SCIENCE AND SOCIETY
SCIENCE AND SOCIETY PHYS 216
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From the Dreams of a Final Theory by Steven Weinberg Physics Nobel prize 1979 CONTENTS PREFACE uv I PROLOGUE I II ON A PIECE OF CHALK 19 III TWO CHEERS FOR REDUCTIONISM 51 IV QUANTUM MECHANICS AND ITS DISCONTENTS 65 V TALES OF THEORY AND EXPERIMENT 90 VI BEAUTIFUL THEORIES VII AGAINST PHILOSOPHY 166 VIII TWENTIETH CENTURY BLUES 191 IX THE SHAPE OF A FINAL THEORY 211 X FACING FINALITY 230 XI WHAT ABOUT GOD XII DOWN IN ELLIS COUNTY 262 317 PERMISSIONS ACKNOWLEDGMENTS 335 CHAPTER II ON A PIECE OF CHALK FOOL The reason why the seven stars are no more than seven is a pretty reason LEAR Because they are not eight FOOL Yes indeed Thou wouldst make a good fool William Shakespeare King Lear cientists have discovered many peculiar things and many beautiful things But perhaps the most beautiful and the most peculiar thing that they have discovered is the pattern of science itself Our scientific discoveries are not independent isolated facts one scientific generalization finds its explanation in another which is itself explained by yet another By tracing these arrows of explanation back toward their source we have discovered a striking convergent patterniperhaps the deepest thing we have yet learned about the universe Consider a piece of chalk Chalk is a substance that is familiar to most people and especially familiar to physicists who talk to each other at blackboards but I use chalk as an example here because it was the subject of a polemic that is famous in the history of science In 1868 the British Association held its annual meeting in the large cathedral and county town of Norwich in the east of England It was an exciting time for the scientists and scholars gathered in Norwich Public attention was drawn to science not only because its importance to technology was becoming unmistakable but even more because science was changing the way that people thought about the world and their place in it Above all the publication of Darwin s On the Origin of Species by Means afNalural Selection nine years earlier had put science squarely in opposition to the dominant religion of the time Present at that meeting was Thom as Henry Huxleyidistinguished anatomist and fierce controversialist known to his contemporaries as Darwin s bulldog As was his usual practice Huxley took the opportunity to speak to the working men of the town The title of his lecture was On a Piece of Chalk I like to imagine Huxley standing at the podium actually holding up a piece of chalk perhaps dug from the chalk formations that underlie Norwich or borrowed from a friendly carpenter or professor He began by describing how the chalk layer hundreds of feet deep extends not only under much of England but also under Europe and the Levant all the way to central Asia The chalk is mostly a simple chemical carbonate of lime or in modern terms calcium carbonate but microscopic examination shows it to consist of countless fossil shells of tiny animals that lived in ancient seas that once covered Europe Huxley vividly described how over millions of years these little corpses drifted down to the sea bottom to be compressed into chalk and how caught here and there in the chalk are fossils of larger animals like crocodiles animals that appear increasingly different from their modern counterparts as we go down to deeper and deeper levels of chalk and so must have been evolving during the millions of years the chalk was being laid down Huxley was trying to convince the working men of Norwich that the world is much older than the six thousand years allowed by scholars of the Bible and that new living species have appeared and evolved since the beginning These issues are now long settledino one with any understanding of science would doubt the great age of the earth or the reality of evolution The point thatl want to make here has to do not with any specific items of scientific knowledge but with the way that they are all connected For this purpose I begin as Huxley did with a piece of chalk Chalk is white Why One immediate answer is that it is white because it is not any other color That is an answer that would have pleased Lear s fool but in fact it is not so far from the truth Already in Huxley s time it was known that each color of the rainbow is associated with light of a definite wavelengthilonger waves for light toward the red end of the spectrum and shorter waves toward the blue or violet White light was understood to be a jumble of light of many different wavelengths When light strikes an opaque substance like chalk only part of it is re ected the rest is absorbed A substance that is any definite color like the greenish blue of many compounds of copper eg the copper aluminum phosphates in turquoise or the violet of compounds of potassium has that color because the substance tends to absorb light strongly at certain wavelengths the color that we see in the light that the substance re ects is the color associated with light of the wavelengths that are not strongly absorbed For the calcium carbonate of which chalk is composed it happens that light is especially strongly absorbed only at infrared and ultraviolet wavelengths that are invisible anyway So light re ected from a piece of chalk has pretty much the same distribution of visible wavelengths as the light that illuminates it This is what produces the sensation of whiteness whether from clouds or snow or chalk Why Why do some substances strongly absorb visible light at particular wavelengths and others not The answer turns out to be a matter of the energies of atoms and of light This began to be understood with the work of Albert Einstein and Niels Bohr in the first two decades of this century As Einstein first realized in 1905 a ray of light consists of a stream of enormous numbers of particles later called photons Photons have no mass or electric charge but each photon has a definite energy inversely proportional to the light wavelength Bohr proposed in 1913 that atoms and molecules can exist only in certain definite slates stable configurations having certain definite energies Although atoms are often likened to little solar systems there is a crucial difference In the solar system any planet could be given a little more or less energy by moving it a little farther from or closer to the sun but the states of an atom are discreleiwe cannot change the energies of atoms except by certain definite amounts Normally an atom or molecule is in the state of lowest energy When an atom or molecule absorbs light it jumps from a state of lower energy to one of higher energy and vice versa when light is emitted Taken together these ideas of Einstein and Bohr tell us that light can be absorbed by an atom or molecule only if the wavelength of the light has one of certain definite values These are the wavelengths that correspond to photon energies that are just equal to the difference in energy between the normal state of the atom or molecule and one of its states of higher energy Otherwise energy would not be conserved when the photon is absorbed by the atom or molecule Typical copper compounds are greenish blue because there is a particular state of the copper atom with an energy 2 volts higher than the energy of the normal state of the atom and that is exceptionally easy for the atom to jump to by absorption of a photon with an energy of 2 volts Note A volt when used as a unit of energy is defined as the energy given to one electron when pushed through a wire by a lvolt electric battery When used in this way it should more properly be termed an electron volt but as is common in physics 1 will just call it a volt A micron is a millionth of a meter Such a photon has a wavelength of 062 microns