2 WINTER 2001

WHAT MAKES the Sun shine?How does it produce the vast amount of energy necessary to

support life on Earth? These questions challenged scientists for a hundred and fifty years, beginning in the middle of the nineteenth century. Theoretical physicists battled geologists and evolutionary biologists in a heated controversy over who had the correct answer.

Why was there so much fuss about this scientific puzzle? The nineteenth-century astronomer John Herschel elo-quently described the fundamental role of sunshine in all of human life in his 1833Treatise on Astronomy:

The sun’s rays are the ultimate source of almost every motion which takes place on the surface of the earth. By its heat are produced all winds, . . .By their vivifying action vegetables are elaborated from inorganic matter, and become, in their turn, the support of animals and of man, and the sources of those great deposits of dynamical efficiency which are laid up for human use in our coal strata.

In this article, I review the development of our under-standing of how the Sun shines, beginning with the nineteenth-century controversy over the age of the Sun. Then I show how seemingly unrelateddiscoveries in fundamental physics led to a theory of nuclear-energy

How the Sun Shinesby JOHN N. BAHCALL

The quest to understand energy productionin the Sun frequently leads to fascinatingdiscoveries about neutrinos.

BEAM LINE 3

generation in stars, which resolved the controversy over the age of the Sun and explained the origin of solar radiation. Finally, I discuss how experiments designed to test the theory of nuclear energy gen-eration in stars revealed a new conundrum—the mystery of the missing neutrinos.

THE AGE OF THE SUN

How old is the Sun? And how does it shine? These questions are two sides of one and the same coin.

The rate at which the Sun radiates energy is easily computed using the measured rate at which

energy reaches the Earth’s surface and the distance between the two bodies. The total energy that the

Sun has radiated away over its lifetime is approxi-mately the product of the rate at which energy is cur-rently being emitted, called the solar luminosity,

times the age of the Sun.The older the Sun is, the greater the total amount

of radiated solar energy. The greater the radiated energy, or the older the Sun is, the more difficult it is to find an explanation for

the source of solar energy.To appreciate this difficulty better, consider an illustration

of the enormous rate at which the Sun radiates energy. Suppose you leave acubic centimeter of ice outside on a summer day in such a way that it absorbs all of the sunshine striking it. The sunshine will melt the ice cube

4 WINTER 2001

in about 40 minutes. Since thiswould happen anywhere in space atthe Earth’s orbit, a huge sphericalshell of ice centered on the Sun and300 million km (187 million miles)in diameter would melt in the sametime. Equivalently, an area ten thou-sand times the area of the Earth’s sur-face and about half a kilometer (athird of a mile) thick would bemelted in 40 minutes by the energypouring out of the Sun. (The lumi-nosity of the Sun exceeds the powergenerated by 100,000,000,000,000,0001-GW power plants.)

Nineteenth-century physicistsbelieved gravitation to be the energysource for solar radiation. In an in-fluential 1854 lecture, Hermann vonHelmholtz, a German professor ofphysiology who became a distin-guished researcher and physics pro-fessor, proposed that the origin of theSun’s enormous radiated energy isthe gravitational contraction of itshuge mass. He echoed Julius Mayer(another German physician) and -J. J. Waterston, who had earlier sug-gested that the origin of solar radia-tion is the conversion of gravitationalenergy into heat. Von Helmholtz andMayer helped to elucidate the law ofconservation of energy, which statesthat energy can be transformed fromone form into another but the totalamount of energy never changes.

Biologists and geologists consid-ered the effects of solar radiation,while physicists concentrated on theorigin of the radiated energy. In 1859Charles Darwin, in the first editionof On The Origin of the Species byNatural Selection, made a crude cal-culation of the age of the Earth byestimating how long it would takeerosion occurring at the then-

observed rate to wash away theWeald, a great valley that stretchesbetween the North and South Downsacross the south of England. Heobtained a time for the “denudationof the Weald” in the range of 300 mil-lion years, which was apparently longenough for natural selection to haveproduced the astounding range ofspecies that exist on Earth.

Darwin’s estimate of a minimumduration of geological activity im-plied a minimum amount of energythat the Sun had radiated.

