does not mark the edge of the observ able universe 39 39 What does mark the edge of observable space Here again 39 there has been confusion If space were not expanding the most distant object we could see would now be about 14 bil lion lightyears away from us the distance light could have traveled in the 14 billion years since the big bang But because the universe is expanding the space traversed by a photon expands behind it during the voyage Consequently the cura rent distance to the most distant object we can see is about three times farther or 46 billion light years The recent discovery that the rateof cosmic expansion is accelerating makes things even more interesting Previously cosmologists thought that we lived in a decelerating universe and that ever more galaxies would come into View In an ac celerating universe however we are surrounded by a bound ary beyond which occur events we will never seea cosmic event horizon Iflight from galaxies receding faster than light wwwsciamcom is to reaCh us the Hubble distance has to increase but in an accelerating universe it stops increasing Distant events may send out light beams aimed in our direction but this light is trapped beyond the Hubble distance by the acceleration of the expansion An accelerating universeythen resembles a black hole in that it has an event horizon an edge beyond which we cannot see The current distance to our Cosmic event horizon is 16 billionlightyears well within our observable range Light emitted from galaxies that are now beyond the event horizon 39 Will never be able to reach us the distance that currently cor responds to 16 billion lightyears will expand too quickly We will still be able to see eVents that took place in those galaxies before they croSsed the horizon but subsequent events will be forever beyond our View Is Brooklyn Expanding 3 39 39I N ANNIE HALL the movie character played by the young Woody Allen explains to his doctor and mother why he can t do his homework The universe is expanding The uni verse is everything and if it s expanding someday it will break apart and that would be the end of everything But his SCIENTIFIC AMERICAN 4 3quot mOther right BrOOklyn is not expanding People of ten assume that39as spaceexpands everything in it expands as well But this is not true Expansion by itself that is a coasting expansion neither accelerating nor decelerating produces no fOI39CCuPhOtO Wavelengths expand with the universe because 39 unlike atoms and cities photOns are not coherent objects whose size has been set by a compromise among forces A changing rate of expansion does add a new force to the mix but even this new force does not make objects expand or contract 1 For example if gravity gOt Stronger your spinal cord would compress until the electrons in your vertebrae reached a new equilibrium slightly 39cIOSer together You would be a shorter person but youwou39ld not continueto shrink In the same way if we lived in a universe dominated bythe attractive force Of graVity as most Vc joS iOlogiSts39thought until a few years ago the eXpansiOn would decelerate putting a gentle squeeze on bodies in the univeise making them reach a small Consid erthe mOSt distant obserVable 39 galaxy one whose photons emitted shortly after the big bang ar eonlg A njow reaching us A lightegearis the 39 1 distance photons travel in one year So a39photon from that galaxy has 39 traveled 14 billion lightgears 39 l i1ii4biillionvlightgeairsiI ini B rooklyn Brooklyn is I TE SVBEUE The universeis gears39old o the RIGH f eeause space is expanding the observable part of our universe I radius ofthe observable lightgears has a radios of more than 14 billion lightgears 39 er equilibrium sizeHaving done so they would not keep 39 shrinking In fact in our universe the expansion is accelerating and that exerts a gentle outward force on bodies Consequently bound objects are slightly larger than they would be in a non accelerating universe because the equilibrium among forces is reached at a slightly larger size At Earth s surface the out ward acceleration away frOm the planet s center equals a tiny fraction 10 30 of the normal inWard gravitational accelera tion If this acceleration39is constant it does not make Earth expand rather the planet simply settles into a static equilib rium size slightly larger than the size it wouldhave attained This reasoning changes if acceleration is nOt constant as some cosmologists have speculated If the acceleration itself increased it could eventually grow strong enough to tear apart all structures leading to a big rip But this rip would occur not because of expansion or acceleration per se but be cause of an aCcelerating acceleration The big bang m39odeljis based on39lobservatiOns of expan As a photon travelsthe space it traverses I 39expandsBgthe time it reaches usthe total distance to the originating galaxy is largerthan a simple calculation based on the traveltime might imply aboutthree times as large nn39 gh39tg ars 7 quot quot V 44 SCIENTlFlCAMERICAN MARCH 2005 AL FRED T KAMAJIAN ALFRED T KAMAJlAN39 Galaxy clUster 00 OBJECS lNSlTH IVERSE EXPAD T00 WRONG Yes Expansion causes the universe and everything in it to grow I Consider galaxies in a cluster As the universe gets bigger so do the galaxies and the overall cluster The edge ofthe cluster yellowoutline moves Outward aonocanaaIcocoovncttoaouucotooooouoIi o a o o o o o u o o I v u o o c v u c o o I o a o n o u o a o o u o o I a on a o c I o I I o o o o o o o I c u I c o o u o o o o o u o o c o I a o I o o a n a c I a o o o o o o o o o o o o v o o a o n o h v u o o u I o o y o o a 00 RIGHT No The universe grows but coherent objects inside it do not Neighboring galaxies initially get pulled apart but eventually their mutual gravity overpowers expansion A cluster forms It settles down into an equilibrium size sion the cosmic microwave background the chemical com position of the universe and the clumping of matter Like all scienti c ideas the model may39one day be superseded But it fits the current data better than any other model we have As new precise measurements enable cosmologists to understand I expansion and acceleration better they can ask even more fundamental questions abOut the earliest times and largest scales of the universe What caused the expansion Many cosmologists attribute it to a process known as in ation a type of accelerating expansion But that can only be a partial answer because it seems that to start inflating the universe 39 already had to be expanding And what about the largest scales beyond what we can see Do different parts of the universe expand by different amounts such that our universe is a single in ationary bubble of a much larger multiverse Nobody knows Although many questions remain increas 39 ingly precise observations suggest that39the universe will ex pand forever We hope though the Confusion about the ex pansion will shrink j r v V wwwscia mcom g MORE TO EXPLORE Cosmology The Science ofthe Universe Edward R Harrison Cambridge University Press 2000 The Cosmic Microwave Background Radiation Temperature at a Redshift of234 R Srianand P Petitjean and C Ledoux in Nature 39 Vol408 No 6815 pages 931 935 December 21 2000Avaiiable online at arxivorgabsastroph0012222v 39 Solutions to the Tethered Galaxy Problem in an Expanding Universe and the Observation of Receding Blueshifted Objects Tamara M Davis Charles H Lineweaver and John K Webb in American Journal of Physics Vol 71 No 4 pages 358 364Ap39ril 2003 astroph0104349 Expanding Confusion Common Misconceptions of Cosmological Horizons and the Superluminal Expansion ofthe Universe Tamara M Davis and Charles H Lineweaver ianuin39cations oftheAstronomical Society ofAustraIia Vol 21 No 1 pages 97 109 February 2004 astroph0310808 An excellent resource for dispelling cosmological misconceptions is Ned Wright s Cosmology Tutorial at wwwastroucaeduwright cosmologhtm 39 SCIENTIFIC AMERICAN 45
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