corresponding to a reddish orange color so the absorption of these photons leaves the remaining reflected light greenish blue This is not just an awkward way of restating that these compounds are greenish blue39 we see the same pattern of atomic energies when we give energy to the copper atom in different ways as eg with a beam of electrons Chalk is white because the molecules of which it is composed do not happen to have any state that is particularly easy to jump to by absorbing photons of any color of visible light Why Why do atoms and molecules come in discrete states each with a definite energy Why are these ener y values what they are Why does light come in individual particles each with an energy inversely proportional to the wavelength of the light And why are some states of atoms or molecules particularly easy to jump to by absorption of photons It was not possible to understand these properties of light or atoms or molecules until the development in the mid1920s of a new framework for physics known as quantum mechanics The particles in an atom or molecule are described in quantum mechanics by what is called a wave function A wave function behaves somewhat like a wave of light or sound but its magnitude actually its magnitude squared gives the probability of finding the particles at any given location Just as air in an organ pipe can vibrate only in certain definite modes of vibration each with its own wavelength so also the wave function for the particles in an atom or molecule can appear only in certain modes or quantum states each with its own energy When the equations of quantum mechanics are applied to the copper atom it is found that one of the electrons in a highenergy outer orbit of the atom is loosely bound and can easily be boosted by absorption of visible light up to the next highest orbit Quantummechanical calculations show that the energies of the atom in these two states differ by 2 volts equal to the energy of a photon of reddish orange light Note In a metal these outer electrons leave the individual atoms and flow between them so there is no special tendency for metallic copper to absorb photons of orange light which is why it is not greenish blue On the other hand the molecules of calcium carbonate in a piece of chalk do not happen to have any similarly loose electrons that could absorb photons of any particular wave length As to photons their properties are explained by applying the principles of quantum mechanics in a similar way to light itself It turns out that light like atoms can exist only in certain quantum states of definite energy For instance reddish orange light with a wavelength of 062 microns can exist only in states with energies equal to zero or 2 volts or 4 volts or 6 volts and so on which we interpret as states containing zero or one or two or three or more photons each photon with an energy of just 2 volts Why Why are the quantummechanical equations that govern the particles in atoms what they are Why does matter consist of these particles the electrons and the atomic nuclei For that matter why is there such a thing as light Most of these things were rather mysterious in the 1920s and 1930s when quantum mechanics was first applied to atoms and light and have only become reasonably well understood in the last fifteen years or so with the success of what is called the standard model of elementary particles and forces A key precondition for this new understanding was the reconciliation in the 1940s of quantum mechanics with the other great revolution in twentiethcentury physics Einstein s theory of relativity The principles of relativity and quantum mechanics are almost incompatible with each other and can coexist only in a limited class of theories In the nonrelativistic quantum mechanics of the 1920s we could imagine almost any kind of force among electrons and nuclei but as we shall see this is not so in a relativistic theory forces between particles can arise only from the exchange of other particles Furthermore all these particles are bundles of the energy or quanta of various sorts of fields A field like an electric or magnetic field is a sort of stress in space something like the various sorts of stress that are possible within a solid body but a field is a stress in space itself There is one type of field for each species of elementary particle there is an electron field in the standard model whose quanta are electrons there is an electromagnetic field consisting of electric and magnetic fields whose quanta are the photons there is no field for atomic nuclei or for the particles known as protons and neutrons of which the nuclei are composed but there are fields for various types of particles called quarks out of which the proton and neutron are composed39 and there are a few other fields I need not go into now The equations of a field theory like the standard model deal not with particles but with fields the particles appear as manifestations of these fields The reason that ordinary matter is composed of electrons protons and neutrons is simply that all the other massive particles are violently unstable The standard model qualifies as an explanation because it is not merely what computer hackers call a kludge an assortment of odds and ends thrown together in whatever way works Rather the structure of the standard model is largely fixed once one specifies the menu of fields that it should contain and the general principles like the principles of relativity and quantum mechanics that govern their interactions Why Why does the world consist of just these fields the fields of the quarks electron photon and so on Why do they have the properties assumed in the standard model And for that matter why does nature obey the principles of relativity and quantum mechanics Sorryithese questions are still unanswered Commenting on the present status of physics the Princeton theorist David Gross gave a list of open questions Now that we understand how it works we are beginning to ask why are there quarks and leptons why is the pattern of matter replicated in three generations of quarks and leptons why are all forces due to local gauge symmetries Why why why Terms used in Gross s list of whys are explained in later chapters It is the hope of answering these questions that makes elementary particle physics so exciting The word why is notoriously slippery The philosopher Ernest Nagel lists ten examples of questions in which why is used in ten different senses such as Why does ice float on water Why did Cassius plot the death of Caesar and Why do human beings have lungs Other examples in which why is used in yet other senses come immediately to mind such as Why wasl born Here my use of why is something like its use in the question Why does ice oat on water and is not intended to suggest any sense of conscious purpose Even so it is a tricky business to say exactly what one is doing when one answers such a question Fortunately it is not really necessary Scientific explanation is a mode of behavior that gives us pleasure like love or art The best way to understand the nature of scientific explanation is to experience the peculiar Zing that you get when someone preferably yourself has succeeded in actually explaining something I do not mean that scientific explanation can be pursued without any constraints any more than can love or art In all three cases there is a standard of truth that needs to be respected though of course truth takes different meanings in science or love or art I also do not mean to say that it is not of any interest to try to formulate some general description of how science is done only that this is not really necessary in the work of science any more than it is in love or art As 1 have been describing it scientific explanation