1
Waiting for a Final Theory
The end of the twentieth century prompted magazines and newspapers to indulge in a good deal of guesswork about the future. As part of this prophetic effort, Time magazine asked me to assess how far we yet have to go in understanding the fundamental laws of nature. My answer: pretty far. This brief essay was published by Time in April 2000.
The twentieth century was quite a time for physicists. By the mid-1970s we had in hand the so-called Standard Model, a theory that accurately describes the forces and particles we observe in our laboratories and that provides a basis for understanding virtually everything else in physical science.
No, we donât actually understand everythingâthere are many things, from the turbulence of ocean currents to the folding of protein molecules, which cannot be understood without new insights and radical improvements in our methods of calculation. They will provide plenty of interesting continued employment for theorists and experimenters for the foreseeable future. But no new freestanding scientific principles will be needed to understand these phenomena. The Standard Model provides all the fundamental principles we need for this.1
There is one force, though, that is not covered by the Standard Model: the force of gravity. Einsteinâs General Theory of Relativity gives a good account of gravitation at ordinary distances, and if we like, we can tack it onto the Standard Model. But serious mathematical inconsistencies turn up when we try to apply it to particles separated by tiny distancesâdistances about 10 million billion times smaller than those probed in the most powerful particle accelerators.
Even apart from its problems in describing gravitation, however, the Standard Model in its present form has too many arbitrary features. Its equations contain too many constants of natureâsuch as the masses of the elementary particles and the strength of the fundamental unit of electric chargeâthat are given specific numerical values for no other reason than that these values seem to work. In writing these equations, physicists simply plugged in whatever values made the predictions of the theory agree with experimental results.
There are reasons to believe that these two problems are really the same problem. That is, we think that when we learn how to make a mathematically consistent theory that governs both gravitation and the forces already described by the Standard Model, all those seemingly arbitrary properties will turn out to be what they are because this is the only way that the theory can be mathematically consistent.
One clue that this should be true is a calculation showing that, although the strengths of the various forces seem very different when measured in our laboratories, they would all be equal if they could be measured at tiny distancesâdistances close to those at which the above-mentioned inconsistencies begin to show up.
Theorists have even identified a candidate for a consistent unified theory of gravitation and all the other forces: superstring theory. In some versions, it proposes that what appear to us as particles are stringy loops or lines that exist in a space-time with ten dimensions. But we donât yet understand all the principles of this theory, and even if we did, we would not know how to use the theory to make predictions that we can test in the laboratory.
Such an understanding could be achieved tomorrow by some bright graduate student, or it might just as well take another century or so. It may be accomplished by pure mathematical deduction from some fundamental new physical principle that just happens to occur to someone, but it is more likely to need the inspiration of new experimental discoveries.
We would like to be able to judge the correctness of a new fundamental theory by making measurements of what happens at scales ten million billion times smaller than those probed in todayâs laboratories, but this may always be impossible. With any technology we can now imagine, measurements like those would take more than the economic resources of the whole human race.
Even without new experiments, it may be possible to judge a final theory by whether it explains all the apparently arbitrary aspects of the Standard Model. But there are explanations and explanations. We would not be satisfied with a theory that explains the Standard Model in terms of something complicated and arbitrary, in the way astronomers before Kepler explained the motions of planets by piling epicycles upon epicycles.
To qualify as an explanation, a fundamental theory has to be simpleânot necessarily a few short equations, but equations that are based on a simple physical principle, in the way that the equations of General Relativity are based on the principle that gravitation is an effect of the curvature of space-time. And the theory also has to be compellingâit has to give us the feeling that it could scarcely be different from what it is.
When at last we have a simple, compelling, mathematically consistent theory of gravitation and other forces that explains all the apparently arbitrary features of the Standard Model, it will be a good bet that this theory really is final. Our description of nature has become increasingly simple. More and more is being explained by fewer and fewer fundamental principles. But simplicity canât increase without limit. It seems likely that the next major theory that we settle on will be so simple that no further simplification would be possible.
The discovery of a final theory is not going to help us cure cancer or understand consciousness, however. We probably already know all the fundamental physics we need for these tasks. The branch of science in which a final theory is likely to have its greatest impact is cosmology. We have pretty good confidence in the ability of the Standard Model to trace the present expansion of the universe back to about a billionth of a second after its supposed start. But when we try to understand what happened earlier than that, we run into the limitations of the model, especially its silence on the behavior of gravitation at very short distances.
The final theory will let us answer the deepest questions of cosmology: Was there a beginning to the present expansion of the universe? What determined the conditions at the beginning? And is what we call our universe, the expanding cloud of matter and radiation extending billions of light-years in all directions, really all there is, or is it only one part of a much larger âmultiverse,â in which the expansion we see is just a local episode?
