Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature

by Steven Weinberg

DREAMS OF A FINAL THEORY

Steven Weinberg

DREAMS OF A FINAL THEORY

Copyright © 1992, 1993 by Steven Weinberg

eISBN: 978-0-307-78786-6

CONTENTS

PREFACE

This book is about a great intellectual adventure, the search for the final laws of nature.

Steven Weinberg Austin, Texas August 1992

CHAPTER I

PROLOGUE

The years since the mid-1970s have been the most frustrating in the history of elementary particle physics. We are paying the price of our own success: theory has advanced so far that further progress will require the study of processes at energies beyond the reach of existing experimental facilities.

As this book goes to press in 1992, funding for the Super Collider, which was cut off by a June vote in the House of Representatives, has been restored by an August vote in the Senate. The future of the Super Collider would be assured if it received appreciable foreign support, but so far that has not been forthcoming. As matters stand, even though funding for the Super Collider has survived in Congress this year, it faces the possibility of cancellation by Congress next year, and in each year until the project is completed. It may be that the closing years of the twentieth century will see the epochal search for the foundations of physical science come to a stop, perhaps only to be resumed many years later.

Our present theories are of only limited validity, still tentative and incomplete. But behind them now and then we catch glimpses of a final theory, one that would be of unlimited validity and entirely satisfying in its completeness and consistency.

Think of the space of scientific principles as being filled with arrows, pointing toward each principle and away from the others by which it is explained. These arrows of explanation have already revealed a remarkable pattern: they do not form separate disconnected clumps, representing independent sciences, and they do not wander aimlessly—rather they are all connected, and if followed backward they all seem to flow from a common starting point. This starting point, to which all explanations may be traced, is what I mean by a final theory.

What do we mean by one scientific principle “explaining” another? How do we know that there is a common starting point for all such explanations? Will we ever discover that point? How close are we now? What will the final theory be like? What parts of our present physics will survive in a final theory? What will it say about life and consciousness? And, when we have our final theory, what will happen to science and to the human spirit? This chapter, barely touching on these questions, leaves a fuller response to the rest of this book.

When we say that one truth explains another, as for instance that the physical principles (the rules of quantum mechanics) governing electrons in electric fields explain the laws of chemistry, we do not necessarily mean that we can actually deduce the truths we claim have been explained. Sometimes we can complete the deduction, as for the chemistry of the very simple hydrogen molecule. But sometimes the problem is just too complicated for us. In speaking in this way of scientific explanations, we have in mind not what scientists actually deduce but instead a necessity built into nature itself.

This is a tricky point in part because it is awkward to talk about one fact explaining another without real people actually doing the deductions. But I think that we have to talk this way because this is what our science is about: the discovery of explanations built into the logical structure of nature.

Not until Galileo, Kepler, and Descartes in the seventeenth century do we find the modern notion of laws of nature.

It is with Isaac Newton that the modern dream of a final theory really begins. Quantitative scientific reasoning had never really disappeared, and by Newton’s time it had already been revitalized, most notably by Galileo. But Newton was able to explain so much with his laws of motion and law of universal gravitation, from the orbits of planets and moons to the rise and fall of tides and apples, that he must for the first time have sensed the possibility of a really comprehensive explanatory theory.

In the folklore of science there is an apocryphal story about some physicist who, near the turn of the century, proclaimed that physics was just about complete, with nothing left to be done but to carry measurements to a few more decimal places. The story seems to originate in a remark made in 1894 in a talk at the University of Chicago by the American experimental physicist Albert Michelson: “While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice.… An eminent physicist has remarked that the future truths of Physical Science are to be looked for in the sixth place of decimals.”

Robert Andrews Millikan, another American experimentalist, was in the audience at Chicago during Michelson’s talk and guessed that the “eminent physicist” Michelson referred to was the influential Scot, William Thomson, Lord Kelvin. A friend has told me that when he was a student at Cambridge in the late 1940s, Kelvin was widely quoted as having said that there was nothing new to be discovered in physics and that all that remained was more and more precise measurement.

The dream of a final unifying theory really first began to take shape in the mid-1920s, with the discovery of quantum mechanics.

Paul Dirac, one of the founders of the new quantum mechanics, announced triumphantly in 1929 that “the underlying physical laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the application of these laws leads to equations much too complicated to be soluble.”

It seems to me that our best hope is to identify the final theory as one that is so rigid that it cannot be warped into some slightly different theory without introducing logical absurdities like infinite energies.

philosophers and scientists. One is likely to be accused of something awful, like reductionism, or even physics imperialism. This is partly a reaction to the various silly things that might be meant by a final theory, as for instance that discovery of a final theory in physics would mark the end of science. Of course a final theory would not end scientific research, not even pure scientific research, nor even pure research in physics. Wonderful phenomena, from turbulence to thought, will still need explanation whatever final theory is discovered.

A final theory will be final in only one sense—it will bring to an end a certain sort of science, the ancient search for those principles that cannot be explained in terms of deeper principles.

CHAPTER II

ON A PIECE OF CHALK

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 pattern—perhaps the deepest thing we have yet learned about the universe.

Chalk is white. Why?

Why?

Why?

Why?

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.

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?”

As I 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.

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; nineteen 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.

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.

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 so-called 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 flesh 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.

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.

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.

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.

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 separation of law and history is a delicate business, one we are continually learning how to do as we go along.

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.

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.

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.

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 system; and the second law of thermodynamics expresses the tendency of isolated systems to become more disorderly.

Nevertheless, even though thermodynamics has been explained in terms of particles and forces, it continues to deal with 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.