clearly has to do with the deduction of one truth from another But there is more to explanation than deduction and also less Merely deducing one statement from another does not necessarily constitute an explanation as we see clearly in those cases where either statement can be deduced from the other Einstein inferred the existence of photons in 1905 from the successful theory of heat radiation that had been proposed five years earlier by Max Planck seventeen years later Satyendra Nath Bose showed that Planck s theory could be deduced from Einstein s theory of photons Explanation unlike deduction carries a unique sense of direction We have an overwhelming sense that the photon theory of light is more fundamental than any statement about heat radiation and is therefore the explanation of the properties of heat radiation And in the same way although Newton derived his famous laws of motion in part from the earlier laws of Kepler that describe the motion of planets in the solar system we say that Newton s laws explain Kepler s not the other way around Talk of more fundamental truths makes philosophers nervous We can say that the more fundamental truths are those that are in some sense more comprehensive but about this too it is difficult to be precise But scientists would be in a bad way if they had to limit themselves to notions that had been satisfactorily formulated by philosophers No working physicist doubts that Newton s laws are more fundamental than Kepler s or that Einstein s theory of photons is more fundamental than Planck s theory of heat radiation A scientific explanation can also be something less than a deduction for we may say that a fact is explained by some principle even though we cannot deduce it from that principle Using the rules of quantum mechanics we can deduce various properties of the simpler atoms and molecules and even estimate the energy levels of complicated molecules like the calciumcarbonate molecules in chalk The Berkeley chemist Henry Shaefer reports that when stateoftheart theoretical methods are intelligently applied to many problems involving molecules as large as naphthalene the results may be treated in the same way that one treats reliable experiments But no one actually solves the equations of quantum mechanics to deduce the detailed wave function or the precise energy of really complicated molecules such as proteins Nevertheless we have no doubt that the rules of quantum mechanics explain the properties of such molecules This is partly because we can use quantum mechanics to deduce the detailed properties of simpler systems like hydrogen molecules and also because we have mathematical rules available that would allow us to calculate all the properties of any molecule to any desired precision if we had a large enough computer and enough computer time We may even say that something is explained even where we have no assurance that we will ever be able to deduce it Right now we do not know how to use our standard model of elementary particles to calculate the detailed properties of atomic nuclei and we are not certain that we will ever know how to do these calculations even with unlimited computer power at our disposal This is because the forces in nuclei are too strong to allow the sort of calculational techniques that work for atoms or molecules Nevertheless we have no doubt that the properties of atomic nuclei are what they are because of the known principles of the standard model This because does not have to do with our ability actually to deduce anything but reflects our view of the order of nature Ludwig Wittgenstein denying even the possibility of explaining any fact on the basis of any other fact warned that at the basis of the whole modern view of the world lies the illusion that the socalled laws of nature are the explanations of natural phenomena Such warnings leave me cold To tell a physicist that the laws of nature are not explanations of natural phenomena is like telling a tiger stalking prey that all esh is grass The fact that we scientists do not know how to state in a way that philosophers would approve what it is that we are doing in searching for scientific explanations does not mean that we are not doing something worthwhile We could use help from professional philosophers in understanding what it is that we are doing but with or without their help we shall keep at it We could follow a similar chain of whys for each physical property of chalkiits brittleness its density its resistance to the flow of electricity But let s try to enter the labyrinth of explanation through a different dooriby considering the chemistry of chalk As Huxley said chalk is mostly carbonate of lime or in modern terms calcium carbonate Huxley did not say so but he probably knew that this chemical consists of the elements calcium carbon and oxygen in the fixed proportions by weight 40 12 and 48 respectively Why Why do we find a chemical compound of calcium carbon and oxygen with just these proportions but not many others with many other proportions The answer was worked out by chemists in the nineteenth century in terms of a theory of atoms actually before there was any direct experimental evidence of the existence of atoms The weights of the calcium carbon and oxygen atoms are in the ratios 40 1216 and a calciumcarbonate molecule consists of one atom of calcium one atom of carbon and three atoms of oxygen so the weights of calcium carbon and oxygen in calcium carbonate are in the ratios 401248 Why Why do the atoms of various elements have the weights that we observe and why do molecules consist of just certain numbers of atoms of each type The numbers of atoms of each type in molecules like calcium carbonate were already known in the nineteenth century to be a matter of the electric charges that the atoms in the molecule exchange with each other In 1897 it was discovered by J J Thomson that these electric charges are carried by negatively charged particles called electrons particles that are much lighter than whole atoms and that flow through wires in ordinary electric currents One element is distinguished from another solely by the number of electrons in the atom one for hydrogen six for carbon eight for oxygen twenty for calcium and so on When the rules of quantum mechanics are applied to the atoms of which chalk is composed it is found that calcium and carbon atoms readily give up two and four electrons respectively and that oxygen atoms easily pick up two electrons Thus the three atoms of oxygen in each molecule of calcium carbonate can pick up the six electrons contributed by one atom of calcium and one atom of carbon39 there are just enough electrons to go around It is the electric force produced by this transfer of electrons that holds the molecule together What about the atomic weights We have known since the work of Rutherford in 1911 that almost all of the mass or weight of the atom is contained in a small positively charged nucleus around which the electrons revolve After some confusion it was finally realized in the 1930s that atomic nuclei consist of two kinds of particles with nearly the same mass protons with positive electric charge equal in magnitude to the electron s negative charge and neutrons with no charge at all The hydrogen nucleus is just one proton The number of protons must equal the number of electrons in order to keep the atom electrically neutral and neutrons are needed because the strong attraction between protons and neutrons is essential in holding the nucleus together Neutrons and protons have nearly the same weight and electrons weigh much less so to a very good approximation the weight of an atom is simply proportional to the total number of protons and neutrons in its nucleus one a proton for hydrogen twelve for carbon