The discovery of a final theory could have a cultural influence as well, one comparable to what was felt at the birth of modern science. It has been said that the spread of the scientific spirit in the seventeenth and eighteenth centuries was one of the things that stopped the burning of witches. Learning how the universe is governed by the impersonal principles of a final theory may not end mankindâs persistent superstitions, but at least it will leave them a little less room.
Since 2000 neither superstring theory nor the multiverse idea has yet achieved the kind of success that would establish their permanent place in science, but they have in a sense come together. In 2001 it was found (by Steven Giddings, Shamit Kachru, and Joseph Polchinski at the University of California at Santa Barbara) that the equations of superstring theory have an enormous number of solutions. Leonard Susskind of Stanford coined the term âstring landscapeâ for this multiplicity of solutions, in analogy with the landscape of possible orientations of protein molecules found in theoretical biochemistry. In accordance with earlier ideas of Andrei Linde at Stanford about chaotic inflation, each of these solutions potentially describes a different sort of big bang cosmology. (This is the subject of article 19 in this collection.) The exploration of the string landscape and its cosmological implications is a formidable task, and has barely begun. Indeed, the distance we still have to go in understanding the fundamental laws of nature seems even greater in 2009 than it did in 2000.
Notes
1. This is a very brief statement of a reductionist viewpoint described in more detail in my book Dreams of a Final Theory (Pantheon, 1992).
2
Can Science Explain Everything? Anything?
This essay, based on a talk given at Amherst College in October 2000, is one of my occasional reluctant ventures into the philosophy of science. I generally feel diffident in writing about philosophy, as there are smart people who do this full time. Still, it seems to me that the task of the philosopher of science is not to tell scientists how to work, but to describe what scientists are doing at their work, so it might be useful for philosophers to hear from time to time what a working scientist thinks that he or she is doing. But I had another reason for accepting when the philosophers at Amherst College invited me to give a talk on the meaning of explanation in science. I live in Texas, and like it here, but I do sometimes miss the autumn in New England, where I used to live. This trip was not a disappointment. On the way from Boston to Amherst, I drove past countless maples and oaks whose red and yellow leaves were lit up by the October sunshine. I think I enjoyed the drive more than the Amherst audience could have enjoyed my talk.
This essay was published in the New York Review of Books in May 2001, and republished in The Best American Science Writing 2002.
One evening a few years ago I was with some other faculty members at the University of Texas, telling a group of undergraduates about work in our respective disciplines. I outlined the great progress we physicists had made in explaining what was known experimentally about elementary particles and fieldsâhow when I was a student I had to learn a large variety of miscellaneous facts about particles, forces, and symmetries; how in the decade from the mid-1960s to the mid-1970s all these odds and ends were explained in what is now called the Standard Model of elementary particles; how we learned that these miscellaneous facts about particles and forces could be deduced mathematically from a few fairly simple principles; and how a great collective Aha! then went out from the community of physicists.
After my remarks, a faculty colleague (a scientist, but not a particle physicist) commented, âWell, of course, you know science does not really explain thingsâit just describes them.â I had heard this remark before, but now it took me aback, because I had thought that we had been doing a pretty good job of explaining the observed properties of elementary particles and forces, not just describing them.
I think that my colleagueâs remark may have come from a kind of positivistic angst that was widespread among philosophers of science in the period between the world wars. Ludwig Wittgenstein famously remarked that âat 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.â
It might be supposed that something is explained when we find its cause, but an influential 1913 paper by Bertrand Russell1 had argued that âthe word âcauseâ is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable.â This left philosophers like Wittgenstein with only one candidate for a distinction between explanation and description, one that is teleological, defining an explanation as a statement of the purpose of the thing explained.
E. M. Forsterâs novel Where Angels Fear to Tread gives a good example of teleology making the difference between description and explanation. Philip is trying to find out why his friend Caroline helped to bring about a marriage between Philipâs sister and a young Italian man of whom Philipâs family disapproves. After Caroline reports all the conversations she had with Philipâs sister, Philip says, âWhat you have given me is a description, not an explanation.â Everyone knows what Philip means by thisâin asking for an explanation, he wants to learn Carolineâs purposes. There is no purpose revealed in the laws of nature, and not knowing any other way of distinguishing description and explanation, Wittgenstein and my friend had concluded that these laws could not be explanations. Perhaps some of those who say that science describes but does not explain mean also to compare science unfavorably with theology, which they imagine to explain things by reference to some sort of divine purpose, a task declined by science.
