Nature’s Biggest Secret

1.

Is there an ultimate theory of nature—a “Final Theory”—from whose principles all laws that govern the workings of the physical universe may be deduced? Such a theory would provide the complete underlying rules that control, in finest detail, every action of inanimate or animate matter—including all the (non-random) activities of our very selves. Might such a theory even be within the actual grasp of today’s physicists? Steven Weinberg, in his new book, Dreams of a Final Theory, provides an unqualified “yes” in answer to the first of these questions, and he also gives expression to a belief in the genuine plausibility of the suggestion put forward in the second. Should we be persuaded by these striking claims? Wherever our sympathies initially lie, we must, indeed, pay close attention to what Weinberg says; for, probably among all of today’s theoretical scientists, he most authoritatively represents the viewpoint of established fundamental physics.

Weinberg himself supplied some of the essential theoretical underpinnings to the standard theory of modern particle physics. With Abdus Salam and Sheldon Glashow, he received the Nobel Prize for that important ingredient of particle physics known as “electroweak theory”—which provides a theoretical unification of the weak nuclear force, which causes radioactive decay, with the electro-magnetic force. (I shall have more to say about this theory shortly.) But his expertise lies more broadly than this. He has written two highly authoritative and widely acclaimed books on another extensive area of fundamental physics—that encompassed by general relativity and cosmology. Thus, he is an expert not only on the physics that controls the tiniest ingredients of matter but also on the theory of space-time itself—from Einstein—which governs the structure of the universe on its largest scales.

In his semi-popular 1977 classic The First Three Minutes, Weinberg presented a vivid and well-authenticated account of the first three minutes of our universe’s very existence, and of the specific nature of its (now observed) contents. For the comprehensive picture of what is believed to have gone on at that very early time, detailed theories of both particle physics and cosmology are needed simultaneously. This picture is now referred to as the “standard model of the big bang.” Weinberg’s own most important theoretical contributions (to the electroweak model referred to above) must be combined with another theory of modern particle physics, worked out by others, that describes strong nuclear forces. These two schemes together provide what is known as the “standard model of particle physics.” To round off his powerful command of physics, Weinberg is well read in matters of history and philosophy (though he regards the latter discipline as having little direct positive influence on the progress of science).

These credentials do not, by themselves, compel us to accept Weinberg’s views on the ultimate nature of reality; but if we are interested in such issues in any serious way, we must indeed pay due attention to his arguments. There is also the question of why we should be interested in the issues that relate to this putative ultimate theory. For myself, it seems clear that these issues are important. They have a profound bearing on the deepest questions of our philosophy and on the basis of whatever religious beliefs we might choose to adhere to. They also have importance to another matter—a practical matter of money! The question is raised: Should the US government continue to authorize the expenditure of many thousands of millions of dollars on one particular scientific project? It is this latter issue that provides an important underlying theme of Weinberg’s Dreams. I shall try to address these matters in as dispassionate a way as I am able—although my own personal opinions will undoubtedly strongly color what I shall have to say.

First, what is this immensely expensive scientific project? It is the proposal to construct, and subsequently operate, the vast particle accelerator referred to as the Superconducting Super Collider, or SSC. It will require a ten-foot-wide underground tunnel, which is to be built in Ellis County in Texas, forming an oval ring some fiftyfour miles long. Along this tunnel, traveling in opposite directions, would be sent two narrow beams of protons, their paths bent and focused by powerful superconducting magnets. These would be arranged so that the oppositely traveling protons would collide with each other with tremendous energy at certain specified places. Multitudes of new particles would inevitably be produced as a result of these collisions, but the physicists would be most interested in one species of particle in particular—a putative entity referred to as a Higgs particle.