sixteen for oxygen and forty for calcium corresponding to the atomic weights known but not yet understood in Huxley s time Why Why is there a neutron and a proton one neutral and one charged both with about the same mass and much heavier than the electron Why do they attract each other with such a strong force that they form atomic nuclei about a hundred thousand times smaller than the atoms themselves We find the explanation again in the details of our present standard model of elementary particles The lightest quarks are called the u and d for up and down and have charges 23 and 13 respectively in units where the electron s charge is taken as i l protons consist of two u s and a d and hence have charge 2323l3 l39 neutrons consist of one u and two d s and hence have charge 2313 13 0 The proton and neutron masses are nearly equal because these masses arise mostly from strong forces that hold the quarks together and these forces are the same for u and d quarks The electron is much lighter because it does not feel these strong forces All these quarks and electrons are bundles of the energy of various fields and their properties follow from the properties of these fields So here we are again at the standard model Indeed any questions about the physical and chemical properties of calcium carbonate lead us in much the same way through a chain of whys down to the same point 0 convergence to our present quantummechanical theory of elementary particles the standard model But physics and chemistry are easy How about something tougher like biology Our piece of chalk is not a perfect crystal of calcium carbonate but it is also not a disorganized mess of individual molecules like a gas Rather as Huxley explained in his talk in Norwich chalk is composed of the skeletons of tiny animals who absorbed calcium salts and carbon dioxide from ancient seas and used these chemicals as raw materials to build little shells of calcium carbonate around their soft bodies It takes no imagination to see why this was to their advantageithe sea is not a safe place for unprotected morsels of protein But this does not in itself explain why plants and animals develop organs like calcium carbonate shells that help them survive39 needing is not the same as getting The key was provided by the work of Darwin and Wallace that Huxley did so much to popularize and defend Living things display inheritable variationsisome helpful and some noti but it is the organisms that happen to carry helpful variations that tend to survive and pass these characteristics on to their offspring But why are there variations and why are they inheritable This was finally explained in the 1940s in terms of the structure of a very large molecule DNA that serves as a template for assembling proteins out of amino acids The DNA molecule forms a double helix that stores genetic information in a code based on the sequence of chemical units along the two strands of the helix Genetic information is propagated when the double helix splits and each of its two strands assembles a copy of itself39 inheritable variations occur when some accident disturbs the chemical units making up the strands of the helix Once down to the level of chemistry the rest is relatively easy True DNA is too complicated to allow us to use the equations of quantum mechanics to work out its structure But the structure is understood well enough through the ordinary rules of chemistry and no one doubts that with a large enough computer we could in principle explain all the properties of DNA by solving the equations of quantum mechanics for electrons and the nuclei of a few common elements whose properties are explained in turn by the standard model So again we find ourselves at the same point of convergence of our arrows of explanation I have papered over an important difference between biology and the physical sciences the element of history If by chalk we mean the material of the white cliffs of Dover or the thing in Huxley s hand then the statement that chalk is 40 calcium 12 carbon and 48 oxygen must find its explanation in a mixture of the universal and the historical including accidents that occurred in the history of our planet or in the life of Thomas Huxley The propositions that we can hope to explain in terms of the final laws of nature are those about universals One such universal is the statement that at sufficiently low temperatures and pressures there exists a chemical compound consisting of precisely these proportions of calcium carbon and oxygen We think that such statements are true everywhere in the universe and throughout all time In the same way we can make universal propositions about the properties of DNA but the fact that there are living creatures on earth that use DNA to pass on random variations from one generation to the next depends on certain historical accidents there is a planet like the earth39 life and genetics somehow got started39 and a long time has been available for evolution to do its work Biology is not unique in involving this element of history The same is true of many other sciences such as geology and astronomy Suppose we pick up our piece of chalk one more time and ask why there is enough calcium carbon and oxygen here on earth to provide raw materials for the fossil shells that make up chalk That is easyithese elements are common throughout most of the universe But why is that Again we must appeal to a blend of history and universal principles Using the standard model of elementary particles we know how to follow the course of nuclear reactions in the standard bigbang theory of the universe well enough to be able to calculate that the matter formed in the first few minutes of the universe was about threequarters hydrogen and onequarter helium with only a trace of other elements chie y very light ones like lithium This is the raw material out of which heavier elements were later formed in stars Calculations of the subsequent course of nuclear reactions in stars show that the elements that are most abundantly produced are those whose nuclei are most tightly bound and these elements include carbon oxygen and calcium The stars dump this material into the interstellar medium in various ways in stellar winds and supernova explosions and it is out of this medium rich in the constituents of chalk that secondgeneration stars like the sun and their planets were formed But this scenario still depends on a historical assumptionithat there was a moreorless homogeneous big bang with about ten billion photons for every quark Efforts are being made to explain this J 39 in various p lath 39 theories but these theories rest in turn on other historical assumptions It is not clear whether the universal and the historical elements in our sciences will remain forever distinct In modern quantum mechanics as well as in Newtonian mechanics there is a clear separation between the conditions that tell us the initial state of a system whether the system is the whole universe or just a part of it and the laws that govern its subsequent evolution But it is possible that eventually the initial conditions will appear as part of the laws of nature One simple example of how this is possible is provided by what is called the steadystate cosmology proposed in the late 1940s by Herman Bondi and Thomas Gold and in a rather different version by Fred Hoyle In this picture although the galaxies are all rushing apart from each other a fact often expressed in the somewhat misleading statement that the universe is expanding Note It is misleading to say that the universe is expanding because solar systems and galaxies are not expanding and space itself is not expanding The galaxies are rushing apart in the way that any cloud of particles will rush apart once they are set in