This mode of reasoning seems to me wrong not only substantively, but also procedurally. It is not the job of philosophers or anyone else to dictate meanings of words different from the meanings in general use. Rather than argue that scientists are incorrect when they say, as they commonly do, that in their work they are explaining things, philosophers who care about the meaning of explanation in science should try to understand what it is that scientists are doing when they say they are explaining something. If I had to give an a priori definition of explanation in physics I would say, âExplanation in physics is what physicists have been doing when they say Aha!â But a priori definitions (including this one) are not much use.
As far as I can tell, this has become well understood by philosophers of science at least since World War II. There is a large modern literature on the nature of explanation, by philosophers like Peter Achinstein, Carl Hempel, Philip Kitcher, and Wesley Salmon. From what I have read in this literature, I gather that philosophers are now going about this the right way: they are trying to develop an answer to the question âWhat is it that scientists do when they explain something?â by looking at what scientists are actually doing when they say they are explaining something.
Scientists who do pure rather than applied research commonly tell the public and funding agencies that their mission is the explanation of some thing or other; so the task of clarifying the nature of explanation can be pretty important to them, as well as to philosophers. This task seems to me to be a bit easier in physics (and chemistry) than in other sciences, because philosophers of science have had trouble with the question of what is meant by an explanation of an event (note Wittgensteinâs reference to ânatural phenomenaâ) while physicists are interested in the explanation of regularities, of physical principles, rather than of individual events.
Biologists, meteorologists, historians, and so on are concerned with the causes of individual events, such as the extinction of the dinosaurs, the blizzard of 1888, the French Revolution, etc., while a physicist only becomes interested in an event, like the fogging of Becquerelâs photographic plates that in 1897 were left in the vicinity of a salt of uranium, when the event reveals a regularity of nature, such as the instability of the uranium atom. Philip Kitcher has tried to revive the idea that the way to explain an event is by reference to its cause, but which of the infinite number of things that could affect an event should be regarded as its cause?2
Within the limited context of physics, I think one can give an answer of sorts to the problem of distinguishing explanation from mere description, which captures what physicists mean when they say that they have explained some regularity. The answer is that we explain a physical principle when we show that it can be deduced from a more fundamental physical principle. Unfortunately, to paraphrase something that Mary McCarthy once said about a book by Lillian Hellman, every word in this definition has a questionable meaning, including âweâ and âa.â But here I will focus on the three words that I think present the greatest difficulties: the words âfundamental,â âdeduced,â and âprinciple.â
The troublesome word âfundamentalâ canât be left out of this definition, because deduction itself doesnât carry a sense of direction; it often works both ways. The best example I know is provided by the relation between the laws of Newton and the laws of Kepler. Everyone knows that Newton discovered not only a law that says the force of gravity decreases with the inverse square of the distance, but also a law of motion that tells how bodies move under the influence of any sort of force. Somewhat earlier, Kepler had described three laws of planetary motion: planets move on ellipses with the sun at the focus; the line from the sun to any planet sweeps over equal areas in equal times; and the squares of the periods (the times it takes the various planets to go around their orbits) are proportional to the cubes of the major diameters of the planetsâ orbits.
It is usual to say that Newtonâs laws explain Keplerâs. But historically Newtonâs law of gravitation was deduced from Keplerâs laws of planetary motion. Edmund Halley, Christopher Wren, and Robert Hooke all used Keplerâs relation between the squares of the periods and the cubes of the diameters (taking the orbits as circles) to deduce an inverse square law of gravitation, and then Newton extended the argument to elliptical orbits. Today, of course, when you study mechanics you learn to deduce Keplerâs laws from Newtonâs laws, not vice versa. We have a deep sense that Newtonâs laws are more fundamental than Keplerâs laws, and it is in that sense that Newtonâs laws explain Keplerâs laws rather than the other way around. But itâs not easy to put a precise meaning to the idea that one physical principle is more fundamental than another.
It is tempting to say that more fundamental means more comprehensive. Perhaps the best-known attempt to capture the meaning that scientists give to explanation was that of Carl Hempel. In his 1948 article written with Paul Oppenheim,3 he remarked that âthe explanation of a general regularity consists in subsuming it under another more comprehensive regularity, under a more general law.â But this doesnât remove the difficulty. One might say for instance that Newtonâs laws govern not only the motions of planets but also the tides on Earth, the falling of fruits from trees, and so on, while Keplerâs laws deal with the more limited context of planetary motions. But that isnât strictly true. Keplerâs laws, to the extent that classical mechanics applies at all, also govern the motion of electrons around the nucleus in atoms,...