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INTRODUCTION—AN OVERVIEW OF PHYSICS

With a brass tube and a few pieces of glass, you canconstruct either a microscope or a telescope. Thedifference is essentially where you place the lenses.With the microscope, you look down into the world ofthe small, with the telescope out into the world of thelarge.

In the twentieth century, physicists and astronomershave constructed ever larger machines to study matteron even smaller or even larger scales of distance. Forthe physicists, the new microscopes are the particleaccelerators that provide views well inside atomicnuclei. For the astronomers, the machines are radioand optical telescopes whose large size allows them torecord the faintest signals from space. Particularlyeffective is the Hubble telescope that sits above theobscuring curtain of the earth’s atmosphere.

The new machines do not provide a direct image likethe ones you see through brass microscopes or tele-scopes. Instead a good analogy is to the MagneticResonance Imaging (MRI) machines that first collect ahuge amount of data, and then through the use of acomputer program construct the amazing images show-ing cross sections through the human body. Thetelescopes and particle accelerators collect the vastamounts of data. Then through the use of the theoriesof quantum mechanics and relativity, the data is puttogether to construct meaningful images.

Some of the images have been surprising. One of thegreatest surprises is the increasingly clear image of theuniverse starting out about fourteen billion years ago

IntroductionAn Overview of Physics

as an incredibly small, incredibly hot speck that hasexpanded to the universe we see today. By lookingfarther and farther out, astronomers have beenlooking farther and farther back in time, closer tothat hot, dense beginning. Physicists, by looking atmatter on a smaller and smaller scale with the evenmore powerful accelerators, have been studyingmatter that is even hotter and more dense. By theend of the twentieth century, physicists and astrono-mers have discovered that they are looking at thesame image.

It is likely that telescopes will end up being the mostpowerful microscopes. There is a limit, both finan-cial and physical, to how big and powerful anaccelerator we can build. Because of this limit, wecan use accelerators to study matter only up to acertain temperature and density. To study matterthat is still hotter and more dense, which is the sameas looking at still smaller scales of distance, the only“machine” we have available is the universe itself.We have found that the behavior of matter under theextreme conditions of the very early universe haveleft an imprint that we can study today with tele-scopes.

In the rest of this introduction we will show you someof the pictures that have resulted from looking atmatter with the new machines. In the text itself wewill begin to learn how these pictures were con-structed.

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SPACE AND TIMEThe images of nature we see are images in both spaceand time, for we have learned from the work of Einsteinthat the two cannot be separated. They are connectedby the speed of light, a quantity we designate by theletter c, which has the value of a billion (1,000,000,000)feet (30 cm) in a second. Einstein’s remarkable discov-ery in 1905 was that the speed of light is an absolutespeed limit. Nothing in the current universe can travelfaster than the speed c.

Because the speed of light provides us with an absolutestandard that can be measured accurately, we use thevalue of c to relate the definitions of time and distance.The meter is defined as the distance light travels in aninterval of 1/299,792.458 of a second. The length of asecond itself is provided by an atomic standard. It is thetime interval occupied by 9,192,631,770 vibrations ofa particular wavelength of light radiated by a cesiumatom.

Using the speed of light for conversion, clocks oftenmake good meter sticks, especially for measuringastronomical distances. It takes light 1.27 seconds totravel from the earth to the moon. We can thus say thatthe moon is 1.27 light seconds away. This is simplerthan saying that the moon is 1,250,000,000 feet or382,000 kilometers away. Light takes 8 minutes toreach us from the sun, thus the earth’s orbit about thesun has a radius of 8 light minutes. Radio signals,which also travel at the speed of light, took 2 1/2 hoursto reach the earth when Voyager II passed the planetUranus (temporarily the most distant planet). ThusUranus is 2 1/2 light hours away and our solar system

has a diameter of 5 light hours (not including the cloudof comets that lie out beyond the planets.)

The closest star, Proxima Centauri, is 4.2 light yearsaway. Light from this star, which started out when youentered college as a freshman, will arrive at the earthshortly after you graduate (assuming all goes well).Stars in our local area are typically 2 to 4 light yearsapart, except for the so called binary stars which arepairs of stars orbiting each other at distances as small aslight days or light hours.

On a still larger scale, we find that stars form islandstructures called galaxies. We live in a fairly typicalgalaxy called the Milky Way. It is a flat disk of starswith a slight bulge at the center much like the SombreroGalaxy seen edge on in Figure (1) and the neighboringspiral galaxy Andromeda seen in Figure (2). OurMilky Way is a spiral galaxy much like Andromeda,with the sun located about 2/3 of the way out in one ofthe spiral arms. If you look at the sky on a dark clearnight you can see the band of stars that cross the skycalled the Milky Way. Looking at these stars you arelooking sideways through the disk of the Milky Waygalaxy.

Figure 2The Andromeda galaxy.

Figure 1The Sombrero galaxy.

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Our galaxy and the closest similar galaxy, Androm-eda, are both about 100,000 light years (.1 million lightyears) in diameter, contain about a billion stars, and areabout one million light years apart. These are more orless typical numbers for the average size, populationand spacing of galaxies in the universe.

To look at the universe over still larger distances, firstimagine that you are aboard a rocket leaving the earthat night. As you leave the launch pad, you see theindividual lights around the launch pad and street lightsin neighboring roads. Higher up you start to see thelights from the neighboring city. Still higher you seethe lights from a number of cities and it becomes harderand harder to see individual street lights. A short whilelater all the bright spots you see are cities, and you canno longer see individual lights. At this altitude youcount cities instead of light bulbs.

Similarly on our trip out to larger and larger distancesin the universe, the bright spots are the galaxies for wecan no longer see the individual stars inside. Ondistances ranging from millions up to billions of lightyears, we see galaxies populating the universe. On thisscale they are small but not quite point like. Instru-ments like the Hubble telescope in space can viewstructure in the most distant galaxies, like those shownin Figure (3) .

The Expanding UniverseIn the 1920s, Edwin Hubble made the surprising dis-covery that, on average, the galaxies are all movingaway from us. The farther away a galaxy is, the fasterit is moving away. Hubble found a simple rule for thisrecession, a galaxy twice as far away is receding twiceas fast.

At first you might think that we are at the exact centerof the universe if the galaxies are all moving directlyaway from us. But that is not the case. Hubble’sdiscovery indicates that the universe is expandinguniformly. You can see how a uniform expansionworks by blowing up a balloon part way, and drawinga number of uniformly spaced dots on the balloon.Then pick any dot as your own dot, and watch it as youcontinue to blow the balloon up. You will see that theneighboring dots all move away from your dot, and youwill also observe Hubble’s rule that dots twice as faraway move away twice as fast.

Hubble’s discovery provided the first indication thatthere is a limit to how far away we can see things. Atdistances of about fourteen billion light years, therecessional speed approaches the speed of light. Re-cent photographs taken by the Hubble telescope showgalaxies receding at speeds in excess of 95% the speedof light, galaxies close to the edge of what we call thevisible universe.

The implications of Hubble’s rule are more dramatic ifyou imagine that you take a moving picture of theexpanding universe and then run the movie backwardin time. The rule that galaxies twice as far away arereceding twice as fast become the rule that galaxiestwice as far away are approaching you twice as fast. Amore distant galaxy, one at twice the distance butheading toward you at twice the speed, will get to youat the same time as a closer galaxy. In fact, all thegalaxies will reach you at the same instant of time.

Now run the movie forward from that instant of time,and you see all the galaxies flying apart from whatlooks like a single explosion. From Hubble’s law youcan figure that the explosion should have occurredabout fourteen billion years ago.

Figure 3Hubble photograph of the most distant galaxies.


Did such an explosion really happen, or are we simplymisreading the data? Is there some other way ofinterpreting the expansion without invoking such acataclysmic beginning? Various astronomers thoughtthere was. In their continuous creation theory theydeveloped a model of the universe that was bothunchanging and expanding at the same time. Thatsounds like an impossible trick because as the universeexpands and the galaxies move apart, the density ofmatter has to decrease. To keep the universe fromchanging, the model assumed that matter was beingcreated throughout space at just the right rate to keep theaverage density of matter constant.

With this theory one is faced with the question of whichis harder to accept—the picture of the universe startingin an explosion which was derisively called the BigBang, or the idea that matter is continuously beingcreated everywhere? To provide an explicit test of thecontinuous creation model, it was proposed that allmatter was created in the form of hydrogen atoms, andthat all the elements we see around us today, the carbon,oxygen, iron, uranium, etc., were made as a result ofnuclear reactions inside of stars.

To test this hypothesis, physicists studied in the labo-ratory those nuclear reactions which should be relevantto the synthesis of the elements. The results were quitesuccessful. They predicted the correct or nearly correctabundance of all the elements but one. The holdout washelium. There appeared to be more helium in theuniverse than they could explain.

By 1960, it was recognized that, to explain the abun-dance of the elements as a result of nuclear reactionsinside of stars, you have to start with a mixture ofhydrogen and helium. Where did the helium comefrom? Could it have been created in a Big Bang?

As early as 1948, the Russian physicist George Gamovstudied the consequences of the Big Bang model of theuniverse. He found that if the conditions in the earlyuniverse were just right, there should be light left overfrom the explosion, light that would now be a faint glowat radio wave frequencies. Gamov talked about thisprediction with several experimental physicists andwas told that the glow would be undetectable. Gamov’sprediction was more or less ignored until 1964 whenthe glow was accidently detected as noise in a radiotelescope. Satellites have now been used to study thisglow in detail, and the results leave little doubt aboutthe explosive nature of the birth of the universe.

What was the universe like at the beginning? In anattempt to find out, physicists have applied the laws ofphysics, as we have learned them here on earth, to thecollapsing universe seen in the time reversed motionpicture of the galaxies. One of the main features thatemerges as we go back in time and the universe getssmaller and smaller, is that it also becomes hotter andhotter. The obvious question in constructing a modelof the universe is how small and how hot do we allowit to get? Do we stop our model, stop our calculations,when the universe is down to the size of a galaxy? astar? a grapefruit? or a proton? Does it make any senseto apply the laws of physics to something as hot anddense as the universe condensed into something smallerthan, say, the size of a grapefruit? Surprisingly, it may.One of the frontiers of physics research is to test theapplication of the laws of physics to this model of thehot early universe.

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We will start our disruption of the early universe at atime when the universe was about a billionth of asecond old and the temperature was three hundredthousand billion ( 3×1014 ) degrees. While this soundslike a preposterously short time and unbelievably hightemperature, it is not the shortest time or highesttemperature that has been quite carefully considered.For our overview, we are arbitrarily choosing that timebecause of the series of pictures we can paint whichshow the universe evolving. These pictures all involvethe behavior of matter as it has been studied in thelaboratory. To go back earlier relies on theories that weare still formulating and trying to test.

To recognize what we see in this evolving picture of theuniverse, we first need a reasonably good picture ofwhat the matter around us is like. With an understand-ing of the building blocks of matter, we can watch thepieces fit together as the universe evolves. Our discus-sion of these building blocks will begin with atomswhich appear only late in the universe, and work downto smaller particles which play a role at earlier times.To understand what is happening, we also need apicture of how matter interacts via the basic forces innature.

When you look through a microscope and change themagnification, what you see and how you interpret it,changes, even though you are looking at the samesample. To get a preliminary idea of what matter ismade from and how it behaves, we will select aparticular sample and magnify it in stages. At eachstage we will provide a brief discussion to help interpretwhat we see. As we increase the magnification, theinterpretation of what we see changes to fit and toexplain the new picture. Surprisingly, when we getdown to the smallest scales of distance using thegreatest magnification, we see the entire universe at itsinfancy. We have reached the point where studyingmatter on the very smallest scale requires an under-standing of the very largest, and vice versa.

STRUCTURE OF MATTERWe will start our trip down to small scales with a ratherlarge, familiar example—the earth in orbit about thesun. The earth is attracted to the sun by a force calledgravity, and its motion can be accurately forecast, usinga set of rules called Newtonian mechanics. The basicconcepts involved in Newtonian mechanics are force,mass, velocity and acceleration, and the rules tell ushow these concepts are related. (Half of the traditionalintroductory physics courses is devoted to learningthese rules.)