motion away from each other New matter is continually being created to fill up the expanding intergalactic voids at a rate that just manages to keep the universe looking always the same We do not have a believable theory of how this continual creation of matter might take place but it is plausible that if we did have such a theory we might be able to use it to show that the expansion of the universe tends to an equilibrium rate at which creation just balances expansion like the way that prices are supposed to adjust themselves until supply equals demand In such a steadystate theory there are no initial conditions because there is no beginning and instead we can deduce the appearance of the universe from the condition that it does not change The original version of the steadystate cosmology has been pretty well ruled out by various astronomical observations chief among them the discovery in 1964 of microwave radiation that seems to be left over from a time when the universe was much hotter and denser It is possible that the steadystate idea may be revived on a grander scale in some future cosmological theory in which the present expansion of the universe appears as merely a fluctuation in an eternal but constantly fluctuating universe that on average is always the same There are also more subtle ways that the initial conditions might perhaps some day be deduced from the final laws James Hartle and Stephen Hawking have proposed one way that this fusion of physics and history might be found in the application of quantum mechanics to the whole universe Quantum cosmology is right now a matter of active controversy among theorists the conceptual and mathematical problems are very difficult and we do not seem to be moving toward any definite conclusions In any case even if the initial conditions of the universe can ultimately be incorporated in or deduced from the laws of nature as a practical matter we will never be able to eliminate the accidental and historical elements of sciences like biology and astronomy and geology Stephen Gould has used the weird fossils of the Burgess Shale in British Columbia to illustrate how little inevitability there is in the pattern of biological evolution on earth Even a very simple system can exhibit a phenomenon known as chaos that defeats our efforts to predict the system s future A chaotic system is one in which nearly identical initial conditions can lead after a while to entirely different outcomes The possibility of chaos in simple systems has actually been known since the beginning of the century the mathematician and physicist Henri Poincare showed then that chaos can develop even in a system as simple as a solar system with only two planets The dark gaps in the rings of Saturn have been understood for many years to occur at just those positions in the rings from which any orbiting particles would be ejected by their chaotic motion What is new and exciting about the study of chaos is not the discovery that chaos exists but that certain kinds of chaos exhibit some nearly universal properties that can be analyzed mathematically The existence of chaos does not mean that the behavior of a system like Saturn s rings is somehow not completely determined by the laws of motion and gravitation and its initial conditions but only that as a practical matter we can not calculate how some things such as particle orbits in the dark gaps in Saturn s rings evolve To put this a little more precisely the presence of chaos in a system means that for any given accuracy with which we specify the initial conditions there will eventually come a time at which we lose all ability to predict how the system will behave but it is still true that however far into the future we want to be able to predict the behavior of a physical system governed by Newton s laws there is some degree of accuracy with which a measurement of the initial conditions would allow us to make this prediction It is like saying that although any automobile that keeps going will eventually run out of gasoline no matter how much we put in the tank still no matter how far we want to go there is always some amount of gasoline that would get us there In other words the discovery of chaos did not abolish the determinism ofprequantum physics but it did force us to be a bit more careful in saying what we mean by this determinism Quantum mechanics is not deterministic in the same sense as Newtonian mechanics Heisenberg s uncertainty principle warns that we cannot measure the position and velocity of a particle precisely at the same time and even if we make all of the measurements that are possible at one time we can predict only probabilities about the results of experiments at any later time Nevertheless we shall see that even in quantum mechanics there is still a sense in which the behavior of any physical system is completely determined by its initial conditions and the laws of nature Of course whatever determinism survives in principle does not help us very much when we have to deal with real systems that are not simple like the stock market or life on earth The intrusion of historical accidents sets permanent limits on what we can ever hope to explain Any explanation of the present forms of life on earth must take into account the extinction of the dinosaurs sixtyfive million years ago which is currently explained by the impact of a comet but no one will ever be able to explain why a comet happened to hit the earth at just that time The most extreme hope for science is that we will be able to trace the explanations of all natural phenomena to final laws and historical accidents The intrusion of historical accidents into science means also that we have to be careful what sort of explanations we demand from our final laws For instance when Newton first proposed his laws of motion and gravitation the objection was raised that these laws did not explain one of the outstanding regularities of the solar system that all the planets are going around the sun in the same direction Today we understand that this is a matter of history The way that the planets revolve around the sun is a consequence of the particular way that the solar system con densed out of a rotating disk of gas We would not expect to be able to deduce it from the laws of motion and gravitation alone The separation of law and history is a delicate business one we are continually learning how to do as we go along Not only is it possible that what we now regard as arbitrary initial conditions may ultimately be deduced from universal lawsiit is also conversely possible that principles that we now regard as universal laws will eventually turn out to represent historical accidents Recently a number of theoretical physicists have been playing with the idea that what we usually call the universe the expanding cloud of galaxies that extends in all directions for at least ten billion light years is merely a subuniverse a small part of a much larger megauniverse consisting of many such parts in each of which what we call the constants of nature the electric charge of the electron the ratios of elementary particle masses and so on may take different values Perhaps even what we now call the laws of nature will be found to vary from one subuniverse to another In that case the explanation for the constants and laws that we have discovered may involve an irreducible historical element the accident that we are in the particular subuniverse we inhabit But even if there turns out to be something in these ideas I do not think that we will have to give up our dreams of discovering final laws of nature the final laws would be megalaws that determine the probabilities of being in different types of subuniverse Sidney Coleman and others have already made brave steps