Firmly opposed to Darwinian nat-ural selection, William Thompson,later Lord Kelvin, was then a profes-sor at the University of Glasgow andone of the great physicists of the nine-teenth century. In addition to hismany contributions to applied sci-ence and to engineering, Thompsonhelped to formulate the second lawof thermodynamics and set up the ab-solute temperature scale, which wassubsequently named the Kelvin scalein his honor. The second law statesthat heat naturally flows from a hot-ter to a colder body, not vice versa.Kelvin therefore realized that the Sunand the Earth will cool unless thereis an external energy source.

Like Helmholtz, Kelvin believedthat the Sun’s luminosity was pro-duced by the conversion of gravita-tional energy into heat. In 1854 hesuggested that the Sun’s heat mightbe produced by the impact of mete-ors continually falling onto its sur-face. Astronomical evidence forcedhim to modify his hypothesis, and hethen argued that the primary sourceof the energy available to the Sun wasthe gravitational energy of the pri-mordial meteors from which it hadbeen formed. With great authority

William Thomson, later known as LordKelvin (Courtesy AIP Emilio Segrè VisualArchives)

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and eloquence Lord Kelvin declaredin 1862:

That some form of the mete-oric theory is certainly the trueand complete explanation ofsolar heat can scarcely bedoubted, when the followingreasons are considered: (1) Noother natural explanation,except by chemical action, canbe conceived. (2) The chemicaltheory is quite insufficient,because the most energeticchemical action we know, tak-ing place between substancesamounting to the whole sun’smass, would only generateabout 3,000 years’ heat. (3) Thereis no difficulty in accountingfor 20,000,000 years’ heat by themeteoric theory.

He continued attacking Darwin’sestimate directly, asking, “What thenare we to think of such geologicalestimates as [Darwin’s] 300,000,000years for the ‘denudation of theWeald’?” Believing Darwin had over-estimated the Earth’s age, Kelvin alsothought that Darwin was wrongabout the time available for naturalselection.

Lord Kelvin estimated the lifetimeof the Sun, and by implication theEarth’s age, as follows: He calculat-ed the gravitational energy of an ob-ject with a mass equal to the Sun’smass and a radius equal to the Sun’sradius, then divided the result by therate at which the Sun radiates awayenergy. This calculation yielded alifetime of just 30 million years—only one tenth of Darwin’s estimate.The corresponding estimate for thelifetime sustainable by release ofchemical energy was much smallerbecause chemical processes generatecomparatively little energy.

During the nineteenth centuryyou could get very different estimatesfor the age of the Sun depending uponwhom you asked. Prominent theo-retical physicists argued, based uponthe sources of energy known at thattime, that the Sun was at most a fewtens of million years old. By contrast,many geologists and biologists con-cluded that the Sun must have beenshining for at least several hundredsof millions of years in order toaccount for geological changes andthe evolution of living things. Thusthe age of the Sun, and the origin ofsolar energy, were important ques-tions not only for physics andastronomy, but also for geology andbiology.

Darwin was so shaken by thepower of Kelvin’s analysis and by theauthority of his theoretical expertise,that in the last editions of On TheOrigin of the Species he eliminatedall mention of specific time scales. Hewrote in 1869 to Alfred Russel Wal-lace, the codiscoverer of natural se-lection, complaining about LordKelvin, “Thomson’s views on therecent age of the world have been forsome time one of my sorest troubles.”

Today we know that Lord Kelvinwas wrong and the geologists andevolutionary biologists were right.Radioactive dating of meteoritesshows that the Sun is 4.6 billion yearsold, and the Earth is almost as old.

An analogy may help us under-stand what was wrong with Kelvin’sanalysis. Suppose a friend tries to fig-ure out how long your laptop com-puter has been operating. A plausi-ble estimate might be no more thana few hours, since that is the maxi-mum duration a battery can supplythe required amount of power. The

flaw in this analysis is his assump-tion that your computer is poweredonly by a battery. This estimate ofa few hours would fall far short ofreality if your computer was alsopowered from an electric outlet inthe wall. The flaw in Kelvin’s analy-sis was his assumption that onlygravitational energy powers the Sun.