AtomsWe will avoid much of the complexity we see aroundus by next focusing in on a single hydrogen atom. If weincrease the magnification so that a garden pea looks asbig as the earth, then one of the hydrogen atoms insidethe pea would be about the size of a basketball. Howwe interpret what we see inside the atom depends uponour previous experience with physics. With a back-ground in Newtonian mechanics, we would see aminiature solar system with the nucleus at the centerand an electron in orbit. The nucleus in hydrogenconsists of a single particle called the proton, and theelectron is held in orbit by an electric force. At thismagnification, the proton and electron are tiny points,too small to show any detail.

Figure 8-25aElliptical orbit of an earth satellite calculatedusing Newtonian mechanics.


There are similarities and striking differences betweenthe gravitational force that holds our solar systemtogether and the electric force that holds the hydrogenatom together. Both forces in these two examples areattractive, and both forces decrease as the square of thedistance between the particles. That means that if youdouble the separation, the force is only one quarter asstrong. The strength of the gravitational force dependson the mass of the objects, while the electric forcedepends upon the charge of the objects.

One of the major differences between electricity andgravity is that all gravitational forces are attractive,while there are both attractive and repulsive electricforces. To account for the two types of electric force,we say that there are two kinds of electric charge, whichBenjamin Franklin called positive charge and negativecharge. The rule is that like charges repel whileopposite charges attract. Since the electron and theproton have opposite charge they attract each other. Ifyou tried to put two electrons together, they would repelbecause they have like charges. You get the samerepulsion between two protons. By the accident ofBenjamin Franklin’s choice, protons are positivelycharged and electrons are negatively charged.

Another difference between the electric and gravita-tional forces is their strengths. If you compare theelectric to the gravitational force between the protonand electron in a hydrogen atom, you find that theelectric force is 2270000000000000000000000000000000000000 times stronger than the gravitationalforce. On an atomic scale, gravity is so weak that it isessentially undetectable.

On a large scale, gravity dominates because of thecancellation of electric forces. Consider, for example,the net electric force between two complete hydrogenatoms separated by some small distance. Call thematom A and atom B. Between these two atoms there arefour distinct forces, two attractive and two repulsive.The attractive forces are between the proton in atom Aand the electron in atom B, and between the electron inatom A and the proton in atom B. However, the two

protons repel each other and the electrons repel to givethe two repulsive forces. The net result is that theattractive and repulsive forces cancel and we end upwith essentially no electric force between the atoms.

Rather than counting individual forces, it is easier toadd up electric charge. Since a proton and an electronhave opposite charges, the total charge in a hydrogenatom adds up to zero. With no net charge on either ofthe two hydrogen atoms in our example, there is no netelectric force between them. We say that a completehydrogen atom is electrically neutral.

While complete hydrogen atoms are neutral, they canattract each other if you bring them too close together.What happens is that the electron orbits are distorted bythe presence of the neighboring atom, the electricforces no longer exactly cancel, and we are left with asmall residual force called a molecular force. It is themolecular force that can bind the two hydrogen atomstogether to form a hydrogen molecule. These molecu-lar forces are capable of building very complex objects,like people. We are the kind of structure that resultsfrom electric forces, in much the same way that solarsystems and galaxies are the kind of structures thatresult from gravitational forces.

Chemistry deals with reactions between about 100different elements, and each element is made out of adifferent kind of atom. The basic distinction betweenatoms of different elements is the number of protons inthe nucleus. A hydrogen nucleus has one proton, ahelium nucleus 2 protons, a lithium nucleus 3 protons,on up to the largest naturally occurring nucleus, ura-nium with 92 protons.

Complete atoms are electrically neutral, having asmany electrons orbiting outside as there are protons inthe nucleus. The chemical properties of an atom aredetermined almost exclusively by the structure of theorbiting electrons, and their electron structure dependsvery much on the number of electrons. For example,helium with 2 electrons is an inert gas often breathed bydeep sea divers. Lithium with 3 electrons is a reactivemetal that bursts into flame when exposed to air. Wego from an inert gas to a reactive metal by adding oneelectron.

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LightThe view of the hydrogen atom as a miniature solarsystem, a view of the atom seen through the “lens” ofNewtonian mechanics, fails to explain much of theatom’s behavior. When you heat hydrogen gas, itglows with a reddish glow that consists of three distinctcolors or so called spectral lines. The colors of the linesare bright red, swimming pool blue, and deep violet.You need more than Newtonian mechanics to under-stand why hydrogen emits light, let alone explain thesethree special colors.

In the middle of the 1800s, Michael Faraday went along way in explaining electric and magnetic phenom-ena in terms of electric and magnetic fields. Thesefields are essentially maps of electric and magneticforces. In 1860 James Clerk Maxwell discovered thatthe four equations governing the behavior of electricand magnetic fields could be combined to make upwhat is called a wave equation. Maxwell could con-struct his wave equation after making a small butcrucial correction to one of the underlying equations.

The importance of Maxwell’s wave equation was thatit predicted that a particular combination of electric andmagnetic fields could travel through space in a wave-like manner. Equally important was the fact that thewave equation allowed Maxwell to calculate what thespeed of the wave should be, and the answer was abouta billion feet per second. Since only light was knownto travel that fast, Maxwell made the guess that he haddiscovered the theory of light, that light consisted of awave of electric and magnetic fields of force.

Visible light is only a small part of what we call theelectromagnetic spectrum. Our eyes are sensitive tolight waves whose wavelength varies only over a verynarrow range. Shorter wavelengths lie in the ultravio-let or x ray region, while at increasingly longer wave-lengths are infra red light, microwaves, and radiowaves. Maxwell’s theory made it clear that these otherwavelengths should exist, and within a few years, radiowaves were discovered. The broadcast industry is nowdependent on Maxwell’s equations for the design ofradio and television transmitters and receivers.(Maxwell’s theory is what is usually taught in thesecond half of an introductory physics course. Thatgets you all the way up to 1860.)

While Maxwell’s theory works well for the design ofradio antennas, it does not do well in explaining thebehavior of a hydrogen atom. When we applyMaxwell’s theory to the miniature solar system modelof hydrogen, we do predict that the orbiting electronwill radiate light. But we also predict that the atom willself destruct. The unambiguous prediction is that theelectron will continue to radiate light of shorter andshorter wavelength while spiraling in faster and fastertoward the nucleus, until it crashes. The combinationof Newton’s laws and Maxwell’s theory is known asClassical Physics. We can easily see that classicalphysics fails when applied even to the simplest ofatoms.

infrared rays

10110 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -126 5 4 3 210

X-rays

wavelength, cm

lightvisible ultraviolet

raysradio, television, radar gamma rays

Figure 32-24The electromagnetic spectrum.


PhotonsIn the late 1890’s, it was discovered that a beam of lightcould knock electrons out of a hydrogen atom. Thephenomenon became known as the photoelectric ef-fect. You can use Maxwell’s theory to get a rough ideaof why a wave of electric and magnetic force might beable to pull electrons out of a surface, but the details allcome out wrong. In 1905, in the same year that hedeveloped his theory of relativity, Einstein explainedthe photoelectric effect by proposing that light con-sisted of a beam of particles we now call photons.When a metal surface is struck by a beam of photons,an electron can be knocked out of the surface if it isstruck by an individual photon. A simple formula forthe energy of the photons led to an accurate explanationof all the experimental results related to the photoelec-tric effect.

Despite its success in explaining the photoelectriceffect, Einstein’s photon picture of light was in conflictnot only with Maxwell’s theory, it conflicted with over100 years of experiments which had conclusivelydemonstrated that light was a wave. This conflict wasnot to be resolved in any satisfactory way until themiddle 1920s.

The particle nature of light helps but does not solve theproblems we have encountered in understanding thebehavior of the electron in hydrogen. According toEinstein’s photoelectric formula, the energy of a pho-ton is inversely proportional to its wavelength. Thelonger wavelength red photons have less energy thanthe shorter wavelength blue ones. To explain thespecial colors of light emitted by hydrogen, we have tobe able to explain why only photons with very specialenergies can be emitted.

The Bohr ModelIn 1913, the year after the nucleus was discovered,Neils Bohr developed a somewhat ad hoc model thatworked surprisingly well in explaining hydrogen. Bohrassumed that the electron in hydrogen could travel ononly certain allowed orbits. There was a smallest,lowest energy orbit that is occupied by an electron incool hydrogen atoms. The fact that this was thesmallest allowed orbit meant that the electron wouldnot spiral in and crush into the nucleus.

Using Maxwell’s theory, one views the electron asradiating light continuously as it goes around the orbit.In Bohr’s picture the electron does not radiate while inone of the allowed orbits. Instead it radiates, it emits aphoton, only when it jumps from one orbit to another.

To see why heated hydrogen radiates light, we need apicture of thermal energy. A gas, like a bottle ofhydrogen or the air around us, consists of moleculesflying around, bouncing into each other. Any movingobject has extra energy due to its motion. If all the partsof the object are moving together, like a car travelingdown the highway, then we call this energy of motionkinetic energy. If the motion is the random motion ofmolecules bouncing into each other, we call it thermalenergy.

The temperature of a gas is proportional to the averagethermal energy of the gas molecules. As you heat a gas,the molecules move faster, and their average thermal

Lyman seriesBalm

er series

Paschen

series

r2

r1

r3

Figure 35-6The allowed orbits of the Bohr Model.

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energy and temperature rises. At the increased speedthe collisions between molecules are also stronger.

Consider what happens if we heat a bottle of hydrogengas. At room temperature, before we start heating, theelectrons in all the atoms are sitting in their lowestenergy orbits. Even at this temperature the atoms arecolliding but the energy involved in a room tempera-ture collision is not great enough to knock an electroninto one of the higher energy orbits. As a result, roomtemperature hydrogen does not emit light.

When you heat the hydrogen, the collisions betweenatoms become stronger. Finally you reach a tempera-ture in which enough energy is involved in a collisionto knock an electron into one of the higher energyorbits. The electron then falls back down, from oneallowed orbit to another until it reaches the bottom,lowest energy orbit. The energy that the electron losesin each fall, is carried out by a photon. Since there areonly certain allowed orbits, there are only certainspecial amounts of energy that the photon can carry out.

To get a better feeling for how the model works,suppose we number the orbits, starting at orbit 1 for thelowest energy orbit, orbit 2 for the next lowest energyorbit, etc. Then it turns out that the photons in the redspectral line are radiated when the electron falls fromorbit 3 to orbit 2. The red photon’s energy is just equalto the energy the electron loses in falling between theseorbits. The more energetic blue photons carry out theenergy an electron loses in falling from orbit 4 to orbit2, and the still more energetic violet photons corre-spond to a fall from orbit 5 to orbit 2. All the other jumpsgive rise to photons whose energy is too large or toosmall to be visible. Those with too much energy areultraviolet photons, while those with too little are in theinfra red part of the spectrum. The jump down to orbit1 is the biggest jump with the result that all jumps downto the lowest energy orbit results in ultraviolet photons.

It appears rather ad hoc to propose a theory where youinvent a large number of special orbits to explain whatwe now know as a large number of spectral lines. Onecriterion for a successful theory in science is that youget more out of the theory than you put in. If Bohr hadto invent a new allowed orbit for each spectral lineexplained, the theory would be essentially worthless.

However this is not the case for the Bohr model. Bohrfound a simple formula for the electron energies of allthe allowed orbits. This one formula in a sense explainsthe many spectral lines of hydrogen. A lot more cameout of Bohr’s model than Bohr had to put in.

The problem with Bohr’s model is that it is essentiallybased on Newtonian mechanics, but there is no excusewhatsoever in Newtonian mechanics for identifyingany orbit as special. Bohr focused the problem bydiscovering that the allowed orbits had special valuesof a quantity called angular momentum.

