Lessons from Kepler and the theory of everythingLincoln Wolfenstein*

Carnegie Mellon University, Pittsburgh, PA 15213

Contributed by Lincoln Wolfenstein, March 5, 2003

Johannes Kepler’s successes and failures provide lessons for re-ductionists seeking the theory of everything as well as for thosewho have proclaimed the end of reductionism.

In trying to describe how fundamental discoveries are made, thework of Johannes Kepler provides a wonderful example. In

contrast to present-day theoretical physics articles, which giveonly the conclusions, Kepler describes his process in agonizingdetail. Furthermore, looking from the present, his failures, evenmore than his successes, may provide an important lesson.

The struggle of Kepler to discover his first laws is described indetail with all the false starts and the near successes in his NewAstronomy (1, 2). The first two laws describe the orbits of theindividual planets. The third law he found only 9 years laterrelates the different orbits giving T2�R3 � constant, where T isthe period and R the semimajor axis. Kepler was motivated bysome idea that the motion of every planet depended on theinfluence of the sun.

Kepler’s three laws are the foundation stones of the Newto-nian synthesis. All the planetary motions are explained in termsof two simple equations: Newton’s second law and the universallaw of gravitational force inversely proportional to the square ofthe distance. Given the initial position and velocity of eachplanet, these two laws predict their positions and velocities forthe indefinite future. Of course, the further from the presenttime one goes, the more precisely those initial conditions mustbe specified and the greater the possibility of perturbations fromcomets, asteroids, etc., not originally considered.

The Newtonian synthesis is the model for the reductionistapproach to physics to explain all phenomena as based on afundamental set of interactions. In our present theoreticalframework there are four interactions: besides gravity there arethe electromagnetic, strong, and weak interactions. The latterthree are described by the ‘‘standard model’’ gange theory. Manyparticle theorists are striving to find the ‘‘final theory’’ or the‘‘theory of everything’’ that would define some single law thatwould unify all four interactions and perhaps even imply someinteractions yet unknown. Some string theorists believe they areon the threshold of discovery, whereas other theorists may only‘‘dream’’ of it (3).

There exist physicists, particularly those specializing in con-densed matter physics, who are very skeptical of, or indeed veryantagonistic toward, the reductionists. Their most vocal spokes-man has been Phil Anderson (4). Their views are summarized inan article titled ‘‘Theory of Everything’’ (5) by David Pines andR. B. Laughlin, who proclaim ‘‘the end of reductionism.’’

They believe that most everything of interest, with the exceptionof some esoteric particle physics experiments, involves systems oflarge numbers of particles. Starting with a fundamental theoryinvolving elementary particles one cannot directly calculate prop-erties of such systems. On the other hand, such complex systemsdisplay ‘‘emergent behavior’’ governed by ‘‘higher organizing prin-ciples’’ relatively independent of the fundamental theory. I willrefer to these physicists as ‘‘emergentists.’’

There was a problem that dominated Kepler much more thanthe problems solved by his three famous laws. He wanted to knowwhy there were just six planets in those particular orbits. Thisrequired some symmetry principle that gave order to the uni-verse following the Platonic–Pythagorean tradition. His first idea

was that the six orbits were determined by the five regular solidsof geometry. This he expounded in great detail in his first book,The Mysterium (6). His second idea was to add musical harmo-nies as expounded in the Harmony of the World (7), which justincidentally contains the third law.

From the reductionist point of view this question that sodominated Kepler was the wrong question. In the first place, ofcourse, there are now nine planets if you include Pluto, not tomention the asteroid belt. More importantly, this is a problemthat we believe has no simple answer. Our solar system wasformed 4.5 billion years ago from some whirling mass of gas,much of which ejected from the explosion of earlier stars. Theresulting sun and circling planets depend on the particular detailsof that original chaotic situation. In fact, we now believe theremay be hundreds of millions of ‘‘solar systems’’ in our own galaxy,each one differing from the other. In the last decade, we havedetected a large number of such planetary systems; thosedetectable thus far are very different from our own (see, forexample, ref. 8).

However, we may consider the development of the solar systemas an emergent phenomenon, and so it may be reasonable to lookfor some organizing principle. In fact, there exists stability criteriawhich limit the possibilities of a planetary system that could last for4.5 billion years. However, for systems in which the planets are allmuch lighter than the central star, these limitations are not veryrestrictive (see, for example, ref. 9). Neither the reductionists northe emergentists can solve Kepler’s problem.