Since nineteenth-century theo-retical physicists knew nothing aboutthe possibility of transformingnuclear mass into energy, they cal-culated a maximum age for the Sunthat was far too short. Nevertheless,Kelvin and his colleagues made a last-ing contribution to the sciences ofastronomy, geology, and biology byinsisting that valid inferences in allfields of research must be consistentwith the fundamental laws of physics.

GLIMPSES OF THE SOLUTION

The turning point in this battlebetween theoretical physicists andempirical geologists and biologistsoccurred in 1896. In the course of anexperiment designed to study X rays,discovered the previous year byWilhelm Roentgen, Henri Becquerelstored some uranium-covered platesin a desk drawer atop photographicplates wrapped in dark paper. Upondeveloping the photographic plates,he found to his surprise strongimages of the uranium crystals. Hehad discovered natural radioactivity,due to nuclear transformations ofuranium atoms.

The significance of Becquerel’sdiscovery became apparent in 1903,when Pierre Curie and his youngassistant, Albert Laborde, announcedthat radium salts constantly releaseheat. The most extraordinary aspect

6 WINTER 2001

of this new discovery was thatradium gave off heat without cool-ing down to the temperature of itssurroundings. This radiation had tohave a previously unknown sourceof energy. William Wilson andGeorge Darwin almost immediatelyproposed that similar radioactivitymight be the source of the Sun’sradiated energy.

Ernest Rutherford, then a profes-sor of physics at McGill Universityin Montreal, soon discovered theenormous energy released by theemission of alpha particles fromradioactive substances. In 1904 heannounced:

The discovery of the radioac-tive elements, which in theirdisintegration liberate enor-mous amounts of energy, thusincreases the possible limit ofthe duration of life on thisplanet, and allows the time

FOR STARS HEAVIER thanthe Sun, theoretical models showthat the CNO (carbon-nitrogen-

oxygen) cycle of nuclear fusion is thedominant source of energy generation.The cycle results in the fusion of fourhydrogen nuclei (1H, protons) into asingle helium nucleus (4He, alphaparticle), which supplies energy to thestar in accordance with Einstein’sequation. Ordinary carbon, 12C, servesas a catalyst in this set of reactions andis regenerated. Only relatively low-energy neutrinos are produced in thiscycle. The figure is adapted from JohnN. Bahcall, “Neutrinos from the Sun,”Scientific American, 221, 1 (1969)28–37.

The CNO Cycle1.7 MeV

(max)

e+

e+ Positronγ Photonν Neutrino

ProtonNeutron

ν

H11

H11

N147

O158

N157

H11

He42

H11

C126

N137

C136

+

+

1.2 MeV(max)

e+

ν+

+

γ

γ

γ

+

+

+

++

+

+

claimed by the geologist andbiologist for the process ofevolution.

The discovery of radioactivityopened up the possibility thatnuclear energy might be the sourceof solar radiation, freeing theoristsfrom reliance in their calculations ongravitational energy. However, sub-sequent astronomical observationsshowed that the Sun does not con-tain much radioactive material, butis instead mostly gaseous hydrogen.Moreover, the rate at which radio-activity delivers energy does not varywith temperature, while observa-tions of stars suggested that theamount of energy radiated by a stardoes indeed depend sensitively uponits interior temperature. Somethingother than radioactivity was requiredto release nuclear energy within astar.

The next fundamental advancecame once again from an unexpecteddirection. In 1905 Albert Einstein de-rived his famous relation betweenmass and energy, E = mc2, as a con-sequence of the special theory of rel-ativity. This equation showed that atiny amount of mass could, in prin-ciple, be converted into a tremendousamount of energy. Einstein’s famousequation generalized and extendedthe nineteenth-century law of energyconservation of Helmholtz andMayer to include the conversion ofmass into energy.

What was the connection be-tween Einstein’s equation and theSun’s energy source? The answer wasnot immediately obvious. Astrono-mers did their part by defining theconstraints that observations of starsimposed on the possible explanationsof stellar energy generation. In 1919Henry Norris Russell, the leadingtheoretical astronomer in the UnitedStates, summarized the astronomi-cal hints about the nature of the stel-lar energy source. The most impor-tant clue, he stressed, was the hightemperature in the interiors of stars.