Angular momentum is related to rotational motion, andin Newtonian mechanics angular momentum increasescontinuously and smoothly as you start to spin anobject. Bohr could explain his allowed orbits byproposing that there was a special unique value ofangular momentum—call it a unit of angular momen-tum. Bohr found, using standard Newtonian calcula-tions, that his lowest energy orbit had one unit ofangular momentum, orbit 2 had two units, orbit 3 threeunits, etc. Bohr could explain his entire model by theone assumption that angular momentum was quan-tized, i.e., came only in units.

Bohr’s quantization of angular momentum is counterintuitive, for it leads to the picture that when we start torotate an object, the rotation increases in a jerky fashionrather than continuously. First the object has noangular momentum, then one unit, then 2 units, and onup. The reason we do not see this jerky motion whenwe start to rotate something large like a bicycle wheel,is that the basic unit of angular momentum is verysmall. We cannot detect the individual steps in angularmomentum, it seems continuous. But on the scale of anatom, the steps are big and have a profound effect.

With Bohr’s theory of hydrogen and Einstein’s theoryof the photoelectric effect, it was clear that classicalphysics was in deep trouble. Einstein’s photons gavea lumpiness to what should have been a smooth wavein Maxwell’s theory of light and Bohr’s model gave ajerkiness to what should be a smooth change in angularmomentum. The bumps and jerkiness needed a newpicture of the way matter behaves, a picture that wasintroduced in 1924 by the graduate student Louis deBroglie.


PARTICLE-WAVE NATURE OFMATTERNoting the wave and particle nature of light,de Broglie proposed that the electron had both a waveand a particle nature. While electrons had clearlyexhibited a particle behavior in various experiments, deBroglie suggested that it was the wave nature of theelectron that was responsible for the special allowedorbits in Bohr’s theory. De Broglie presented a simplewave picture where, in the allowed orbits, an integernumber of wavelengths fit around the orbit. Orbit 1 hadone wavelength, orbit 2 had two wavelengths, etc. InDe Broglie’s picture, electron waves in non allowedorbits would cancel themselves out. Borrowing somefeatures of Einstein’s photon theory of light waves, deBroglie could show that the angular momentum of theelectron would have the special quantized values whenthe electron wave was in one of the special, noncancelling orbits.

With his simple wave picture, de Broglie had hit uponthe fundamental idea that was missing in classicalphysics. The idea is that all matter, not just light, hasa particle wave nature.

It took a few years to gain a satisfactory interpretationof the dual particle wave nature of matter. The currentinterpretation is that things like photons are in factparticles, but their motion is governed, not by Newto-nian mechanics, but by the laws of wave motion. How

this works in detail is the subject of our chapter onQuantum Mechanics. One fundamental requirementof our modern interpretation of the particle wave is that,for the interpretation to be meaningful, all forms ofmatter, without exception, must have this particle wavenature. This general requirement is summarized by arule discovered by Werner Heisinberg, a rule known asthe uncertainty principle. How the rule got that nameis also discussed in our chapter on quantum mechanics.

In 1925, after giving a seminar describing de Broglie’smodel of electron waves in hydrogen, ErwinSchrödinger was chided for presenting such a “child-ish” model. A colleague reminded him that waves donot work that way, and suggested that since Schrödingerhad nothing better to do, he should work out a real waveequation for the electron waves, and present the resultsin a couple of weeks.

It took Schrödinger longer than a couple of weeks, buthe did succeed in constructing a wave equation for theelectron. In many ways Schrödinger’s wave equationfor the electron is analogous to Maxwell’s wave equa-tion for light. Schrödinger’s wave equation for theelectron allows one to calculate the behavior of elec-trons in all kinds of atoms. It allows one to explain andpredict an atom’s electron structure and chemicalproperties. Schrödinger’s equation has become thefundamental equation of chemistry.

r

Figure 35-9De Broglie picture of an electronwave cancelling itself out.

Figure 35-10If the circumference of the orbit is an integernumber of wavelengths, the electron wave will goaround without any cancellation.

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CONSERVATION OF ENERGYBefore we go on with our investigation of the hydrogenatom, we will take a short break to discuss the idea ofconservation of energy. This idea, which originated inNewtonian mechanics, survives more or less intact inour modern particle-wave picture of matter.

Physicists pay attention to the concept of energy onlybecause energy is conserved. If energy disappearsfrom one place, it will show up in another. We saw thisin the Bohr model of hydrogen. When the electron lostenergy falling down from one allowed orbit to a lowerenergy orbit, the energy lost by the electron was carriedout by a photon.

You can store energy in an object by doing work on theobject. When you lift a ball off the floor, for example,the work you did lifting the ball, the energy yousupplied, is stored in a form we call gravitationalpotential energy. Let go of the ball and it falls to thefloor, loosing its gravitational potential energy. Butjust before it hits the floor, it has a lot of energy ofmotion, what we have called kinetic energy. All thegravitational potential energy the ball had before wedropped it has been converted to kinetic energy.

After the ball hits the floor and is finally resting there,it is hard to see where the energy has gone. One placeit has gone is into thermal energy, the floor and the ballare a tiny bit warmer as a result of your dropping theball.

Another way to store energy is to compress a spring.When you release the spring you can get the energyback. For example, compress a watch spring bywinding up the watch, and the energy released as thespring unwinds will run the watch for a day. We couldcall the energy stored in the compressed spring springpotential energy. Physicists invent all sorts of namesfor the various forms of energy.

One of the big surprises in physics was Einstein’sdiscovery of the equivalence of mass and energy, arelationship expressed by the famous equation

E = mc2 . In that equation, E stands for the energy ofan object, m its mass, and c is the speed of light. Sincethe factor c2 is a constant, Einstein’s equation isbasically saying that mass is a form of energy. The c2

is there because mass and energy were initially thoughtto be different quantities with different units like kilo-grams and joules. The c2 simply converts mass unitsinto energy units.

What is amazing is the amount of energy that is in theform of mass. If you could convert all the mass of apencil eraser into electrical energy, and sell the electri-cal energy at the going rate of 10¢ per kilowatt hour,you would get about 10 million dollars for it. Theproblem is converting the mass to another, more useful,form of energy. If you can do the conversion, however,the results can be spectacular or terrible. Atomic andhydrogen bombs get their power from the conversionof a small fraction of their mass energy into thermalenergy. The sun gets its energy by “burning” hydrogennuclei to form helium nuclei. The energy comes fromthe fact that a helium nucleus has slightly less mass thanthe hydrogen nuclei out of which it was formed.

If you have a particle at rest and start it moving, theparticle gains kinetic energy. In Einstein’s view theparticle at rest has energy due to its rest mass. Whenyou start the particle moving, it gains energy, and sincemass is equivalent to energy, it also gains mass. Formost familiar speeds the increase in mass due to kineticenergy is very small. Even at the speeds travelled byrockets and spacecraft, the increase in mass due tokinetic energy is hardly noticeable. Only when aparticle’s speed gets up near the speed of light does theincrease in mass become significant.


One of the first things we discussed about the behaviorof matter is that nothing can travel faster than the speedof light. You might have wondered if nature had trafficcops to enforce this speed limit. It does not need one,it uses a law of nature instead. As the speed of an objectapproaches the speed of light, its mass increases. Thecloser to the speed of light, the greater increase in mass.To push a particle up to the speed of light would giveit an infinite mass and therefore require an infiniteamount of energy. Since that much energy is notavailable, no particle is going to exceed nature’s speedlimit.

This raises one question. What about photons? Theyare particles of light and therefore travel at the speed oflight. But their energy is not infinite. It depends insteadon the wavelength or color of the photon. Photonsescape the rule about mass increasing with speed bystarting out with no rest mass. You stop a photon andnothing is left. Photons can only exist by traveling atthe speed of light.

When a particle is traveling at speeds close enough tothe speed of light that its kinetic energy approaches itsrest mass energy, the particle behaves differently thanslowly moving particles. For example, push on aslowly moving particle and you can make the particlemove faster. Push on a particle already moving atnearly the speed of light, and you merely make theparticle more massive since it cannot move faster.Since the relationship between mass and energy cameout of Einstein’s theory of relativity, we say thatparticles moving near the speed of light obey relativis-tic mechanics while those moving slowly are nonrela-tivistic. Light is always relativistic, and all automobileson the earth are nonrelativistic.

ANTI-MATTERSchrödinger’s equation for electron waves is a nonrela-tivistic theory. It accurately describes electrons that aremoving at speeds small compared to the speed of light.This is fine for most studies in chemistry, wherechemical energies are much much less than rest massenergies. You can see the difference for example bycomparing the energy released by a conventional chemi-cal bomb and an atomic bomb.

Schrödinger of course knew Einstein’s theory of rela-tivity, and initially set out to derive a relativistic waveequation for the electron. This would be an equationthat would correctly explain the behavior of electronseven as the speed of the electrons approached the speedof light and their kinetic energy became comparable toor even exceeded their rest mass energy.

Schrödinger did construct a relativistic wave equation.The problem was that the equation had two solutions,one representing ordinary electrons, the other an appar-ently impossible particle with a negative rest mass. Inphysics and mathematics we are often faced withequations with two or more solutions. For example, theformula for the hypotenuse c of a right triangle withsides of lengths a and b is

c2 = a2 + b2

This equation has two solutions, namely c = + a2 + b2 and c = – a2 + b2 . The negative

solution does not give us much of a problem, we simplyignore it.

Schrödinger could not ignore the negative mass solu-tions in his relativistic wave equation for the followingreason. If he started with just ordinary positive masselectrons and let them interact, the equation predictedthat the negative mass solutions would be created! Thepeculiar solutions could not be ignored if the equationwas to be believed. Only by going to his nonrelativisticequation could Schrödinger avoid the peculiar solu-tions.

a

bc

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A couple years later, Dirac tried again to develop arelativistic wave equation for the electron. At first itappeared that Dirac’s equation would avoid the nega-tive mass solutions, but with little further work, Diracfound that the negative mass solutions were still there.Rather than giving up on his new equation, Dirac founda new interpretation of these peculiar solutions. Insteadof viewing them as negatively charged electrons witha negative mass, he could interpret them as positivemass particles with a positive electric charge. Accord-ing to Dirac’s equation, positive and negative chargedsolutions could be created or destroyed in pairs. Thepairs could be created any time enough energy wasavailable.

Dirac predicted the existence of this positively chargedparticle in 1929. It was not until 1933 that CarlAnderson at Caltech, who was studying the elementaryparticles that showered down from the sky (particlescalled cosmic rays), observed a positively chargedparticle whose mass was the same as that of theelectron. Named the positron, this particle was imme-diately identified as the positive particle expected fromDirac’s equation.

In our current view of matter, all particles are describedby relativistic wave equations, and all relativistic waveequations have two kinds of solutions. One solution isfor ordinary matter particles like electrons, protons,and neutrons. The other solution, which we now callantimatter, describes anti particles, the antielectronwhich is the positron, and the antiproton and theantineutron. Since all antiparticles can be created ordestroyed in particle-anti particle pairs, the antiparticlehas to have the opposite conserved property so that theproperty will remain conserved. As an example, thepositron has the opposite charge as the electron so thatelectric charge is neither created or destroyed whenelectron-positron pairs appear or disappear.

While all particles have antiparticles, some particleslike the photon, have no conserved properties otherthan energy. As a result, these particles are indistin-guishable from their antiparticles.

PARTICLE NATURE OF FORCESDe Broglie got his idea for the wave nature of theelectron from the particle-wave nature of light. Theparticle of light is the photon which can knock electronsout of a metal surface. The wave nature is the wave ofelectric and magnetic force that was predicted byMaxwell’s theory. When you combine these twoaspects of light, you are led to the conclusion thatelectric and magnetic forces are ultimately caused byphotons. We call any force resulting from electric ormagnetic forces as being due to the electric interaction.The photon is the particle responsible for the electricinteraction.

Let us see how our picture of the hydrogen atom hasevolved as we have learned more about the particlesand forces involved. We started with a miniature solarsystem with the heavy proton at the center and anelectron in orbit. The force was the electric force thatin many ways resembled the gravitational force thatkeeps the earth in orbit around the sun. This picturefailed, however, when we tried to explain the lightradiated by heated hydrogen.