When we start analyzing the world around us, we don’t knowwhich aspects will have a beautiful ‘‘simple’’ explanation andwhich will remain very complicated. Thus, the motions of theplanets and the moon and the moons of Jupiter are all explainedby Newton’s laws, but the ‘‘cast of characters’’ that is moving isnot explained.

It is interesting to look at our present fundamental physics withthe lessons from Kepler in mind. We believe that all physicalphenomena ultimately depend on the four fundamental inter-actions; however, these interactions affect a strange cast ofcharacters consisting of 12 fermions: 6 quarks, 3 charged leptons,and 3 neutrinos. They have a great range of masses from the tquark with a mass of 1011 eV (1 eV � 1.602 � 10�19 J) to theneutrinos with masses �1 eV. Many theorists are fascinated withexplaining this using symmetry principles (see, for example, ref.10 and references therein). These are usually taken from grouptheory rather than geometry or music. Is it possible that there isno simple solution to this problem?

Both in the case of Newton and present-day particle physics wehave a set of laws that allows us to make predictions given initialconditions. (Our predictions today are probability statements,but they became very accurate for large numbers of particles orrepeated observations.) We can even use these laws to gobackward in time. Thus, Newton could tell us quite accuratelythe positions of the planets 1 million years ago. However, it isimpossible in this way to track our planetary system 4.6 billionyears back in time, because then we are trying to recreate thevery complex formation of the solar system.

In modern cosmology, we also go backward in time. The trickhere is first to skip the complex stage of structure formation and

*E-mail: lincoln@cmuhep2.phys.cmu.edu.

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go back �14 billion years to an early stage of a plasma ofneutrons, protons, electrons, and neutrinos. Then it is possible touse the reductionist approach to calculate the consequences ofthe elementary particle and atomic processes going on in theearly universe. Using this approach Alpher, Herman, and Ga-mow (for a first-hand account, see ref. 11) predicted the exis-tence of a background of black-body radiation with a tempera-ture of a few degrees. This seemed such an extreme form ofreductionism that no one searched for this radiation; 15 yearslater it was discovered by accident by Penzias and Wilson (12).Over the last decade the cosmic microwave background radia-tion has been explored in wonderful detail. The results areunderstood in terms of fundamental physics (13).

One can go still farther back in time when the temperature ofthe universe was a few megaelectronvolts and, by analyzingelementary particle and nuclear reactions, successfully calculate(14) the relative abundances of hydrogen, helium, deuterium,and possibly even 7Li in the universe. Thus modern cosmologyallows us to trace the evolution of the entire universe from theformation of the first elements to the present day in terms of afew initial parameters. This exciting success of reductionismresembles that of Kepler and Newton in the 17th century. Theend of reductionism has been proclaimed prematurely.

The formation of structure in the universe emerged from thesmall initial matter fluctuations in the period between the forma-tion of hydrogen atoms and the present time. As we have notedabove, it is probably impossible to calculate the details of structuressuch as individual planetary systems. On the other hand, it is hopedthat some general features of the large-scale structure, such as thedistribution and sizes of galaxy clusters, could be understood. Thereductionists have engaged in huge simulations (see, for example,ref. 15) starting with the fluctuation spectrum revealed by micro-wave background studies and applying fundamental physical laws.Nevertheless, much important physics must be left out. Pines andLaughlin suggest that this is an emergent system subject to orga-nizing principles independent of the particle physics so that thelarge-scale structure ends up similar to ‘‘the structure of Styrofoam,popcorn or puffed cereal’’ (5).

In fact the simulations, despite their limitations, have dem-onstrated an important dependence on the particle physics. Thelarge-scale structure cannot be fit if the dark matter consists ofvery light particles similar to neutrinos, referred to as hot darkmatter, because the particles would be moving with large veloc-ities when structure formation began (16). What is requiredinstead seems to be cold dark matter consisting of some still-undiscovered heavy particles.

The reductionists will continue to increase the size of theirsimulations with the latest supercomputers, and yet many details ofthe physics must be omitted. The hope clearly is that once the majoringredients such as cold dark matter are determined, a pattern willbe seen to emerge that is independent of further details. Thesolution may require a collaboration of reductionists and emergen-tists, if they can be persuaded to talk with one another.