No Higgs particle has ever been produced in any of the powerful particle accelerators that have been built to date. It could not have been, because the anticipated mass of this particle is too large. In order to be conjured into existence, it needs the kind of enormous energies which the Texas machine is designed to achieve, but which none of its predecessors could muster. Why are physicists so interested in the “Higgs” (as this putative particle is sometimes succinctly described)? Indeed, their interest sometimes borders on passion. Weinberg’s book makes a reasoned and not overstated case for the SSC, but some others have allowed themselves to be carried away in expressions of hyperbole. “The God Particle,” cries out the title of a recent book by the distinguished Nobel Prize-winning experimentalist Leon Lederman and his associate Dick Teresi.^* It is clear from such terminology that some researchers must indeed feel that there is something awesomely fundamental about this putative particle. The Higgs is not to be just another of the long list of successfully predicted particles, like the positron, omega-minus, neutrino, anti-proton, or tau-particle—nor is its status comparable even with the yet-unobserved elusive top-quark. No, the Higgs is seen as something with a fundamentally more honored status than any of these.

To a (presumably) dispassionate outside observer such as myself, there are many things that seem odd about this passionate interest in the Higgs. When I first learned about this object, it was presented to me as something that had a theoretical “existence” only. It was not necessarily intended to be a real, observable particle at all, but just a term in a mathematical expression, with a certain formal similarity to the kind of term that would have arisen had an actually real particle been involved. The Higgs object appeared, at that time, to be an ingenious theoretical device, and not necessarily appearing as an actual particle. As a device, it allowed other particles to acquire mass, where all particles were described according to a theoretical scheme in which everything was initially massless. This seems to have been the original viewpoint of Peter Higgs himself, who (along with Tom Kibble) first postulated the hypothetical procedure that now leads physicists to predict the existence of an actual Higgs particle. Higgs is a mild-mannered and modest Englishman who is now a professor at the University of Edinburgh, and who finds himself somewhat disconcerted—even embarrassed—by all the hype and controversy surrounding the SSC project.

Yet, as time has moved forward, this original viewpoint has shifted, because the theories themselves have evolved from some original but tentative ideas into something with a much more specific purpose. The Higgs procedure is still to be the magic wand that dispatches a mass to all those other particles that we now find actually do possess mass. But also it yields forth a special actual particle whose own large mass is there from the start, and which is believed to lie within the projected scope of physical experiment. The Higgs mechanism, in its specific new role, is still the giver of mass to other particles, but it also provides a new, real, observable particle with a finite intrinsic mass of its own. Its complete role is not just as a God in Heaven, but as a God who also deigns to live among His mortal subjects.

There seems, indeed, to be an odd tendency for people to assign some kind of mystical or religious significance to the Higgs particle and to the aims of the SSC. In an exchange between two representatives at the House Committee on Science, Space, and Technology, following a testimony by Weinberg in support of SSC funding, one of them commented: “[W]ill this make us find God?” Weinberg wisely abstained from this exchange. Yet the grand terms in which he had put forward his testimony must have elicited that Representative’s particular question.

With arguments presented in such forceful terms, one may begin to perceive why the proposed discovery of the Higgs indeed raises such great passions and conflict. As Weinberg comments, the executive director of the American Physical Society’s office of public affairs remarked in 1987 that the SSC project “is perhaps the most divisive issue ever to confront the physics community.” If the Higgs is regarded by some as so fundamental as to have religious implications, then its discovery might be well worth the spending of such vast sums of taxpayer’s money. Indeed, if it actually does provide the key to the mystery of mass, then its status is surely unique among fundamental particles. The importance of the Higgs within the scheme of particle physics would, accordingly, be quite different from those of the particles which had been studied before. Perhaps the Higgs will supply the remaining key unlocking the secrets of the Final Theory of fundamental physics. If so, then a vastly expensive machine designed solely for the actual discovery of this magical particle could seem almost to serve as a shrine to science itself, where the discovery of the Higgs ties up the loose ends of this Final Theory and represents the ultimate achievement of fundamental science.