The next real improvement comes with Schrödinger’swave equation describing the behavior of the electronin hydrogen. Rather than there being allowed orbits asin Bohr’s model, the electron in Schrödinger’s picturehas allowed standing wave patterns. The chemicalproperties of atoms can be deduced from these wavepatterns, and Schrödinger’s equation leads to accuratepredictions of the wavelengths of light radiated notonly by hydrogen but other atoms as well.

There are two limitations to Schrödinger’s equation.One of the limitations we have seen is that it is a nonrelativistic equation, an equation that neglects anychange in the electron’s mass due to motion. While thisis a very good approximation for describing the slowspeed electron in hydrogen, the wavelengths of lightradiated by hydrogen can be measured so accuratelythat tiny relativistic effects can be seen. Dirac’s relativ-istic wave equation is required to explain these tinyrelativistic corrections.


The second limitation is that neither Schrödinger’s orDirac’s equations take into account the particle natureof the electric force holding hydrogen together. In thehydrogen atom, the particle nature of the electric forcehas only the very tiniest effect on the wavelength of theradiated light. But even these effects can be measuredand the particle nature must be taken into account. Thetheory that takes into account both the wave nature ofthe electron and the particle nature of the electric forceis called quantum electrodynamics, a theory finallydeveloped in 1947 by Richard Feynman and JulianSchwinger. Quantum electrodynamics is the mostprecisely tested theory in all of science.

In our current picture of the hydrogen atom, as de-scribed by quantum electrodynamics, the force be-tween the electron and the proton nucleus is caused bythe continual exchange of photons between the twocharged particles. While being exchanged, the photoncan do some subtle things like create a positron electronpair which quickly annihilates. These subtle thingshave tiny but measurable effects on the radiated wave-lengths, effects that correctly predicted by the theory.

The development of quantum electrodynamics camenearly 20 years after Dirac’s equation because ofcertain mathematical problems the theory had to over-come. In this theory, the electron is treated as a pointparticle with no size. The accuracy of the predictionsof quantum electrodynamics is our best evidence thatthis is the correct picture. In other words, we have noevidence that the electron has a finite size, and a veryaccurate theory which assumes that it does not. How-ever, it is not easy to construct a mathematical theory inwhich a finite amount of mass and energy is crammedinto a region of no size. For one thing you are lookingat infinite densities of mass and energy.

RenormalizationThe early attempts to construct the theory of quantumelectrodynamics were plagued by infinities. Whatwould happen is that you would do an initial approxi-mate calculation and the results would be good. Youwould then try to improve the results by calculatingwhat were supposed to be tiny corrections, and thecorrections turned out to be infinitely large. One of themain accomplishments of Feynman and Schwingerwas to develop a mathematical procedure, sort of amathematical slight of hand, that got rid of the infini-ties. This mathematical procedure became known asrenormalization.

Feynman always felt that renormalization was simplya trick to cover up our ignorance of a deeper moreaccurate picture of the electron. I can still hear himsaying this during several seminars. It turned outhowever that renormalization became an importantguide in developing theories of other forces. We willshortly encounter two new forces as we look down intothe atomic nucleus, forces called the nuclear interac-tion and the weak interaction. Both of these forceshave a particle-wave nature like the electric interaction,and the successful theories of these forces usedrenormalization as a guide.

Figure 8-33Einstein’s theory of gravity predicted that Mercury’selliptical orbit “precessed” or rotated somewhat like therotation seen in the above orbit. Mercury’s precessionis much, much smaller.

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GravityThe one holdout, the one force for which we do nothave a successful theory, is gravity. We have come along way since Newton’s law of gravity. After Einsteindeveloped his theory of relativity in 1905, he spent thenext 12 years working on a relativistic theory ofgravity. The result, known as general relativity, is atheory of gravity that is in many ways similar toMaxwell’s theory of electricity. Einstein’s theorypredicts, for example, that a planet in orbit about a starshould emit gravitational waves in much the same waythat Maxwell’s theory predicts that an electron in orbitabout a nucleus should emit electromagnetic radiationor light.

One of the difficulties working with Einstein’s theoryof gravity is that Newton’s theory of gravity explainsalmost everything we see, and you have to look veryhard in places where Newton’s law is wrong andEinstein’s theory is right. There is an extremely smallbut measurable correction to the orbit of Mercury thatNewton’s theory cannot explain and Einstein’s theorydoes.

Einstein’s theory also correctly predicts how muchlight will be deflected by the gravitational attraction ofa star. You can argue that because light has energy andenergy is equivalent to mass, Newton’s law of gravityshould also predict that starlight should be deflected bythe gravitational pull of a star. But this Newtonianargument leads to half the deflection predicted byEinstein’s theory, and the deflection predicted by Ein-stein is observed.

The gravitational radiation predicted by Einstein’stheory has not been detected directly, but we have verygood evidence for its existence. In 1974 Joe Taylorfrom the University of Massachusetts, working at thelarge radio telescope at Arecibo discovered a pair ofneutron stars in close orbit about each other. We willhave more to say about neutron stars later. The point isthat the period of the orbit of these stars can bemeasured with extreme precision.

Einstein’s theory predicts that the orbiting stars shouldradiate gravitational waves and spiral in toward eachother. This is reminiscent of what we got by applyingMaxwell’s theory to the electron in hydrogen, but in thecase of the pair of neutron stars the theory worked. Theperiod of the orbit of these stars is changing in exactlythe way one would expect if the stars were radiatinggravitational waves.

If our wave-particle picture of the behavior of matter iscorrect, then the gravitational waves must have aparticle nature like electromagnetic waves. Physicistscall the gravitational particle the graviton. We think weknow a lot about the graviton even though we have notyet seen one. The graviton should, like the photon,have no rest mass, travel at the speed of light, and havethe same relationship between energy and wavelength.

One difference is that because the graviton has energyand therefore mass, and because gravitons interact withmass, gravitons interact with themselves. This selfinteraction significantly complicates the theory of grav-ity. In contrast photons interact with electric charge,but photons themselves do not carry charge. As aresult, photons do not interact with each other whichconsiderably simplifies the theory of the electric inter-action.

An important difference between the graviton and thephoton, what has prevented the graviton from beingdetected, is its fantastically weak interaction with mat-ter. You saw that the gravitational force between theelectron and a proton is a thousand billion billion billionbillion times weaker than the electric force. In effectthis makes the graviton a thousand billion billionbillion billion times harder to detect. The only reasonwe know that this very weak force exists at all is that itgets stronger and stronger as we put more and moremass together, to form large objects like planets andstars.


Not only do we have problems thinking of a way todetect gravitons, we have run into a surprising amountof difficulty constructing a theory of gravitons. Thetheory would be known as the quantum theory ofgravity, but we do not yet have a quantum theory ofgravity. The problem is that the theory of gravitonsinteracting with point particles, the gravitational anal-ogy of quantum electrodynamics, does not work. Thetheory is not renormalizable, you cannot get rid of theinfinities. As in the case of the electric interaction thesimple calculations work well, and that is why we thinkwe know a lot about the graviton. But when you try tomake what should be tiny relativistic corrections, thecorrection turns out to be infinite. No mathematicalslight of hand has gotten rid of the infinities.

The failure to construct a consistent quantum theory ofgravity interacting with point particles has suggested tosome theoretical physicists that our picture of theelectron and some other particles being point particlesis wrong. In a new approach called string theory, theelementary particles are view not as point particles butinstead as incredibly small one dimensional objectscalled strings. The strings vibrate, with differentmodes of vibration corresponding to different elemen-tary particles.

String theory is complex. For example, the strings existin a world of 10 dimensions, whereas we live in a worldof 4 dimensions. To make string theory work, you haveto explain what happened to the other six dimensions.

Another problem with string theory is that it has not ledto any predictions that distinguish it from other theo-ries. There are as yet no tests, like the deflection ofstarlight by the sun, to demonstrate that string theory isright and other theories are wrong.

String theory does, however, have one thing going forit. By spreading the elementary particles out from zerodimensions (points) to one dimensional objects (strings),the infinities in the theory of gravity can be avoided.

A SUMMARYUp to this point our focus has been on the hydrogenatom. The physical magnification has not been toogreat, we are still picturing the atom as an objectmagnified to the size of a basketball with two particles,the electron and proton, that are too small to see. Theymay or may not have some size, but we cannot tell atthis scale.

What we have done is change our perception of theatom. We started with a picture that Newton wouldrecognize, of a small solar system with the massiveproton at the center and the lighter electron held in orbitby the electric force. When we modernize the pictureby including Maxwell’s theory of electricity and mag-netism, we run into trouble. We end up predicting thatthe electron will lose energy by radiating light, sooncrashing into the proton. Bohr salvaged the picture byintroducing his allowed orbits and quantized angularmomentum, but the success of Bohr’s theory onlystrengthened the conviction that something was funda-mentally wrong with classical physics.

Louis de Broglie pointed the way to a new picture of thebehavior of matter by proposing that all matter, not justlight, had a particle-wave nature. Building on deBroglie’s idea, Schrödinger developed a wave equa-tion that not only describes the behavior of the electronin hydrogen, but in larger and more complex atoms aswell.

While Schrödinger’s non relativistic wave equationadequately explains most classical phenomena, even inthe hydrogen atom, there are tiny but observable rela-tivistic effects that Dirac could explain with his relativ-istic wave equation for the electron. Dirac handled theproblem of all relativistic wave equations having twosolutions by reinterpreting the second solution as rep-resenting antimatter.

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Dirac’s equation is still not the final theory for hydro-gen because it does not take into account the fact thatelectric forces are ultimately caused by photons. Thewave theory of the electron that takes the photon natureof the electric force into account is known as quantumelectrodynamics. The predictions of quantum electro-dynamics are in complete agreement with experiment,it is the most precisely tested theory in science.

The problems resulting from treating the electron as apoint particle were handled in quantum electrodynam-ics by renormalization. Renormalization does notwork, however, when one tries to formulate a quantumtheory of gravity where the gravitational force par-ticle—the graviton—interacts with point particles. Thishas led some theorists to picture the electron not as apoint but as an incredibly small one dimensional objectcalled a string. While string theory is renormalizable,there have been no experimental tests to show thatstring theory is right and the point particle picture iswrong. This is as far as we can take our picture of thehydrogen atom without taking a closer look at thenucleus.

THE NUCLEUSTo see the nucleus we have to magnify our hydrogenatom to a size much larger than a basketball. When theatom is enlarged so that it would just fill a footballstadium, the nucleus, the single proton, would be aboutthe size of a pencil eraser. The proton is clearly not apoint particle like the electron. If we enlarge the atomfurther to get a better view of the nucleus, to the pointwhere the proton looks as big as a grapefruit, the atomis about 10 kilometers in diameter. This grapefruitsized object weighs 1836 times as much as the electron,but it is the electron wave that occupies the 10 kilometersphere of space surrounding the proton.

Before we look inside the proton, let us take a brief lookat the nuclei of some other atoms. Once in a great whileyou will find a hydrogen nucleus with two particles.One is a proton and the other is the electrically neutralparticles called the neutron. Aside from the electriccharge, the proton and neutron look very similar. Theyare about the same size and about the same mass. Theneutron is a fraction of a percent heavier than theproton, a small mass difference that will turn out to havesome interesting consequences.

As we mentioned, the type of element is determined bythe number of protons in the nucleus. All hydrogenatoms have one proton, all helium atoms 2 protons, etc.But for the same element there can be different num-bers of neutrons in the nucleus. Atoms with the samenumbers of protons but different numbers of neutronsare called different isotopes of the element. Anotherisotope of hydrogen, one that is unstable and decays inroughly 10 years, is a nucleus with one proton and twoneutrons called tritium.

The most stable isotope of helium is helium 4, with 2protons and 2 neutrons. Helium 3 with 2 protons andone neutron is stable but very rare. Once we get beyondhydrogen we name the different isotopes by adding anumber after the name, a number representing the totalnumber of protons and neutrons. For example theheaviest, naturally occurring atom is the isotope Ura-nium 238, which has 92 protons and 146 neutrons fora total of 238 nuclear particles, or nucleons as wesometimes refer to them.