If one tries to go still farther back in time to an era when theenergies are measured in thousands of megaelectrovolts, therearises the problem that we might not know all the relevantfundamental laws. This troublesome but intriguing possibilityoften arises in the reductionist approach to astrophysics andcosmology. A recent example concerns the study of solar neu-trinos (17). The theory explaining the energy generation near thecenter of the sun in terms of a set of nuclear reactions predictedthat �3% of the energy would leave in the form of neutrinos thatcould penetrate the sun and arrive at the Earth in 8 min. A setof experiments pioneered by Raymond Davis (18), who won theNobel Prize in Physics in 2002, discovered these neutrinos,demonstrating the existence of the reactions, but the flux ofneutrinos was a factor 3 below the prediction. The proposedexplanation was a new feature of the fundamental physics that

resulted in the oscillation of two-thirds of the electron neutrinos(the type emitted by the sun and the type the experiments weremeasuring) into other types of neutrinos (muon and tau type,that were known to exist). During the last year the SudburyNeutrino Observatory experiment actually measured the flux ofthese other types (19) and indeed found that it was twice that ofthe electron type. Thus our theory of the source of solar energyreceived confirmation, and we also discovered some new aspectsof the fundamental physics.

One of the great problems of cosmology today is that itrequires that most of the matter in the universe consists of somenew, as-yet-undiscovered kind of particles (ref. 20 and referencestherein). The most popular theory is that these are the lightestof a new class of particles, additions to the cast of characters,called supersymmetric particles. If this is true, these particles willbe discovered by experiments at the Large Hadron Collider, alarge new accelerator to commence operation in 2007 at Euro-pean Center for Nuclear Research in Geneva.

Many new aspects of fundamental physics have been proposedthat affect the very early stages in the history of the universe. Oneexample is the origin of the baryon–antibaryon asymmetry: thevisible universe seems to contain matter made of protons andneutrons with practically no antiparticles, which would annihilatethem. If one assumes that at some initial stage the universe wassymmetric, there must have been some process that produced thisasymmetry. After the discovery of the violation of charge–conjugation–parity invariance, Sakharov (21) proposed that a re-action or a decay that violated this invariance and baryon numberin the early universe could have produced this asymmetry. A largenumber of models involving hypothetical new interactions and newparticles have been proposed (22). However, most of them cannever be tested directly in terrestrial experiments, because the newphysics is restricted to a very high energy scale.

Thus we come back to our lesson from Kepler. Does thisasymmetry have an explanation in terms of reductionist physics, oris it just part of the cast of characters that emerged from somechaotic state of the early universe? Indeed, it has been proposedthat from the initial chaos many universes evolved, each presumablydifferent from ours (see, for example, ref. 23). In some of theseperhaps antibaryons predominate, although presumably inhabit-ants of such a universe will label our baryons as the ‘‘anti’’ ones. Incontrast to the case of other solar systems, it seems very unlikely thatwe will ever detect any other universes even if they exist.

There is, however, at lease one selection criterion among themany possible planetary systems and the many possible uni-verses. The planet must in its temperature and composition behospitable to human life and the fundamental physics of theuniverse must allow for biological evolution. This is referred toas the ‘‘anthropic principle’’ and has been the subject of muchdebate and considerable scorn. Rees (23) refers to it as ‘‘an-thropic reasoning.’’ From the particle physicist’s reductionistpoint of view it provides no answer at all to the question, but froman earlier ‘‘teleological’’ tradition it might be considered theanswer. If ours is just one of a multitude of universes, that maybe the best we can do.

The lesson from Kepler is not that we must refrain from askingwhat seem to be fundamental questions; the lesson is that wecannot know whether there is any simple answer or where it maycome from. For the reductionist the lesson is that there may bemuch that will not be encompassed by their final theory: manyclasses of emergent phenomena. For the emergentist the lessonsare that (i) reductionism has been surprisingly successful inunderstanding the largest of many-body systems, our universe,and (ii) there may be emerging systems that cannot be under-stood simply by the use of their organizing principles.

I thank J. David Jackson, Stephen Brush, Joel Primack, and FreemanDyson for useful comments.

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Gesammelte Werke (Beck, Munich), Vol. 1.7. Kepler, J. (1619) Harmonice Mundi; reprinted in Kepler, J. (1937) Gesammelte

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E. W., Bercovitch, M., Bigu, J., Biller, S. D., Black, R. A., et al. (2002) Phys.Rev. Lett. 89, 011301.

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