There are obvious dangers in presenting the case for the SSC in this grossly overstated way, and Weinberg wisely refrains from doing so in his book. (I should mention, however, that in a lecture I attended in 1987 that Weinberg gave in Cambridge. England, in honor of the three-hundredth anniversary of Newton’s Principia, he did argue the case for the SSC as a vital quest for a single particle: the Higgs.) In Dreams, Weinberg’s case is a much more balanced one. He does not regard the Higgs as the one remaining link we need for forging the Final Theory; he views the search for it in much more appropriately modest terms. There might be a single Higgs particle, or there might be a number of different ones. There might even be no Higgs particle at all, and some unanticipated phenomenon shows up instead, such as a mysterious hidden extra-strong force. But whatever turns out to be the case, there should be something of fundamental importance to be learned from the collisions between protons at the enormous energies that the SSC will provide. Specifically, the SSC energies should be sufficient either to create a Higgs particle (whose mass is considered to be “almost certainly” no greater than one thousand times that of a proton, so that it is supposed not to be outside the SSC’s range) or else to reveal some phenomenon other than an actual Higgs particle, but which serves a corresponding purpose. Whatever is indeed found, it must elucidate the status of the Higgs mechanism and the “spontaneous symmetry breaking” that is crucial to its use in “electroweak theory.”

I should attempt to explain what “spontaneous symmetry breaking” means, for it is indeed the central plank upon which a great deal of modern fundamental physics rests. It is a source of many of the successes of modern theory, but also, in my opinion, of some of its profound difficulties. It is a powerful idea that, for good or for bad, has propelled the modern theories of basic physics in many of the particular directions in which it has moved. Its universal role seems to be largely unquestioned, but I cannot help asking: Is it actually correct in all of these contexts? The issue is a technical one, but I believe it is important to give some impression of the basic idea. Let us try to see what this idea is.

Much of modern theory at the fundamental level depends upon the idea of “symmetry.” A symmetry of a physical theory arises if, when some of the parameters of the theory are replaced by some different combination of them, then the theory remains unchanged. Thus the theory “looks just the same” if it is turned around in some way and viewed from another angle. Einstein’s special theory of relativity provides a good example. If we replace the space and time coordinates by certain other combinations of these coordinates, then the theory remains unaltered. (This expresses the fact that the transformation from one state of uniform motion to another cannot be physically detected.) Another example occurs with the standard theory of electric forces: if the signs of all electric charges are reversed—so that positive charges become negative and negative ones positive—then the effects of the theory are totally unaltered.

The electroweak theory of the standard model depends fundamentally on another symmetry. This theory describes not only the electromagnetic forces (thus incorporating the famous equations due to the great nineteenth-century physicist James Clerk Maxwell which gave a united description of both electric and magnetic fields—and of light!) but also the “weak nuclear forces”—the forces responsible for radioactive decay. The required symmetry is one in which the electromagnetic and the weak forces are transformed among one another, rather in the way in which time and space are transformed among one another according to the symmetries of Einstein’s special relativity. However, there is now an essential difference. In Einstein’s theory, the symmetry is taken to be exact, with the implication that there is, for example, no way of distinguishing the state of rest from the states of uniform motion in any direction. (This exactness does not imply that time and space have to be on an equal footing with each other; just that they get mixed up with one another.) In electroweak theory the symmetry is not at all exact—at least not at the ordinary temperatures or energies that are encountered in normal experimental conditions.

I shall try to be a little more explicit. This is not easy, because the ideas cannot be properly explained without bringing in the underlying principles of quantum mechanics that feature in all modern particle theories. The first point about quantum theory in this connection is that any “field of force” manifests itself in the form of discrete particles, or quanta. In the case of the electromagnetic field of Maxwell’s theory, these quanta are the photons, the individual particles that constitute light. In the case of the weak forces, there are four corresponding types of quanta, referred to as the Z-boson and the three W-bosons, the latter being distinguished by their electric charge and referred to individually as W⁺, W⁰, and W^?. The successful experimental confirmation of the existence of the W and Z particles was, in fact, one of the crowning achievements of electroweak theory. Now the symmetry that is exhibited by electroweak theory is one in which the photon, W-bosons, and Z-boson get transformed among themselves, very much like the way in which the time-dimension and the three space-dimensions get transformed among themselves in Einstein’s special relativity.