Hydrogen-2(Deuterium)

Hydrogen-1

Hydrogen-3 (Tritium)

p

p

p

n

n nHelium-4

Helium-3

p

p

n

n

pn

p

Figure 19-2Isotopes of hydrogen and helium.


The nucleons in a nucleus pack together much like thegrapes in a bunch, or like a bag of grapefruit. At ourenlargement where a proton looks as big as a grapefruit,the uranium nucleus would be just over half a meter indiameter, just big enough to hold 238 grapefruit.

When you look at a uranium nucleus with its 92positively charged protons mixed in with electricallyneutral neutrons, then you have to wonder, what holdsthe thing together? The protons, being all positivelycharged, all repel each other. And because they are soclose together in the nucleus, the repulsion is extremelystrong. It is much stronger than the attractive force feltby the distant negative electrons. There must beanother kind of force, and attractive force, that keepsthe protons from flying apart.

The attractive force is not gravity. Gravity is so weakthat it is virtually undetectable on an atomic scale. Theattractive force that overpowers the electric repulsion iscalled the nuclear force. The nuclear force betweennucleons is attractive, and essentially blind to thedifference between a proton and a neutron. To thenuclear force, a proton and a neutron look the same.The nuclear force has no effect whatsoever on anelectron.

One of the important features of the nuclear forcebetween nucleons is that it has a short range. Comparedto the longer range electric force, the nuclear force ismore like a contact cement. When two protons are nextto each other, the attractive nuclear force is strongerthan the electric repulsion. But separate the protons bymore than about 4 protons diameters and the electricforce is stronger.

If you make nuclei by adding nucleons to a smallnucleus, the object becomes more and more stablebecause all the nucleons are attracting each other. Butwhen you get to nuclei whose diameter exceeds around4 proton diameters, protons on opposite sides of thenucleus start to repel each other. As a result nucleilarger than that become less stable as you make thembigger. The isotope Iron 56 with 26 protons and 30neutrons, is about 4 proton diameters across and is themost stable of all nuclei. When you reach Uraniumwhich is about 6 proton diameters across, the nucleushas become so unstable that if you jostle it by hitting itwith a proton, it will break apart into two roughly equalsized more stable nuclei. Once apart, the smaller nucleirepel each other electrically and fly apart releasingelectric potential energy. This process is called nuclearfission and is the source of energy in an atomic bomb.

While energy is released when you break apart thelarge unstable nuclei, energy is also released when youadd nucleons to build up the smaller, more stablenuclei. For example, if you start with four protons (fourhydrogen nuclei), turn two of the protons into neutrons(we will see how to do this shortly) and put themtogether to form stable helium 4 nucleus, you get aconsiderable release of energy. You can easily figureout how much energy is released by noting that 4protons have a mass that is about .7 percent greater thana helium nucleus. As a result when the protonscombine to form helium, about .7 percent of their massis converted to other forms of energy. Our sun ispowered by this energy release as it “burns” hydrogento form helium. This process is called nuclear fusionand is the source of the energy of the powerful hydro-gen bombs.

Figure 19-1Styrofoam ball model of the uranium nucleus..

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STELLAR EVOLUTIONOur sun is about half way through burning up thehydrogen in its hot, inner core. When the hydrogen isexhausted in another 5 billion years, the sun willinitially cool and start to collapse. But the collapse willrelease gravitational potential energy that makes thesmaller sun even hotter than it was before running outof hydrogen. The hotter core will emit so much lightthat the pressure of the light will expand the surface ofthe sun out beyond the earth’s orbit, and the sun willbecome what is known as a red giant star. Soon, overthe astronomically short time of a few million years, thestar will cool off becoming a dying, dark ember aboutthe size of the earth. It will become what is known asa black dwarf.

If the sun had been more massive when the hydrogenran out and the star started to collapse, then moregravitational potential energy would have been re-leased. The core would have become hotter, hot enoughto ignite the helium to form the heavier nucleus carbon.Higher temperatures are required to burn helium be-cause the helium nuclei, with two protons, repel eachother with four times the electric repulsion than hydro-gen nuclei. As a result more thermal energy is requiredto slam the helium nuclei close enough for the attractivenuclear force to take over.

Once the helium is burned up, the star again starts tocool and contract, releasing more gravitational poten-tial energy until it becomes hot enough to burn thecarbon to form oxygen nuclei. This cycle keepsrepeating, forming one element after another until weget to Iron 56. When you have an iron core and the starstarts to collapse and gets hotter, the iron does not burn.You do not get a release of energy by making nucleilarger than iron. As a result the collapse continuesresulting in a huge implosion.

Once the center collapses, a strong shock wave racesout through the outer layers of the star, tearing the starapart. This is called a supernova explosion. It is inthese supernova explosions with their extremely hightemperatures that nuclei larger than iron are formed.All the elements inside of you that are down theperiodic table from iron were created in a supernova.Part of you has already been through a supernovaexplosion.

What is left behind of the core of the star depends onhow massive the star was to begin with. If what remainsof the core is 1.4 times as massive as our sun, then thegravitational force will be strong enough to cram theelectrons into the nuclei, turning all the protons intoneutrons, and leaving behind a ball of neutrons about20 kilometers in diameter. This is called a neutron star.A neutron star is essentially a gigantic nucleus heldtogether by gravity instead of the nuclear force.

If you think that squeezing the mass of a star into a ball20 kilometers in diameter is hard to picture (at thisdensity all the people on the earth would fit into thevolume of a raindrop), then consider what happens ifthe remaining core is about six times as massive as thesun. With such mass, the gravitational force is so strongthat the neutrons are crushed and the star becomessmaller and smaller.

The matter in a neutron star is about as rigid as mattercan get. The more rigid a substance is, the faster soundwaves travel through the substance. For example,sound travels considerably faster through steel than air.The matter in a neutron star is so rigid, or shall we sayso incompressible, that the speed of sound approachesthe speed of light.

Figure 41987 supernova as seen by the Hubble telescope.


When gravity has crushed the neutrons in a neutronstar, it has overcome the strongest resistance anyknown force can possibly resist. But, as the collapsecontinues, gravity keeps getting stronger. Accordingto our current picture of the behavior of matter, a ratherunclear picture in this case, the collapse continues untilthe star becomes a point with no size. Well before itreaches that end, gravity has become so strong that lightcan no longer escape, with the result that these objectsare known as black holes.

We have a fuzzy picture of what lies at the center of ablack hole because we do not have a quantum theory ofgravity. Einstein’s classical theory of gravity predictsthat the star collapses to a point, but before that happenswe should reach a state where the quantum effects ofgravity are important. Perhaps string theory will giveus a clue as to what is happening. We will not learn bylooking because light cannot get out.

The formation of neutron stars and black holes empha-sizes an important feature of gravity. On an atomicscale, gravity is the weakest of the forces we havediscussed so far. The gravitational force between anelectron and a proton is a thousand billion billion billionbillion ( 1039 ) times weaker than the electric force. Yetbecause gravity is long range like the electric force, andhas no cancellation, it ends up dominating all otherforces, even crushing matter as we know it, out ofexistence.

The Weak InteractionIn addition to gravity, the electric interaction and thenuclear force, there is one more basic force or interac-tion in nature given the rather bland name the weakinteraction. While considerably weaker than electricor nuclear forces, it is far far stronger than gravity on anuclear scale.

A distinctive feature of the weak interaction is its veryshort range. A range so short that only with theconstruction of the large accelerators since 1970 hasone been able to see the weak interaction behave morelike the other forces. Until then, the weak interactionwas known only by reactions it could cause, likeallowing a proton to turn into a neutron or vice versa.

Because of the weak interaction, an individual neutronis not stable. Within an average time of about 10minutes it decays into a proton and an electron. Some-times neutrons within an unstable nucleus also decayinto a proton and electron. This kind of nuclear decaywas observed toward the end of the nineteenth centurywhen knowledge of elementary particles was verylimited, and the electrons that came out in these nucleardecays were identified as some kind of a ray called abeta ray. (There were alpha rays which turned out tobe helium nuclei, beta rays which were electrons, andgamma rays which were photons.) Because the elec-trons emitted during a neutron decay were called betarays, the process is still known as the beta decayprocess.

The electron is emitted when a neutron decays in orderto conerve electric charge. When the neutral neutrondecays into a positive proton, a negatively chargedparticle must also be emitted so that the total chargedoes not change. The lightest particle available to carryout the negative charge is the electron.

Early studies of the beta decay process indicated thatwhile electric charge was conserved, energy was not.For example, the rest mass of a neutron is nearly 0.14percent greater than the rest mass of a proton. Thismass difference is about four times larger than the restmass of the electron, thus there is more than enough

Figure 5Hubble telescope’s first view of a lone neutron star invisible light. This star is no greater than 16.8 miles (28kilometers) across.

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mass energy available to create the electron when theneutron decays. If energy is conserved, you wouldexpect that the energy left over after the electron iscreated would appear as kinetic energy of the electron.

Careful studies of the beta decay process showed thatsometimes the electron carried out the expected amountof energy and sometimes it did not. These studies werecarried out in the 1920s, when not too much was knownabout nuclear reactions. There was a serious debateabout whether energy was actually conserved on thesmall scale of the nucleus.

In 1929, Wolfgang Pauli proposed that energy wasconserved, and that the apparenty missing energy wascarried out by an elusive particle that had not yet beenseen. This elusive particle, which became known as theneutrino or “little neutral one”, had to have some ratherpeculiar properties. Aside from being electricallyneutral, it had to have essentially no rest mass becausein some reactions the electron was seen to carry out allthe energy, leaving none to create a neutrino rest mass.

The most bizarre property f the neutrino was itsundetectability. It had to pass through matter leavingno trace. It was hard to believe such a particle couldexist, yet on the other hand, it was hard to believeenergy was not conserved. The neutrino was finallydetected thirty years later and we are now quite confi-dent that energy is conserved on the nuclear scale.

The neutrino is elusive because it interacts with matteronly through the weak interaction (and gravity). Pho-tons interact via the strong electric interaction and arequickly stopped when they encounter the electric chargesin matter. Neutrinos can pass through light years oflead before there is a good chance that they will bestopped. Only in the collapsing core of an explodingstar or in the very early universe is matter dense enoughto significantly absorb neutrinos. Because neutrinoshave no rest mass, they, like photons, travel at the speedof light.

LeptonsWe now know that neutrinos are emitted in the betadecay process because of another conservation law, theconservation of leptons. The leptons are a family oflight particles that include the electron and the neutrino.When an electron is created, an anti neutrino is alsocreated so that the number of leptons does not change.

Actually there are three distinct conservation laws forleptons. The lepton family consists of six particles, theelectron, two more particles with rest mass and threedifferent kinds of neutrino. The other massive particlesare the muon which is 207 times as massive as theelectron, and the recently discovered tau particle whichis 3490 times heavier. The three kinds of neutrino arethe electron type neutrino, the muon type neutrinoand the tau type neutrino. The names come from thefact that each type of particle is separately conserved.For example when a neutron decays into a proton andan electron is created, it is an anti electron type neu-trino that is created at the same time to conserveelectron type particles.

In the other common beta decay process, where aproton turns into a neutron, a positron is created toconserve electric charge. Since the positron is the antiparticle of the electron, its opposite, the electron typeneutrino, must be created to conserve leptons.


Nuclear StructureThe light nuclei, like helium, carbon, oxygen, gener-ally have about equal numbers of protons and neutrons.As the nuclei become larger we find a growing excessof neutrons over protons. For example when we get upto Uranium 238, the excess has grown to 146 neutronsto 92 protons.

The most stable isotope of a given element is the onewith the lowest possible energy. Because the weakinteraction allows protons to change into neutrons andvice versa, the number of protons and neutrons in anucleus can shift until the lowest energy combinationis reached.