In 1920 Francis Aston discoveredthe key experimental piece of thepuzzle. He made precise measure-ments of the masses of many differ-ent atoms, among them hydrogenand helium. Aston found that fourhydrogen nuclei were slightly heav-ier than a helium nucleus.

The importance of these mea-surements was immediately recog-nized by Sir Arthur Eddington, thebrilliant English astrophysicist. Heargued in his 1920 presidentialaddress to the British Association forthe Advancement of Science thatAston’s determination of the mass

BEAM LINE 7

difference between hydrogen andhelium meant that the Sun couldshine by converting hydrogen atomsinto helium. This thermonuclearfusion would (according to Einstein’srelation between mass and energy)release the energy equivalent to 0.7percent of the hydrogen mass. Inprinciple, such a process could allowthe Sun to shine for about 100 billionyears.

In a frighteningly prescient in-sight, Eddington went on to remarkabout the connection between stel-lar energy generation and the futureof humanity:

If, indeed, the sub-atomicenergy in the stars is beingfreely used to maintain theirgreat furnaces, it seems to bringa little nearer to fulfi llment ourdream of controlling this latentpower for the well-being of thehuman race— or for its suicide.

UNDERSTANDING THE PROCESS

The next big step in understandinghow stars produce energy resultedfrom applying quantum mechanicsto the explanation of nuclear radio-activity. This application was madewithout any reference to what hap-pens in stars. Two particles with thesame sign of electrical charge willrepel each other. According to clas-sical physics, the probability that twopositively charged particles can getvery close together is essentially zero.But, some things that cannot happenin classical physics can occur in thequirky microscopic world describedby quantum mechanics.

In 1928 George Gamow, theRussian-American theoretical physi-cist, derived a quantum-mechanical

formula that predicted that twocharged particles could occasionallyovercome their mutual electrostaticrepulsion and approach one anotherextremely closely. This quantum-mechanical probability, now knownas the “ Gamow factor, ” is widelyused to explain the measured ratesof certain radioactive decays.

In the decade that followed,Robert Atkinson and Fritz Houter-mans and later George Gamow andEdward Teller used the Gamow fac-tor to derive the rate of nuclearreactions at the high temperaturesbelieved to exist in the interiors ofstars. It allowed them to estimatehow often two hydrogen nucleiwould get close enough together tofuse and thereby release energy.

In 1938 Carl Friedrich vonWeizsä cker came close to solving theproblem of how some stars shine. Hediscovered a nuclear cycle, nowknown as the carbon-nitrogen-oxygen (CNO) cycle (see box on pre-vious page), in which hydrogennuclei could fuse using carbon as acatalyst. But von Weizsä cker did notinvestigate the rate at which energywould be produced in a star by theCNO cycle, nor did he study the cru-cial dependence of this reaction uponstellar temperature.

The scientifi c stage had been setfor the entry of Hans Bethe, theacknowledged master of nuclearphysics. He had just completed aclassic set of three papers in whichhe reviewed and analyzed all thatwas then known about nuclearphysics, works known among his col-leagues as “ Bethe’s bible. ” Gamowassembled a small conference ofphysicists and astrophysicists inWashington, DC, to discuss the state

Hans Bethe in 1935, Ann Arbor, Michigan(Courtesy AIP Emilio Segrè VisualArchives)

S. A

. Gou

dsm

it

8 WINTER 2001

of knowledge, and the unsolved prob-lems, concerning the internal con-stitution of the stars. In the courseof the next six months, Bethe workedout the basic nuclear processes bywhich hydrogen is burned (fused)into helium in stellar interiors. Hy-drogen is the most abundant con-stituent of the Sun and similar stars,and indeed the most abundant ele-ment in the Universe.