toward calculating these probabilities by applying quantum mechanics to the whole megauniverse I should stress that these are very speculative ideas not fully formulated mathematically and so far without experimental support I have so far confessed to two problems in the notion of chains of explanation that lead down to final laws the intrusion of historical accidents and the complexity that prevents our being actually able to explain everything even when we consider only universals free of the element of history There is one other problem that must be confronted one associated with the buzzword emergence As we look at nature at levels of greater and greater complexity we see phenomena emerging that have no counterpart at the simpler levels least of all at the level of the elementary particles For instance there is nothing like intelligence on the level of individual living cells and nothing like life on the level of atoms and molecules The idea of emergence was well captured by the physicist Philip Anderson in the title of a 1972 article More Is Different The emergence of new phenomena at high levels of complexity is most obvious in biology and the behavioral sciences but it is important to recognize that such emergence does not represent something special about life or human affairs it also happens within physics itself The example of emergence that has been historically most important in physics is thermodynamics the science of heat As originally formulated in the nineteenth century by Carnot Clausius and others thermodynamics was an autonomous science not deduced from the mechanics of particles and forces but built on concepts like entropy and temperature that have no counterparts in mechanics Only the first law of thermodynamics the conservation of energy provided a bridge between mechanics and thermodynamics The central principle of thermodynamics was the second law according to which in one formulation physical systems possess not only an energy and a temperature but also a certain quantity called entropy which always increases with time in any closed system and reaches a maximum when the system is in equilibrium This is the principle that forbids the Pacific Ocean from spontaneously transferring so much heat energy to the Atlantic that the Pacific freezes and the Atlantic boils such a cataclysm need not violate the conservation of energy but it is forbidden because it would decrease the entropy Nineteenthcentury physicists generally took the second law of thermodynamics as an axiom derived from experience as fundamental as any other law of nature At the time this was not unreasonable Thermodynamics was seen to work in vastly different contexts from the behavior of steam the problem that gave thermodynamics its start to freezing and boiling and chemical reactions Today we would add more exotic examples astronomers have discovered that the clouds of stars in globular clusters in our own and other galaxies behave like gases with definite temperatures and the work of Jacob Bekenstein and Hawking has shown theoretically that a black hole has an entropy proportional to its surface area If thermodynamics is this universal how can it be logically related to the physics of specific types of particles and forces Then in the second half of the nineteenth century the work of a new generation of theoretical physicists including Maxwell in Scotland Ludwig Boltzmann in Germany and Josiah Willard Gibbs in America showed that the principles of thermodynamics could in fact be deduced mathematically by an analysis of the probabilities of different configurations of certain kinds of system those systems whose energy is shared among a very large number of subsystems as for instance a gas whose energy is shared among the molecules of which it is composed Ernest Nagel gave this as a paradigmatic example of the reduction of one theory to another In this statistical mechanics the heat energy of a gas is just the kinetic energy of its particles the entropy is a measure of the disorder of the system39 and the second law of thermodynamics expresses the tendency of isolated systems to become more disorderly The flow of all the heat of the oceans into the Atlantic would represent an increase of order which is why it does not happen For a while during the 1880s and 1890s a battle was fought between the supporters of the new statistical mechanics and those like Planck and the chemist Wilhelm Ostwald who continued to maintain the logical independence of thermodynamics Ernst Zermelo went even further and argued that because on the basis of statistical mechanics the decrease of entropy would be very unlikely but not impossible the assumptions about molecules on which statistical mechanics is based must be wrong This battle was won by statistical mechanics after the reality of atoms and molecules became generally accepted early in this century Nevertheless even though thermodynamics has been explained in terms of particles and forces it continues to deal wit emergent concepts like temperature and entropy that lose all meaning on the level of individual particles Thermodynamics is more like a mode of reasoning than a body of universal physical law wherever it applies it always allows us to justify the use of the same principles but the explanation of why thermodynamics does apply to any particular system takes the form of a deduction using the methods of statistical mechanics from the details of what the system contains and this inevitably leads us down to the level of the elementary particles In terms of the image of arrows of explanation thatl invoked earlier we can think of thermodynamics as a certain pattern of arrows that occurs again and again in very different physical contexts but wherever this pattern of explanation oc curs the arrows can be traced back by the methods of statistical mechanics to deeper laws and ultimately to the principles of elementary particle physics As this example shows the fact that a scientific theory finds applications to a wide variety of different phenomena does not imply anything about the autonomy of this theory from deeper physical laws The same maxim applies to other areas of physics such as the related topics of chaos and turbulence Physicists working in these areas have found certain patterns of behavior that occur again and again in very different contexts for instance there is thought to be a universality of a sort in the distribution of energy in eddies of various size in turbulent uids of all sorts from the turbulence of the tidal ow in Puget Sound to the turbulence in the interstellar gas produced by a passing star But not all uid ows are turbulent and turbulence when it occurs does not always exhibit these universal properties Whatever the mathematical reasoning that accounts for the universal properties of turbulence we still have to explain why this reasoning should apply to any particular turbulent uid and this question inevitably will be answered in terms of accidents the speed of the tidal ow and the shape of the channel and universals the laws of uid motion and the properties of water that in turn must be explained in terms of deeper laws Similar remarks apply to biology Here most of what we see depends on historical accidents but there are some roughly universal patterns like the rule of population biology that dictates that males and females tend to be born in equal numbers In 1930 the geneticist Ronald Fisher explained that once a species develops a tendency to produce say more males than females any gene that gives individuals a tendency to produce more females than males spreads through the population because the female offspring of individuals carrying this gene encounter less competition in finding a mate Rules like this apply to a wide variety of