Two forms of energy that play an important role in theirproess are the extra mass energy of the neutrons, andthe electric potential energy of the protons. It takes a lotf to shove two protons together against their electricrepulsion. The work you do in shoving them togetheris stored as electric potential energy which will bereleased if you let go and the particles fly apart. Thisenergy will not be released, however, if the protons arelatched together by the nuclear force. But in that casethe electric potential energy can be released by turningone of the protons into a neutron. This will happen ifenough electric potential energy is available not only tocreate the extra neutron rest mass energy, but also thepositron required to conserve electric charge.

The reason that the large nuclei have an excess ofneutrons over protons is that electric potential energyincreases faster with increasing number of protons thanneutron mass energy does with increasing numbers ofneutrons. The amount of extra neutron rest massenergy is more or less proportional to the number ofneutrons. But the increase in electric potential energyas you add a proton depends on the number of protonsalready in the nucleus. The more protons already there,the stronger the electric repulsion when you try to addanother proton, and the greater the potential energystored. As a result of this increasing energy cost ofadding more protons, the large nuclei find their lowestenergy balance having an excess of neutrons.

A CONFUSING PICTUREBy 1932, the basic picture of matter looked about assimple as it can possibly get. The elementary particleswere the proton, neutron, and electron. Protons andneutrons were held together in the nucleus by thenuclear force, electrons were bound to nuclei by theelectric force to form atoms, a residual of the electricforce held atoms together to form molecules, crystalsand living matter, and gravity held large chunks ofmatter together for form planets, stars and galaxies.The rules governing the behavior of all this was quan-tum mechanics on a small scale, which became New-tonian mechanics on the larger scale of our familiarworld. There were a few things still to be straightenedout, such as the question as to whether energy wasconserved in beta decays, and in fact why beta decaysoccurred at all, but it looked as if these loose endsshould be soon tied up.

The opposite happened. By 1960, there were well over100 so called elementary particles, all of them unstableexcept for the familiar electron, proton and neutron.Some lived long enough to travel kilometers downthrough the earth’s atmosphere, others long enough tobe observed in particle detectors. Still others had suchshort lifetimes that, even moving at nearly the speed oflight, they could travel only a few proton diametersbefore decaying. With few exceptions, these particleswere unexpected and their behavior difficult to explain.Where they were expected, they were incorrectly iden-tified.

One place to begin the story of the progression ofunexpected particles is with a prediction made in 1933by Heidi Yukawa. Yukawa proposed a new theory ofthe nuclear force. Noting that the electric force wasultimately caused by a particle, Yukawa proposed thatthe nuclear force holding the protons and neutronstogether in the nucleus was also caused by a particle, aparticle that became known as the nuclear force me-son. The zero rest mass photon gives rise to the longrange electric force. Yukawa developed a wave equa-tion for the nuclear force meson in which the range ofthe force depends on the rest mass of the meson. Thebigger the rest mass of the meson, the shorter the range.(Later in the text, we will use the uncertainty principleto explain this relationship between the range of a forceand the rest mass of the particle causing it.)

Int-23

From the fact that iron is the most stable nucleus,Yukawa could estimate that the range of the nuclearforce is about equal to the diameter of an iron nucleus,about four proton diameters. From this, he predictedthat the nuclear force meson should have a rest massbout 300 times the rest mass of the electron (about 1/6the rest mass of a proton).

Shortly after Yukawa’s prediction, the muon wasdiscovered in the rain of particles that continually strikethe earth called cosmic rays. The rest mass of the muonwas found to be about 200 times that of the electron, nottoo far off the predicted mass of Yukawa’s particle. Fora while the muon was hailed as Yukawa’s nuclear forcemeson. But further studies showed that muons couldtravel considerable distances through solid matter. Ifthe muon were the nuclear force meson, it shouldinteract strongly with nuclei and be stopped rapidly.Thus the muon was seen as not being Yukawa’sparticle. Then there was the question of what role themuon played. Why did nature need it?

In 1947 another particle called the π meson wasdiscovered. (There were actually three π mesons, onewith a positive charge, the π+ , one neutral, the π° , andone with a negative charge, the π– .) The π mesonsinteracted strongly with nuclei, and had the mass closeto that predicted by Yukawa, 274 electron masses. Theπ mesons were then hailed as Yukawa’s nuclear forcemeson.

However, at almost the same time, another particlecalled the K meson, 3.5 times heavier than the πmeson, was discovered. It also interacted strongly withnuclei and clearly played a role in the nuclear force.The nuclear force was becoming more complex thanYukawa had expected.

Experiments designed to study the π and K mesonsrevealed other particles more massive than protons andneutrons that eventually decayed into protons andneutrons. It became clear that the proton and neutronwere just the lightest members of a family of proton likeparticles. The number of particles in the proton familywas approaching 100 by 1960. During this time it wasalso found that the π and K mesons were just thelightest members of another family of particles whosenumber exceeded 100 by 1960. It was rather mind

boggling to think of the nuclear force as being causedby over 100 different kinds of mesons, while theelectric force had only one particle, the photon.

One of the helpful ways of viewing matter at that timewas to identify each of the particle decays with one ofthe four basic forces. The very fastest decays wereassumed to be caused by the strong nuclear force.Decays that were about 100 times slower were identi-fied with the slightly weaker electric force. Decays thattook as long as a billionth of a second, a relatively longlifetime, were found to be caused by the weak interac-tion. The general scheme was the weaker the force, thelonger it took to cause a particle decay.

e

e πp

γ

γ

+

+

e+

K

K

K

+

Λ

Ξ

Ω

0

0

0

e–

–

π–

–

–

–Figure 6First bubble chamberphotograph of the Ω–

particle. The Ω–,Ξ0,Λ0

and p + are all membersof the proton family, theK’s and π’s are mesons,the γ ’s are photons andthe e– and e+ areelectrons and positrons.Here we see twoexamples of the creationof an electron-positronpair by a photon.


QUARKSThe mess seen in 1960 was cleaned up, brought intofocus, primarily by the work of Murray Gell-Mann. In1961 Gell-Mann and Yval Neuman found a schemethat allowed one to see symmetric patterns in themasses and charges of the various particles. In 1964Gell-Mann and George Zweig discovered what theythought was the reason for the symmetries. Thesymmetries would be the natural result if the proton andmeson families of particles were made up of smallerparticles which Gell-Mann called quarks.

Initially Gell-Mann proposed that there were threedifferent kinds of quark, but the number has sincegrown to six. The lightest pair of the quarks, the socalled up quark and down quark are found in protonsand neutrons. If the names “up quark” and “downquark” seem a bit peculiar, they are not nearly asconfusing as the names strange quark, charm quark,bottom quark and top quark given the other fourmembers of the quark family. It is too bad that theGreek letters had been used up naming other particles.

In the quark model, all members of the proton familyconsist of three quarks. The proton and neutron, aremade from the up and down quarks. The protonconsists of two up and one down quark, while theneutron is made from one up and two down quarks. Theweak interaction, which as we saw can change protonsinto neutrons, does so by changing one of the proton’sup quarks into a down quark.

The π meson type of particles, which were thought tobe Yukawa’s nuclear force particles, turned out insteadto be quark-antiquark pairs. The profusion of whatwere thought to be elementary particles in 1960 re-sulted from the fact that there are many ways tocombine three quarks to produce members of the

proton family or a quark and an antiquark to create ameson. The fast elementary particle reactions were theresult of the rearrangement of the quarks within theparticle, while the slow reactions resulted when theweak interaction changed one kind of quark into an-other.

A peculiar feature of the quark model is that quarkshave a fractional charge. In all studies of all elemen-tary particles, charge was observed to come in units ofthe amount of charge on the electron. The electron had(–1) units, and the neutron (0) units. All of the morethan 100 “elementary” particles had either +1, 0, or –1units of change. Yet in the quark model, quarks had acharge of either (+2/3) units like the up quark or (-1/3)units like the down quark. (The anti particles have theopposite charge, -2/3 and +1/3 units respectively.) Youcan see that a proton with two up and one down quarkhas a total charge of (+2/3 +2/3 -1/3) = (+1) units, andthe neutron with two down and one up quark has a totalcharge (-1/3 -1/3 +2/3) = (0) units.

The fact that no one had ever detected an individualquark, or ever seen a particle with a fractional charge,made the quark model hard to accept at first. WhenGell-Mann initially proposed the model in 1963, hepresented it as a mathematical construct to explain thesymmetries he had earlier observed.

The quark model gained acceptance in the early 1970swhen electrons at the Stanford high energy acceleratorwere used to probe the structure of the proton. Thismachine had enough energy, could look in sufficientdetail to detect the three quarks inside. The quarks werereal.

In 1995, the last and heaviest of the six quarks, the topquark, was finally detected at the Fermi Lab Accelera-tor. The top quark was difficult to detect because it is185 times as massive as a proton. A very high energyaccelerator was needed to create and observe thismassive particle.

Int-25

With the quark model, our view of matter has becomerelatively simple again: there are two families of par-ticles called quarks and leptons. Each family containssix particles. It is not a coincidence that there are thesame number of particles in each family. In the currenttheory of matter called the standard model, each pairof leptons is intimately connected to a pair of quarks.The electron type leptons are associated with the downand up quarks, the muon and muon type neutrino withthe strange and charm quarks, and the tau and tau typeneutrino with the bottom and top quarks.

Are there more than six quarks and six leptons? Arethere still heavier lepton neutrino pairs associated withstill heavier quarks? That the answer is no, that six isthe limit, first came not from accelerator experiments,but from studies of the early universe. Here we have aquestion concerning the behavior of matter on the verysmallest of scales of distance, at the level of quarksinside proton like particles, and we find the answer bylooking at matter on the very largest of scales, the entireuniverse. The existence of more than six leptons andquarks would have altered the relative abundance ofhydrogen, deuterium, and helium remaining after thebig bang. It would have led to an abundance that is notconsistent with what we see now. Later experimentswith particle accelerators confirmed the results we firstlearned from the early universe.

Our picture of the four basic interactions has alsobecome clearer since the early 1930s. The biggestchange is in our view of the nuclear force. The basicnuclear force is now seen to be the force betweenquarks that holds them together to form protons, neu-trons and other particles. What we used to call thenuclear force, that short range force binding protonsand neutrons together in a nucleus, is now seen as aresidual effect of the force between quarks. The oldnuclear force is analogous to the residual electric forcethat binds complete atoms together to form molecules.

As the electric interaction is caused by a particle, thephoton, the nuclear force is also caused by particles,eight different ones called gluons. The nuclear force ismuch more complex than the electric force becausegluons not only interact with quarks, they also interactwith themselves. This gives rise to a very strange forcebetween quarks. Other forces get weaker as youseparate the interacting particles. The nuclear forcebetween quarks gets stronger! As a result quarks areconfined to live inside particles like protons, neutronsand mesons. This is why we have still never seen anindividual quark or an isolated particle with a fractionalcharge.

Figure 28-28Fermi Lab accelerator magnets.

Figure 28-29Fermi Lab accelerator where thetop quark was first observed.


THE ELECTROWEAK THEORYAnother major advance in our understanding of thenature of the basic interactions came in 1964 whenSteven Weinberg, Abdus Salam and Sheldon Glashowdiscovered a basic connection between the electric andweak interactions. Einstein had spent the latter part ofhis life trying without success to unify, find a commonbasis for, the electric and the gravitational force. Itcame somewhat as a surprise that the electric and weakinteractions, which appear so different, had commonorigins. Their theory of the two forces is known as theelectroweak theory.

In the electroweak theory, if we heat matter to atemperature higher than 1000 billion degrees, we willfind that the electric and weak interaction are a singleforce. If we then let the matter cool, this singleelectroweak force splits into the two separate forces,the electric interaction and the weak interaction. Thissplitting of the forces is viewed as a so called phasetransition, a transition in the state of matter like the onewe see when water turns to ice at a temperature of 0°C.The temperature of the phase transition for theelectroweak force sounds impossibly hot, but it isattainable if we build a big enough accelerator. The

cancelled superconducting supercollider was supposedto allow us to study the behavior of matter at thesetemperatures.