Bethe described the results of hiscalculations in a 1939 paper entitled“ Energy Production in Stars. ” Heanalyzed the different possibilitiesfor nuclear fusion reactions andselected as most important the twoprocesses that we now believe areresponsible for sunshine. One process,

the so-called pp chain (see box above),builds helium out of hydrogen and isthe dominant energy source in starslike the Sun and less massive stars.The second process is the CNO cycleconsidered by von Weizs ä cker; it ismost important in stars that are moremassive than the Sun. Bethe esti-mated the central temperature of theSun, obtaining a value within 20 per-cent of the value (16 million degreeskelvin) that we currently believe iscorrect.* Moreover, he showed that

IN THEORETICAL MODELS of theSun, the pp chain of nuclear reactionsillustrated here is the dominant source of

energy production. Each reaction is labeled by anumber to the left of the box in which it is con-tained. In reaction 1, two hydrogen nuclei (1H,protons) are fused to produced a heavy hydro-gen nucleus (2H, a deuteron). This is the usualway nuclear burning gets started in the Sun. On rare occasions, the process is started byreaction 2. Deuterons produced in reactions 1and 2 fuse with protons to produce light nuclei ofhelium (3He). At this point, the pp chain breaksinto three branches, whose relative frequenciesare given on the right. The net result of thischain is the fusion of four protons into a singleordinary helium nucleus (4He) with energy beingreleased to the star in accordance withEinstein’s equation. Neutrinos are emitted insome of these fusion processes. Their energiesare shown in the figure in units of millions ofelectron volts (MeV).

+ ++pp reaction

e+ ν

+ + +pep reaction

e – ν

+ + γ

H11 H1

1 H21

H11 H1

1 H21

H21 H1

1 He32

0.42 MeV

1.44 MeV

1

2

3

(max)

The pp Cha

*According to the modern theory of stellarevolution, the Sun is heated to the enor-mous temperatures at which nuclearfusion can occur by gravitational energyreleased as the solar mass contracts froman initially large gas cloud. Thus Kelvinand other nineteenth-century physicistswere partially right; the release of gravita-tional energy ignited nuclear energygeneration in the Sun.

his calculations led to a relation be-tween the mass and luminosity ofstars that was in agreement with as-tronomical observations.

In the fi rst two decades after theend of World War II, many importantdetails were added to Bethe’s theoryof nuclear burning in stars. Distin-guished physicists and astrophysi-cists, especially Al Cameron, Wil-liam Fowler, Fred Hoyle, EdwinSalpeter, Martin Schwarzschild, andtheir experimental colleagues, re-turned eagerly to the question of howstars like the Sun generate energy.From Bethe’s work, the answer wasknown in principle: the Sun producesenergy by burning hydrogen. Accord-ing to this theory, the solar interior

[Figures adapted from John N. Bahcall, “Neutrinos from theSun,” Scientific American, 221, 1 (1969) 28–37.]

BEAM LINE 9

+ ++Branch 1(85%)

Branch 2(15%)

+ + γ

+ +

He32 He3

2 H11 H1

1He42

He32 He4

2 Be74

Li73 H1

1 He42 He4

2

0.86 MeV

+ e– Li73

Li73

(90%)

0.38 MeV(10%)

+ ν

+ νBe74

4

5

6

7

Branch 3(0.01%)

15 MeV(max)

++

+

γ

+ γ

ν

He42

H11

Be84

Be84B8

5

B85

Be74

Be74

He32

11

8

9

10

+

+ +

He42 He4

2

e+

in Reaction

is a sort of controlled thermonuclearbomb on a gigantic scale (The sen-sitive dependence of the Gamow fac-tor upon the relative energy of thetwo charged particles is, we nowunderstand, what provides the tem-perature “ thermostat” for stars.) Thetheory leads to the successful cal-culation of the observed luminosi-ties of stars similar to the Sun andprovides the basis for our currentunderstanding of how stars shine andevolve over time.

William Fowler led a team of col-leagues in his Caltech KelloggLaboratory and inspired physiciststhroughout the world to measure orcalculate the most important detailsof the pp chain and the CNO cycle.

There was plenty of work to do, andthe experiments and calculationswere diffi cult. But the work got donebecause understanding the speci fi csof solar energy generation was sointeresting. Most of the efforts ofFowler and his colleagues soonshifted to the problem of how theheavier elements are produced instars.