species and might be expected to apply even to life discovered on other planets if it reproduced sexually The reasoning that leads to these rules is the same whether it is applied to humans or birds or extraterrestrials but the reasoning always rests on certain assumptions about the organisms involved and if we ask why these assumptions should be found to be correct we must seek the answer partly in terms of historical accidents and partly in terms of universals like the properties of DNA or whatever takes its place on other planets that must in turn find their explanation in physics and chemistry and hence in the standard model of elementary particles This point tends to get obscured because in the actual work of thermodynamics or uid dynamics or population biology scientists use languages that are special to their own fields speaking of entropy or eddies or reproductive strategies and not the language of elementary particles This is not only because we are unable to use our first principles actually to calculate complicated phenomena39 it is also a re ection of the sort of question we want to ask about these phenomena Even if we had an enormous computer that could follow the history of every elementary particle in a tidal ow or a fruit y this mountain of computer printout would not be of much use to someone who wanted to know whether the water was turbulent or the y was alive There is no reason to suppose that the convergence of scientific explanations must lead to a convergence of scientific methods Thermodynamics and chaos and population biology will each continue to operate with its own language under its own rules whatever we learn about the elementary particles As the chemist Roald Hoffman says Most of the useful concepts of chemistry are imprecise When reduced to physics they tend to disappear In an attack on those who seek to reduce chemistry to physics Hans Primas listed some of the useful concepts of chemistry that were in danger of being lost in this reduction valence bond structure localized orbitals arom aticity acidity color smell and water repellency I see no reason why chemists should stop speaking of such things as long as they find it useful or interesting But the fact that they continue to do so does not cast doubt on the fact that all these notions of chemistry work the way they do because of the underlying quantum mechanics of electrons protons and neutrons As Linus Pauling puts it There is no part of chemistry that does not depend in its fundamental theory upon quantum principles Of all the areas of experience that we try to link to the principles of physics by arrows of explanation it is consciousness that presents us with the greatest difficulty We know about our own conscious thoughts directly without the intervention of the senses so how can consciousness ever be brought into the ambit of physics and chemistry The physicist Brian Pippard who held Maxwell s old chair as Cavendish Professor at the University of Cambridge has put it thus What is surely impossible is that a theoretical physicist given unlimited computing power should deduce from the laws of physics that a certain complex structure is aware of its own exrstence l have to confess thatl find this issue terribly difficult and l have no special expertise on such matters Butl thinkl disagree with Pippard and the many others who take the same position It is clear that there is what a literary critic might call an objective correlative to consciousness there are physical and chemical changes in my brain and body thatl observe to be correlated either as cause or effect with changes in my conscious thoughts ltend to smile when pleased39 my brain shows different electrical activity whenl am awake or asleep39 powerful emotions are triggered by hormones in my blood39 and I sometimes speak my thoughts These are not consciousness itself39 I can never express in terms of smiles or brain waves or hormones or words what it feels like to be happy or sad But setting consciousness to one side for a moment it seems reasonable to suppose that these objective correlatives to consciousness can be studied by the methods of science and will eventually be explained in terms of the physics and chemistry of the brain and body By explained I do not necessarily mean that we will be able to predict everything or even very much but that we will understand why smiles and brain waves and hormones work the way they do in the same sense that although we cannot predict next month s weather still we understand why the weather works the way it does In Pippard s own Cambridge there is a group of biologists headed by Sydney Brenner who have completely worked out the wiring diagram of the nervous system of a small nematode worm C elegans so that they already have a basis for understanding in some sense everything about why that worm behaves the way it does What is lacking so far is a program based on this wiring diagram that can generate the worm s observed behavior Of course a worm is not a human But between a worm and a human there is a continuum of animals with increasingly complex nervous systems spanning insects and fishes and mice and apes Where is one to draw the line Suppose then that we will come to understand the objective correlatives to consciousness in terms of physics including chemistry and that we will also understand how they evolved to be what they are It is not unreasonable to hope that when the objective correlatives to consciousness have been explained somewhere in our explanations we shall be able to recognize something some physical system for processing information that corresponds to our experience of consciousness itself to what Gilbert Ryle has called the ghost in the machine That may not be an explanation of consciousness but it will be pretty close There is no guarantee that progress in other fields of science will be assisted directly by anything new that is discovered about the elementary particles But I repeat and not for the last time I am concerned here not so much with what scientists do because this inevitably re ects both hum an limitations and human interests as I am with the logical order built into nature itself It is in this sense that branches of physics like thermodynamics and other sciences like chemistry and biology may be said to rest on deeper laws and in particular on the laws of elementary particle physics In speaking here of a logical order of nature I have been tacitly taking what a historian of philosophy would call a realist positionirealist not in the everyday modern sense of being hardheaded and without illusions but in a much older sense of believing in the reality of abstract ideas A medieval realist believed in the reality of universals like Plato s forms in opposition to nominalists like William of Ockham who declared them to be mere names My use of the word realist would have pleased one of my favorite authors the Victorian George Gissing who wished that the words realism and realist might never again be used save in their proper sense by writers on scholastic philosophy I certainly do not want to enter this debate on the side of Plato My argument here is for the reality ofthe laws ofnature in opposition to the modern positivists who accept the reality only of that which can be directly observed When we say that a thing is real we are simply expressing a sort of respect We mean that the thing must be taken seriously because it can affect us in ways that are not entirely in our control and because we cannot learn about it without making an effort that goes beyond our own imagination This much is true for instance of the chair on whichl sit to take a favorite example of philosophers and does not so much constitute evidence that the chair is real but is rather just what we mean