One of the major predictions of the electroweak theorywas that after the electric and weak interactions hadseparated, electric forces should be caused by zero restmass photons and the weak interaction should becaused by three rather massive particles given thenames W+ , W– and Z0 mesons. These mesons werefound, at their predicted mass, in a series of experi-ments performed at CERN in the late 1970s.

We have discussed Yukawa’s meson theory of forces,a theory in which the range of the force is related to therest mass of the particle responsible for the force. Asit turns out, Yukawa’s theory does not work for nuclearforces for which it was designed. The gluons have zerorest mass but because of their interaction, gives rise toa force unlike any other. What Yukawa’s theory doesdescribe fairly well is the weak interaction. The veryshort range of the weak interaction is a consequence ofthe large masses of the weak interaction mesons W+ ,

W– and Z0 . (The W mesons are 10 times as massiveas a proton, the Z0 is 11 times as massive.)

Figure 28-30Paths for the large particle accelerators at CERN. The Geneva airport is in the foreground.

Int-27

THE EARLY UNIVERSEIn the reverse motion picture of the expanding uni-verse, the universe becomes smaller and smaller andhotter as we approach the big bang that created it. Howsmall and how hot are questions we are still studying.But it now seems that with reasonable confidence wecan apply the laws of physics to a universe that is aboutone nanosecond old and at a temperature of threehundred thousand billion degrees. This is the tempera-ture of the electroweak transition where the weak andelectric interactions become separate distinct forces.We have some confidence in our knowledge of thebehavior of matter at this temperature because thistemperature is being approached in the largest of theparticle accelerators.

3×1014 degrees

At three hundred thousand billion degrees the onlystructures that survive the energetic thermal collisionsare the elementary particles themselves. At this timethe universe consists of a soup of quarks and antiquarks, leptons and anti leptons, gravitons and gluons.Photons and the weak interaction mesons W+ , W–

and Z° are just emerging from the particle that gaverise to the electroweak force. The situation may notactually be that simple. When we get to that tempera-ture we may find some of the exotic elementary par-ticles suggested by some recent attempts at a quantumtheory of gravity.

1013 degrees

When the universe reaches the ripe old age of amillionth of a second, the time it takes light to travel1000 feet, the temperature has dropped to 10 thousandbillion degrees. At these temperatures the gluons areable to hold the quarks together to form protons,neutrons, mesons, and their anti particles. It is stillmuch too hot, however, for protons and neutrons tostick together to form nuclei.

When we look closely at the soup of particles at 10thousand billion degrees, there is activity in the form ofthe annihilation and creation of particle-antiparticlepairs. Proton-antiproton pairs, for example, are rapidlyannihilating, turning into photons and mesons. But justas rapidly photons and mesons are creating proton-antiproton pairs.

In the next 10 millionths of a second the universeexpands and cools to a point where the photons andmesons no longer have enough energy to recreate therapidly annihilating proton and neutron pairs. Soon theprotons and neutrons and their antiparticles will haveessentially disappeared from the universe.

Matter particles surviveThe protons and neutrons will have almost disappearedbut not quite. For some reason, not yet completelyunderstood, there was a tiny excess of protonsover antiprotons and neutrons overantineutrons. The estimate is that there were100,000,000,001 matter particles for every100,000,000,000 antimatter particles. It wasthe tiny excess of matter over antimatter that survivedthe proton and neutron annihilation.

3×1010 degrees

After this annihilation, nothing much happens until theuniverse approaches the age of a tenth of a second andthe temperature has dropped to 30 billion degrees.During this time the particles we see are photons,neutrinos and antineutrinos and electrons and positrons.These particles exist in roughly equal numbers. Theelectron-positron pairs are rapidly annihilating to pro-duce photons, but the photons are equally rapidlycreating electron positron pairs.

38% neutronsThere are still the relatively few protons and neutronsthat survived the earlier annihilation. The weak inter-action allows the protons to turn into neutrons and viceversa, with the result there are roughly equal numbersof protons and neutrons. The numbers are not quiteequal, however, because at those temperatures there isa slightly greater chance for the heavier neutron todecay into a lighter proton than vice versa. It isestimated that the ratio of neutrons to protons hasdropped to 38% by the time the universe is .11 secondsold. The temperature is still too high for protons andneutrons to combine to form nuclei.


Neutrinos escape at one secondAs we noted, neutrinos are special particles in that theonly way they interact with matter is through the weakinteraction. Neutrinos pass right through the earth withonly the slightest chance of being stopped. But theearly universe is so dense that the neutrinos interactreadily with all the other particles.

When the universe reaches an age of about one second,the expansion has reduced the density of matter to thepoint that neutrinos can pass undisturbed throughmatter. We can think of the neutrinos as decouplingfrom matter and going on their own independent way.From a time of one second on, the only thing that willhappen to the neutrinos is that they will continue to coolas the universe expands. At an age of 1 second, theneutrinos were at a temperature of 10 billion degrees.By today they have cooled to only a few degrees aboveabsolute zero. This is our prediction, but these coolneutrinos are too elusive to have been directly ob-served.

24% neutronsSome other interesting things are also beginning tohappen at the time of 1 second. The photons havecooled to a point that they just barely have enoughenergy to create electron-positron pairs to replace thosethat are rapidly annihilating. The result is that theelectrons and positrons are beginning to disappear. Atthese temperatures it is also more favorable for neu-trons to turn into protons rather than vice versa, with theresult that the ratio of neutrons to protons has droppedto 24%.

3×109 degrees (13.8 seconds)

When the temperature of the universe has dropped to 3billion degrees, at the time of 13.8 seconds, the energyof the photons has dropped below the threshold ofbeing able to create electron-positron pairs and theelectrons and the positrons begin to vanish from theuniverse. There was the same tiny excess of electronsover positrons as there had been of protons overantiprotons. Only the excess of electrons will survive.

Positrons annihilatedAfter about three minutes the positrons are gone andfrom then on the universe consists of photons, neutri-nos, anti neutrinos and the few matter particles. Theneutrinos are not interacting with anything, and thematter particles are outnumbered by photons in a rationof 100,000,000,000 to one. The photons essentiallydominate the universe.

Deuterium bottleneckAt the time of 13.8 seconds the temperature was 3billion degrees, cool enough for helium nuclei tosurvive. But helium nuclei cannot be made withoutfirst making deuterium, and deuterium is not stable atthat temperature. Thus while there are still neutronsaround, protons and neutrons still cannot form nucleibecause of this deuterium bottleneck.

Helium createdWhen the universe reaches an age of three minutes and2 seconds, and the ratio of neutrons to protons hasdropped to 13%, finally deuterium is stable. Thesesurviving neutrons are quickly swallowed up to formdeuterium which in turn combine to form the verystable helium nuclei. Since there are equal numbers ofprotons and neutrons in a helium nucleus, the 13% ofneutrons combined with an equal number of protons togive 26% by weight of helium nuclei and 74% protonsor hydrogen nuclei.

By the time the helium nuclei form, the universe hasbecome too cool to burn the helium to form heavierelements. The creation of the heavier elements has towait until stars begin to form one third of a million yearslater.

The formation of elements inside of stars was the basisof the continuous creation theory. As we mentioned,one could explain the abundance of all the elementsexcept helium as being a by product of the evolution ofstars. To explain the helium abundance it was neces-sary to abandon his continuous creation theory andaccept that there might have been a big bang after all.

Int-29

The Thermal PhotonsAfter the electron positron pairs had vanished, what isleft in the universe are the photons, neutrinos, antineutrinos, and the few matter particles consisting ofprotons, helium nuclei and a trace of deuterium andlithium. There are enough electrons to balance thecharge on the hydrogen and helium nuclei, but thephotons are energetic enough to break up any atomsthat might try to form. The neutrinos have stoppedinteracting with anything and the matter particles areoutnumbered by photons in a ratio of 100 billion to one.At this time the photons dominate the universe.

One way to understand why the universe cools as itexpands is to picture the expansion of the universe asstretching the wavelength of the photons. Since theenergy of a photon is related to its wavelength (thelonger the wavelength the lower the energy), thisstretching of wavelengths lowers the photon energies.Because the photons dominate the young universe,when the photons lose energy and cool down, so doeseverything else that the photons are interacting with.

.7 million yearsUntil the universe reaches the age of nearly a millionyears, the photons are knocking the matter particlesaround, preventing them from forming whole atoms orgravitational structures like stars. But at the age of .7million years the temperature has dropped to 3000degrees, and something very special happens at thatpoint. The matter particles are mostly hydrogen, and ifyou cool hydrogen below 3000 degrees it becomestransparent. The transition in going from above 3000degrees to below, is like going from inside the surfaceof the sun to outside. We go from an opaque, glowinguniverse to a transparent one.

Transparent universeWhen the universe becomes transparent, the photonsno longer have any effect on the matter particles and thematter can begin to form atoms, stars, and galaxies.Everything we see today, except for the primordialhydrogen and helium, was formed after the universebecame transparent.

Think about what it means that the universe becametransparent at an age of .7 million years. In ourtelescopes, as we look at more and more distant galax-ies, the light from these galaxies must have taken moreand more time to reach us. As we look farther out weare looking farther back in time. With the Hubbletelescope we are now looking at galaxies formed whenthe universe was less than a billion years old, less than10% of its current age.

Imagine that you could build a telescope even morepowerful than the Hubble, one that was able to see asfar out, as far back to when the universe was .7 millionyears old. If you could look that far out what would yousee? You would be staring into a wall of heated opaquehydrogen. You would see this wall in every directionyou looked. If you tried to see through the wall, youwould be trying to look at the universe at earlier, hottertimes. It would be as futile as trying to look inside thesun with a telescope.

Although this wall at .7 million light years consists ofessentially the same heated hydrogen as the surface ofthe sun, looking at it would not be the same as lookingat the sun. The light from this wall has been travelingtoward us for the last 14 billion years, during whichtime the expansion of the universe has stretched thewavelength and cooled the photons to a temperature ofless than 3 degrees, to a temperature of 2.74 degreesabove absolute zero to be precise.

Photons at a temperature of 2.74 degrees can be ob-served, not by optical telescopes but by radio antennasinstead. In 1964 the engineers Arno Penzias andRobert Wilson were working with the radio antennathat was communicating with the Telstar satellite. Thesatellite was a large aluminized balloon that was sup-posed to reflect radio signals back to earth. The radioantenna had to be very sensitive to pick up the weakreflected signals.


In checking out the antenna, Penzias and Wilson weretroubled by a faint noise that they could not eliminate.Further study showed that the noise was characteristicof a thermal bath of photons whose temperature wasaround 3 degrees. After hearing a seminar on the theoryof the big bang and on the possibility that there mightbe some light remaining from the explosion, Penziasand Wilson immediately realized that the noise in theirantenna was that light. Their antenna in effect waslooking at light from the time the universe becametransparent. At that time, only a few astronomers andphysicists were taking the big bang hypothesis seri-ously. The idea of the universe beginning in anexplosion seemed too preposterous. After Penzias andWilson saw the light left over from the hotter universe,no other view has been acceptable.

The fact that the universe became transparent at an ageof .7 million years, means that the photons, now calledthe cosmic background radiation, travelled undis-turbed by matter. By studying these photons carefully,which we are now doing in various rocket and satelliteexperiments, we are in a sense, taking an accuratephotograph of the universe when the universe was .7million years old.

This photograph shows an extremely uniform uni-verse. The smoothness shows us that stars and galaxieshad not yet begun to form. In fact the universe was sosmooth that it is difficult to explain how galaxies didform in the time between when the universe wenttransparent and when we see galaxies in the mostdistant Hubble telescope photographs. The COBE(Cosmic Background Explorer) satellite was able todetect tiny fluctuations in the temperatures of thebackground radiation, indicating that there was per-haps just enough structure in the early hot universe togive us the stars, galaxies and clustering of galaxies wesee today.

One of the questions you may have had reading ourdiscussion of the early universe, is how do we knowthat the photons, and earlier the particle-anti particlepairs outnumbered the matter particles by a ratio of 100billion to one? How do we estimate the tiny excess ofmatter over anti matter that left behind all the matter wesee today? The answer is that the thermal photons wesee today outnumber protons and neutrons by a factorof 100 billion to one and that ratio should not havechanged since the universe was a few minutes old.