DISCOVERY, CONFIRMATION,AND SURPRISE

Science progresses as a result of theclash between theory and experi-ment — between speculation andmeasurement. In the same lecture inwhich he fi rst discussed the burning

of hydrogen nuclei in stars, Edding-ton remarked:

I suppose that the applied mathe-matician whose theory has justpassed one still more stringenttest by observation ought not tofeel satisfaction, but ratherdisappointment—‘ Foiled again!This time I had hoped to fi nd adiscordance which would throwlight on the points where mymodel could be improved.’

Is there any way to test the theorythat the Sun shines because verydeep in its interior hydrogen isburned into helium? At fi rst thought,it seems impossible to make a directtest of the nuclear-burning hypothe-sis. Light takes tens of thousands of

10 WINTER 2001

years to leak out from the center ofthe Sun to its surface. When it fi nallyemerges, this light tells us mainlyabout the conditions in the outmostregions. Nevertheless, there is a wayof “ seeing ” into the solar interiorusing neutrinos — exotic particlesthat were first proposed in 1930 byWolfgang Pauli and fi nally detectedin 1956 by Clyde Cowan andFrederick Reines.

A neutrino is a subatomic parti-cle that interacts very weakly withmatter and travels at essentially thespeed of light. Neutrinos are pro-duced in stars when hydrogen nucleiare fused to form helium nuclei;neutrinos are also produced on Earthin particle accelerators, nuclearreactors, and natural radioactivity.Based upon the work of Bethe and hiscolleagues, we believe that theprocess by which stars like the Sungenerate energy can be described bythe relation

41H→ 4He + 2e+ + 2ν + energy,

in which four hydrogen nuclei (1H)are fused into a single helium nu-cleus (4He) plus two positrons (e+) andtwo neutrinos (ν) plus energy. Thisprocess releases energy to the starsince, as Aston showed, four hydro-gen atoms are heavier than a heliumatom. (In fact, they are heavier thana helium atom plus two positronsand two neutrinos.) The samenuclear reactions that supply theenergy of the Sun’s radiation also pro-duce telltale neutrinos that we cantry to detect in the laboratory.

Because of their weak interac-tions, however, neutrinos are diffi-cult to detect. How diffi cult? A solarneutrino passing through the entireEarth has less than one chance in a

trillion of interacting with terres-trial matter. According to standardsolar theory, about a hundred billionsolar neutrinos pass through yourthumbnail every second, and youdon’t even notice them. Neutrinoscan travel unaffected through ahundred light-years thickness of iron.But if you put enough material in theway of a suffi ciently high flux of neu-trinos, as Cowan and Reines showed,you can observe occasional interac-tions.

In 1964 Raymond Davis Jr. and Iproposed that an experiment with100,000 gallons of cleaning fluid (per-chloroethylene, which is mostlycomposed of chlorine) could providea critical test of the idea that nuclearfusion reactions are the ultimatesource of solar radiation. We arguedthat if our understanding of nuclearprocesses in the interior of the Sunwas correct, then solar neutrinoswould be captured at a rate thatDavis could measure with a largetank filled with this fluid. Whenneutrinos interact with chlorine,they occasionally produce a radio-active isotope of argon. Davis hadshown that he could extract tinyamounts of neutrino-produced argonfrom large quantities of perchloro-ethylene. To do the solar neutrinoexperiment, he had to be spectacu-larly clever since according to mycalculations, only a few atomswould be produced per week in ahuge volume of cleaning fluid thesize of an Olympic swimming pool!

Our sole motivation for urgingthis experiment was to use neutrinosto “ enable us to see into the interiorof a star and thus verify directly thehypothesis of nuclear-energy gener-ation in stars.” We did not anticipate

Nuclear Burning

Photosphere

Sunspot

A cross section of the Sun. The featuresthat are usually studied by astronomerswith normal telescopes that detect lightare labeled on the outside, for example,sunspots. Neutrinos enable us to lookdeep inside the Sun, into the solar corewhere nuclear burning occurs.