when we say that the chair is real As a physicistl perceive scientific explanations and laws as things that are what they are and cannot be made up as I go along so my relation to these laws is not so different from my relation to my chair and I therefore accord the laws of nature to which our present laws are an approximation the honor of being real This impression is reinforced when it turns out that some law of nature is not what we thought it was an experience similar to finding that a chair is not in place when one sits down But I have to admit that my willingness to grant the title of real is a little like Lloyd George s willingness to grant titles of nobility39 it is a measure of how little difference I think the title makes This discussion of the reality of the laws of nature might become less academic if we made contact with other intelligent beings on distant planets who had also worked out scientific explanations for natural phenomena Would we find that they had discovered the same laws of nature Whatever laws were discovered by extraterrestrials would naturally be expressed in different language and notation but we could still ask whether there is some sort of correspondence between their laws and our laws If so it would be hard to deny the objective reality of these laws Of course we do not know what the answer would be but here on earth we have already seen a small scale test of a similar question What we call modern physical science happened to get started in Europe at the end of the sixteenth century Those who doubt the reality of the laws of nature might have guessed that just as other parts of the world have kept their own languages and religions so they would also have kept their own scientific traditions eventually developing laws of physical science completely different from those of Europe Of course that did not happen the physics of modern Japan and India is the same as that ofEurope and America I admit that this argument is not entirely convincing because the whole world has been profoundly influenced by other aspects of Western civilization from military organization to blue jeans Nevertheless the experience of listening to a discussion of quantum field theory or weak interactions in a seminar room in Tsukuba or Bombay gives me a powerful impression that the laws of physics have an existence of their own Our discovery of the connected convergent pattern of scientific explanation has profound implications and not just for scientists Alongside the main stream of scientific knowledge there are isolated little pools of what to choose a neutral term I might call wouldbe sciences astrology precognition channeling clairvoyance telekinesis creationism and their kin If it could be shown that there is any truth to any of these notions it would be the discovery of the century much more exciting and important than anything going on today in the normal work of physics So what should a thoughtful citizen conclude when it is claimed by a professor or a film star or Time Life Books that there is evidence for the validity of one of the wouldbe sciences Now the conventional answer would be that this evidence must be tested with an open mind and without theoretical preconceptions I do not think that this is a useful answer but this view seems to be widespread Once in a television interview I said that in believing in astrology one would be turning one s back on all of modern science I then received a polite letter from a former chemist and metallurgist in New Jersey who took me to task because I had not personally studied the evidence for astrology Similarly when Philip Anderson recently wrote dis paragingly of belief in clairvoyance and telekinesis he was upbraided by a Princeton colleague Robert Jahn who was experimenting with what Jahn calls consciousnessrelated anomalous phenomena J ahn complained that although his Anderson s office is only a few hundred yards from my own he has not visited our laboratory discussed any of his concerns with me directly or apparently even read with care any of our technical literature What Jahn and the New Jersey chemist and others who agree with them are missing is the sense of the connectedness of scientific knowledge We do not understand everything but we understand enough to know that there is no room in our world for telekinesis or astrology What possible physical signal from our brains could move distant objects and yet have no effect on any scientific instruments Defenders of astrology sometimes point to the undoubted effects of the moon and sun in producing tides but the effects of the gravitational fields of the other planets are much too small to have detectable effects on the earth s oceans much less on anything as small as a person I will not belabor the point but similar remarks apply to any effort to explain clairvoyance or precognition or the other wouldbe sciences in terms of standard science In any case the correlations predicted by astrologers are not of the sort that might arise from some very subtle gravitational effect39 the astrologers do not claim merely that a certain configuration of planets affects life here on earth but that these effects differ for each person according to the date and hour of his birth In fact I do not think that most people who believe in astrology imagine that it works the way it does because of gravitation or any other agency within the scope of physics 1 think they believe that astrology is an autonomous science with its own fundamental laws not to be explained in terms of physics or anything else One of the great services provided by the discovery of the pattern of scientific explanation is to show us that there are no such autonomous sciences But still should we not test astrology and telekinesis and the rest to make sure that there is nothing to them I have nothing against anyone testing anything they want to but I do want to explain why I would not bother to do so myself and would not recommend the task to anyone else At any one moment one is presented with a wide variety of innovative ideas that might be followed up not only astrology and such but many ideas much closer to the main stream of science and others that are squarely within the scope of modern scientific research It does no good to say that all these ideas must be thoroughly tested there is simply no time I receive in the mail every week about fifty preprints of articles on elementary particle physics and astrophysics along with a few articles and letters on all sorts of wouldbe science Even if I dropped everything else in my life I could not begin to give all of these ideas a fair hearing So what am I to do Not only scientists but everyone else faces a similar problem For all of us there is simply no alternative to making a judgment as well as we can that some of these ideas perhaps most of them are not worth pursuing And our greatest aid in making this judgment is our understanding of the pattern of scientific explanation When the Spanish settlers in Mexico began in the sixteenth century to push northward into the country known as Tejas they were led on by rumors of cities of gold the seven cities of Cibola At the time that was not so unreasonable Few Europeans had been to Tejas and for all anyone knew it might contain any number of wonders But suppose that someone today reported evidence that there are seven golden cities somewhere in modern Texas Would you openmindedly recommend mounting an expedition to search every corner of the state between the Red River and the Rio Grande to look for these cities I think you would make the judgment that we already know so much about Texas so much of it has been explored and settled that it is simply not worthwhile to look for
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