We also mentioned that it would be futile to try to lookunder the surface of the sun using a telescope. That istrue if we try to use a photon telescope. However wecan, in effect, see to the very core of the sun usingneutrinos. In the burning of hydrogen to form helium,for each helium nucleus created, two protons are con-verted to neutrons via the weak interaction. In theprocess two neutrinos are emitted. As a result the coreof the sun is a bright source of neutrinos which we candetect and study here on earth.

While it would be futile to use photons to see fartherback to when the universe was about .7 million yearsold, we should be able to see through that barrier usingneutrinos. The universe became transparent to neutri-nos at the end of the first second. If we could detectthese neutrinos, we would have a snapshot of theuniverse as it looked when it was one second old. Thusfar, we have not found a way to detect these cosmicbackground neutrinos.Figure 34-11

Penzias and Wilson, and the Holmdel radio telescope.

Int-31

IndexSymbols10 dimensions, String theory int-16100 billion to one, Matter over anti matter int-301836 times, proton/electron mass ratio int-172.74 degrees, cosmic background radiation int-294 dimensions int-16

AAccelerators, particle int-1Allowed orbits, Bohr theory int-8Anderson, C., positrons int-13Andromeda galaxy int-2, int-3Angular momentum

Quantized int-9Antielectron int-13Antielectron type neutrino int-22Antimatter

Introduction to int-12Neutrino int-22Neutron int-13Positron int-13Proton int-13

Antiparticle int-13Arecibo radio telescope int-15Astronomy

1987 supernova int-19Binary stars int-2Black dwarf star int-19Black holes

Introduction to int-19Early universe int-27Expanding universe, Hubble int-3Galaxy

Andromeda int-2Introduction to int-2Most distant int-3Sombrero int-2

Hubble rule for expanding universe int-3Light years int-2Neutron star

Introduction to int-19Radio telescope, three degree radiation int-30Red shift and expanding universe int-3Stellar evolution int-19Three degree cosmic radiation int-29Visible universe int-3

AtomsBohr model int-8Introductory view of int-16Particle-wave nature of matter int-10

BBeta decay

And energy conservation int-21Beta ray int-21Big bang model of universe int-4Binary stars int-2Black dwarf star int-19Black holes

Introduction to int-19Stellar evolution int-20

Bohr model int-8Introduction to int-8

Bottom quark int-24

Cc (speed of light) int-2CERN

Electroweak theory int-26Charge

Conservation of int-21Discussion of int-6Fractional (quarks) int-24Positive and negative int-6

Charm quark int-24Chemistry. See Atoms: Angular momentum quantum

numberClassical physics int-7Conservation of

Energy int-11Continuous creation theory int-4Cosmic background neutrinos int-30Cosmic background radiation int-30Cosmic radiation int-30Cosmic rays int-13

DDe Broglie

Electron waves int-10Dirac equation

Antimatter int-13Dirac, P. A. M., prediction of antiparticles int-13Distant galaxies, Hubble photograph int-3Down quark int-24

EE = mc2, mass energy int-11Einstein

General relativity int-15Photoelectric effect int-8

Electric fieldAnd light int-7

Electric force or interaction int-6, int-13Electroweak theory int-26Strength of

Comparison to gravity int-6Comparison to nuclear force int-18


Electric potential energy. See Potential energy: ElectricElectrically neutral int-6Electromagnetic spectrum int-7Electron

Lepton family int-22Electron type neutrino int-22Electroweak interaction

Theory of int-26Weak interaction int-26Z and W mesons int-26

Elementary particlesA confusing picture int-22

ElementsCreation of int-4

EnergyConservation of energy

Overview int-11Electric potential energy

In hydrogen atom int-11In nuclear fission int-18

From sun int-18Gravitational potential energy int-11Kinetic energy int-8

Overview int-8Mass energy int-18Neutron mass energy int-22Nuclear potential energy

Fusion int-18Nuclear structure int-22

Spring potential energy int-11Thermal energy int-8Work

Conservation of energy int-11Evolution

Of stars int-19Expanding universe

Hubble, Edwin int-3Hubble rule for int-3

ExpansionUniform, of the universe int-3

FFeynman, R. P. int-14Force

Nuclear force int-18Particle nature of forces int-13

Four basic interactions int-25Fractional charge int-24Fusion, nuclear int-18

GGalaxy

Andromeda int-2Introduction to int-2Most distant int-3Sombrero int-2

Gamov, George, big bang theory int-4Gell-Mann

Quarks int-24General relativity int-15Gluons, strong nuclear force int-25Gravitational force. See GravityGravitational potential energy

Energy conservation int-11Graviton int-15Gravity int-15

Black hole int-20Einstein's general relativity int-15Gravitational potential energy

Energy conservation int-11Newton's universal law int-15Quantum theory of int-16Strength, comparison to electricity int-6Weakness & strength int-20

HHelium

Creation of in universe int-4Isotopes helium 3 and 4 int-17

Hot early universe int-4Hubble, Edwin, expanding universe int-3Hubble photograph of most distant galaxies int-3Hubble rule for expanding universe int-3Hydrogen atom

Big bang theory int-4Hydrogen bomb int-18Hydrogen nucleus int-6Hydrogen spectrum

Bohr model int-8

IInfrared light

In the electromagnetic spectrum int-7Interactions

Electric int-14Gravitational int-15Nuclear int-14Weak int-14

Iron 56, most tightly bound nucleus int-18Isotopes of nuclei int-17

Stability of int-22

KK meson and direction of time int-23Kinetic energy

Overview int-8

LLargest scale of distance int-25Lepton family

Electron int-22Electron type neutrino int-22

Int-33

Muon int-22Muon type neutrino int-22Tau int-22Tau type neutrino int-22

Leptons, conservation of int-22Light int-7

Electromagnetic spectrum int-7Hydrogen spectrum

Bohr model. See Bohr ModelInfra red. See Infrared lightMaxwell’s theory of int-7Microwaves. See MicrowavesPhoton

Introduction to int-8Thermal, 2.74 degrees int-29

Radio waves. See Radio wavesSpectral lines, hydrogen int-7Ultraviolet. See Ultraviolet lightVisible. See Visible lightWave equation for int-7X rays. See X-rays

Light-hour int-2Light-minute int-2Light-second int-2Light-year int-2Lithium

Nucleus int-6

MMagnetic field

In light wave int-7Mass

EnergyIn nuclei int-18Of neutron int-22

Gravitational force on int-6Rest mass int-11

Matter over antimatter, in early universe int-30Maxwell’s theory of light int-7Maxwell's wave equation int-7Mechanics

Relativistic int-12Meter, definition of int-2Microscope int-1Microwaves

Electromagnetic spectrum int-7Milky Way int-2Molecular forces int-6Muon

Discovery of int-23Lepton family int-22Muon type neutrino int-21

NNature’s speed limit int-12Neutrinos

Cosmic background int-30Electron type int-21Muon type int-21Passing through matter int-22Pauli's prediction of int-21Tau type int-21

NeutronDecay

Charge conservation in int-21Energy problems int-21

In isotopes int-17Quark structure of int-24Rest mass energy int-22

Neutron starAnd black holes int-20Binary int-15Stellar evolution int-19

Newton’s lawsClassical physics int-7Gravity int-15

Nonrelativistic wave equation int-12Nuclear

Fission int-18Force int-18

Meson, Yukawa theory int-22Range vs. electric force int-18

Fusion int-18Nuclear interaction int-14Nuclear reactions, element creation int-4Nuclear structure int-22

Nucleon int-17Nucleus int-17

Hydrogen int-6Large int-22Lithium int-6

OOrbits

Allowed, Bohr theory int-8Overview of physics int-1

PParticle

Point size int-14Particle decays and four basic interactions int-23Particle-wave nature

De Broglie picture int-10Of electrons

De Broglie picture int-10Of forces int-13Of matter int-10

Pauli, W., neutrinos int-21Penzias and Wilson, cosmic background radiation int-

29Phase transition, electroweak theory int-26Photoelectric effect int-8


Photon int-8Electric interaction int-23Rest mass int-12Thermal, 2.74 degrees int-29

Pi mesons int-23Point

Particle int-14Positron (antimatter) int-13Potential energy

Electric potential energyIn hydrogen atom int-11In nuclear fission int-18

Energy conservation int-11Gravitational potential energy int-11Nuclear potential energy int-18Spring potential energy int-11Work int-11

Proton int-17Quark structure int-24

QQuantized angular momentum int-9Quantum electrodynamics int-14Quantum theory of gravity int-16, int-20Quarks int-24

RRadiation

Three degree cosmic radiation int-30Radio telescope int-15

Arecibo int-15Radio waves

In the electromagnetic spectrum int-7Reactive metal, lithium int-6Relativistic physics

Antimatter int-12Mass-energy relationship int-11Nature's speed limit int-2, int-12Relativistic mechanics int-12Relativistic wave equation int-12Zero rest mass int-12

Relativity, general int-15Renormalization int-14, int-17Rest mass int-11

SSchrödinger wave equation

Particle-wave nature of matter int-10Schrödinger, Erwin int-10Schwinger, J., quantum electrodynamics int-14Second, unit of time, definition of int-2Smallest scale of distance, physics at int-25Sombrero galaxy int-2Space

And time int-2Spectral lines

Bohr's explanation of int-9Hydrogen

Colors of int-7Introduction to int-7

Speed and mass increase int-11Speed limit, nature’s int-12Speed of light

Absolute speed limit int-2, int-12Spring

Spring potential energy int-11Standard model of basic interactions int-25Standing waves

Particle wave nature int-13Star

Binary int-2Black dwarf int-19Black hole int-20Neutron int-20

Stellar evolutionGeneral discussion int-19

Strange quark int-24Strength of the electric interaction

In comparison to gravity int-6In comparison to nuclear force int-18

String theory int-16SU3 symmetry

Gell-Mann and Neuman int-24Sun

Energy source int-18Supernova, 1987

Photograph of int-19Symmetry

SU3Gell-Mann and Neuman int-24

TTau particle, lepton family int-22Tau type neutrino int-22Taylor, Joe, binary neutron stars int-15Telescopes int-1

RadioArecibo, binary neutron stars int-15Holmdel, three degree radiation int-30

TemperatureHeated hydrogen int-9

Thermal energyIn a bottle of hydrogen int-8

Thermal photons. See Three degree radiationThree degree cosmic radiation int-30Time

And the speed of light int-2In early universe int-27

Top quarkMass of int-24Quark family int-24

Tritium, a hydrogen isotope int-17

Int-35

UUltraviolet light

Electromagnetic spectrum int-7Uncertainty principle

Particle/wave nature int-10Uniform expansion of universe int-3Unit of angular momentum int-9Universe

Age of int-3As a laboratory int-1Big bang model int-4Continuous creation theory int-4Excess of matter over antimatter int-27Expanding int-3Three degree cosmic radiation int-30Visible int-3

Universe, early int-2710 to the 10 degrees int-2710 to the 13 degrees int-2710 to the 14 degrees int-2713.8 seconds int-2824% neutrons int-2838% neutrons int-27At .7 million years, decoupling int-29Deuterium bottleneck int-28Helium created int-28Hot int-4Matter particles survive int-27Neutrinos escape at one second int-28Overview int-27Positrons annihilated int-28Thermal photons int-29Three degree cosmic radiation int-30Transparent universe int-29

Up quark int-24Uranium

Nuclear structure int-17

VVisible light int-7Visible universe int-3

WW and Z mesons, electroweak interaction int-26Wave equation int-7

For light int-7Nonrelativistic int-12Relativistic int-12

Weak interaction int-14, int-20Electroweak theory int-26Range of int-21Strength of int-21

Wilson, Robert, 3 degree radiation int-29Work int-11

XX-rays

Electromagnetic spectrum int-7

YYukawa, H. int-22Yukawa's theory int-22

ZZ and W mesons, electroweak interaction int-26

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