BEAM LINE 11

some of the most interesting aspectsof this proposal.

Davis performed the experimentand in 1968 announced the firstresults: he observed fewer neutrinosthan predicted. As the experimentand the theory were refined, thedisagreement appeared more andmore robust. Scientists rejoiced thatsolar neutrinos had been detected butworried about why there were few-er neutrinos than expected.

What was wrong? Was our under-standing of how the Sun shinesincorrect? Had I made an error in cal-culating the rate at which solar neu-trinos would be captured in Davis’stank? Was the experiment wrong?Or, did something happen to the neu-trinos after they were created in theSun?

Over the next twenty years, manydifferent possibilities were examinedby hundreds of physicists, chemists,and astronomers. Both the experi-ment and the theoretical calculationappeared to be correct.

Once again experiment rescuedpure thought. In 1986 Japanese physi-cists led by Masatoshi Koshiba andYoji Totsuka, together with theirAmerican colleagues Eugene Beierand Alfred Mann, reinstrumented ahuge tank of water designed tomeasure the stability of matter. Theexperimenters increased the sensi-tivity of their detector so that itcould also serve as a large under-ground observatory of solar neutri-nos. Their goal was to explore thereason for the quantitative disagree-ment between the predicted and themeasured rates in Davis’s chlorineexperiment.

The new experiment (Kamio-kande) in the Japanese Alps also

few percent. If someone had told mein 1964 that number of solar neutri-nos observed would be within a fac-tor of 3 of the predicted value, Iwould have been astonished anddelighted.

In fact, the agreement betweennormal astronomical observations(using light rather than neutrinos)and theoretical calculations of solarcharacteristics is much more precise.Studies of the internal structure ofthe Sun based on observations ofsolar vibrations show that the stan-dard solar model predicts tempera-tures at the Sun’s core that are con-sistent with observations to anaccuracy of better than 0.1 percent.Then what can explain the dis-agreement by a factor of 2 to 3 be-tween the measured and the pre-dicted solar neutrino rates?

Physicists and astronomers wereonce again forced to reexamine theirtheories. This time, the discrepancywas not between different estimatesof the Sun’s age, but rather betweenpredictions based upon a widelyaccepted theory and direct measure-ments of particles produced bynuclear burning in the Sun’s interior.This situation was sometimesreferred to as the “ mystery of themissing neutrinos ” or, in languagethat sounded more scientific, “ thesolar neutrino problem.”

As early as 1969, two scientistsworking in Russia, Bruno Pontecorvoand Vladimir Gribov, had proposedthat the discrepancy between theoryand the first solar neutrino experi-ment could be due to an inadequacyin the textbook description ofparticle physics, rather than in thestandard solar model. (Incidentally,Pontecorvo was also the fi rst person

detected solar neutrinos. Moreover,it confirmed that the neutrino ratewas substantially less than predict-ed by standard physics and standardmodels of the Sun; it also clearlydemonstrated that the detectedneutrinos indeed came from the Sun.Subsequently experiments in Russia(called SAGE, led by VladimirGavrin), Italy (GALLEX and laterGNO led by Till Kirsten and EnricoBelotti, respectively), and in Japan(Super-Kamiokande, led by Yoji Tot-suka and Yoichiro Suzuki), each withdifferent characteristics, all observedneutrinos from the solar interior.In each detector, the number of neu-trinos observed was significantlylower than standard theories pre-dicted.

What do all of these experimentalresults tell us? Neutrinos producedin the center of the Sun have beendetected in fi ve experiments. Theirdetection proves that the source ofthe energy that the Sun radiates is in-deed the fusion of hydrogen nucleiin the solar interior. The nineteenth-century debate between theoreticalphysicists, geologists, and biologistshas been settled empirically.

From an astrophysical perspec-tive, the agreement between neutrinoobservations and theory is good. Theobserved energies of the solarneutrinos match the predicted val-ues. The rates at which neutrinos aredetected are less than predicted butby factors of only 2– 3. Since the pre-dicted neutrino flux at the Earthdepends approximately upon the 25thpower of the core temperature of theSun, the agreement that has beenachieved indicates that we haveempirically measured this tempera-ture of the Sun to an accuracy of a

12 WINTER 2001

to propose using a chlorine detectorto study neutrinos.) Gribov and Pon-tecorvo suggested that neutrinos pos-sess a dual personality— that they os-cillate back and forth betweendifferent states or types. Physicistscall this propensity “ neutrino oscil-lations.”

According to this idea, neutrinosare produced in the Sun in a mixtureof individual states: they have a sortof split personality. The individualstates have different, small masses,rather than the zero masses attrib-uted to them by standard particletheory. As they travel to the Earth,neutrinos oscillate between theeasier-to-detect neutrino state (theelectron neutrino νe) and a moredifficult-to-detect neutrino state.Davis’s chlorine experiment couldonly detect neutrinos in the easier-to-observe state. If many of the neu-trinos arrive at Earth in a state thatis diffi cult to observe, then they arenot counted. It seems as if some ormany of the neutrinos have vanished,explaining the apparent mystery ofthe missing neutrinos.

Building upon this idea, LincolnWolfenstein in 1978 and StanislavMikheyev and Alexei Smirnov in1985 showed that matter can affectneutrinos as they travel through theSun. If Nature has chosen to givethem masses in a particular range,this effect can increase the oscilla-tion probability of the neutrinos.

Neutrinos are also produced bythe collisions of cosmic rays withparticles in the Earth’s atmosphere.In 1998 the Super-Kamiokande teamannounced that they had observedoscillations among atmosphericneutrinos. This finding providedindirect support for the theoretical

idea that solar neutrinos oscillateamong different states. Many scien-tists working on the subject believethat, in retrospect, we have hadevidence for oscillations of solar neu-trinos since 1968.

But we do not yet know whatcauses the multiple personality dis-order of solar neutrinos. The answerto this question may provide a clue tophysics beyond the current StandardModel of elementary particles andtheir interactions. Does the identitychange occur while the neutrinos aretraveling to the Earth from the Sun,as originally proposed by Gribov andPontecorvo? Or does matter inducesolar neutrinos to “fl ip out” ? Exper-iments under way in Canada, Italy,Japan, Russia, and the United Statesare attempting to pin down the exactcause of solar neutrino oscillations,by measuring their masses and howthey transform from one type into an-other. Non-zero neutrino masses mayprovide a clue to a still undiscoveredrealm of physical theory.

A WONDERFUL MYSTERY

Nature has written a wonderful mys-tery story. The plot continuallychanges and the most importantclues come from seemingly unrelatedinvestigations. These sudden anddrastic changes of scene appear to beNature’s way of revealing the unityof all fundamental science.

The mystery began in the middleof the nineteenth century with thepuzzle: How does the Sun shine?Almost immediately, the plot shiftedto questions about how fast naturalselection occurs and the rate atwhich geological formations arecreated. One of the best theoretical

physicists of the nineteenth centurygave the wrong answer to all thesequestions. The fi rst hint of the cor-rect answer came, at the very endof the nineteenth century, from thediscovery of radioactivity with ac-cidentally darkened photographicplates.

The right direction in which tosearch for the detailed solution wasrevealed by the 1905 discovery of thespecial theory of relativity, by the1920 measurement of the nuclearmasses of hydrogen and helium, andby the 1928 quantum-mechanicalexplanation of how charged particlescan get close to one another. Thesecrucial investigations were notdirectly related to the study of stars.

By the middle of the twentieth cen-tury, nuclear physicists and astro-physicists could calculate theoreticallythe rate of nuclear burning in theinteriors of stars like the Sun. But, justwhen we thought we had Nature fi g-ured out, experiments showed thatfewer solar neutrinos were observed atEarth than were predicted by the stan-dard models of how stars shine andhow subatomic particles behave.

As the twenty-first century be-gins, we have learned that solar neu-trinos tell us not only about theinterior of the Sun, but also some-thing about the nature of neutrinosthemselves. No one knows whatsurprises will be revealed by the newsolar neutrino experiments currentlyunder way. The richness with whichNature has written her mystery, inan international language that can beread by curious people of all nations,is beautiful, awesome, and humbling.