The difference, in the case of electroweak theory, is that the symmetry is now clearly observed not to be exact, as it is exact in the case of special relativity. Indeed, in electroweak theory, it is very far from exact. The most obvious way in which this non-exactness can be seen is in the fact that photons are massless, whereas the W- and Z-bosons are massive particles. If there were an exact symmetry between them then the masses of all these particles would have to be the same. To explain this difference, the Higgs mechanism is brought into play, in order to provide the W and Z particles with mass. It is here that the idea of spontaneous symmetry breaking comes in. The contention is that at extremely high temperatures, such as would have been the case in the early stages of the universe, the symmetry is taken to be indeed exact, and there is now nothing to choose between photons and W- or Z-bosons. As the temperature cools, however, the symmetry spontaneously gets broken. At this point, some particular combination of these particles “freezes out” as being the massless one, and that combination becomes the particle that we now call the “photon.” It is taken to be a matter of pure chance which particular combination it is that turns out to be favored in this way. (It is one of the odd features of quantum mechanics that particles can be “rotated” into other combinations of particles, and it is this kind of thing that is supposed to be happening here. I do not wish to trouble the uninitiated reader about this in detail.) Likewise, the particular combinations that we now call W⁺, W⁰, W^?, and Z are also spontaneously frozen out.

This procedure is analogous to what happens in a quite different physical situation, taken from condensed matter physics, called ferromagnetism. This example is frequently cited to illustrate the procedure of spontaneous symmetry breaking. Imagine a spherical ball of iron that is heated to a temperature of over 770°C. At this temperature the iron does not behave as a magnet. Although each individual atom itself behaves as a little magnet, and there is a natural tendency for the atoms to align themselves with one another, this tendency to alignment is continually being swamped by the jiggling caused by the surrounding thermal activity. On the other hand, when the temperature is lowered to below 770°C, this tendency to mutual alignment wins out, and a magnet is indeed formed. We may ask: In which direction will the poles of this magnet point? There is taken to be complete symmetry between all the different spatial directions, so this choice is dictated by pure chance—or else, perhaps, by the presence of tiny stray fields which might break the exact directional symmetry. Thus, one particular direction of magnetization—one that cannot be predicted—is “frozen out” from all the alternatives.

The symmetry breaking that is taken to occur in electroweak theory is similar. There is to be complete symmetry between the photon and the W and Z particles (and between their various combinations) at high temperatures—as with the complete symmetry between the different spatial directions in the case of our ball of iron—but now it is at the enormously larger temperature of some million million million degrees. Such stupendous temperatures would have been achieved moments after the big bang occurred, according to the standard model. As the universe cools to below this temperature, however, the symmetry is spontaneously broken and the different states of these particles that we observe today are “frozen out.” The actual massless photon, and the particular massive particles we call Ws and Zs are determined by chance at this stage.

As a parenthetic comment, I should mention one inevitable difficulty that is frequently encountered in popular writing, which I found to be somewhat irritatingly dealt with in Weinberg’s book. This concerns the way in which the very large (or very small) numbers that so often occur in science are specified. Although there is some dramatic effect in describing a “million million million” in such verbal terms as I have done above, it becomes very confusing to denote large numbers generally in this way. In this review I shall hence-forth use the much simpler scientific notation, such as “10¹⁸” to denote that same quantity. In Dreams, on the other hand, Weinberg confusingly uses various different kinds of iterated combinations of the words “million,” “billion,” and “trillion” rather than resort to simple scientific notation. (To add to my personal confusion, the words “trillion” and “billion” do not mean the same thing to this nostalgic oldfashioned—but logical—Britisher as they do to Americans and, alas, now to most of the rest of the world.)

2.

Spontaneous symmetry breaking is an essential feature of the standard model of particle physics, and it is a notion that is quite crucial to the whole issue of the Higgs particle. But is spontaneous symmetry breaking actually true? It might seem to be shockingly unorthodox to question the genuineness of such a pillar of establishment particle theory. I should make it clear that there is no reasonable doubt concerning the validity of this notion in the case of ferromagnetism. It also plays an indisputable role in such phenomena as superconductivity. I am not arguing about that. What I am questioning is whether spontaneous symmetry breaking is a true feature of the electroweak interactions. Perhaps, instead, it is an artifact of the historical development of the now-standard electroweak theory. If it is such an artifact, then the search for a genuine Higgs particle will end in failure.

The essential question is: Is the standard viewpoint with regard to electroweak phenomena correct, where the symmetry is to be taken at the fundamental level, and the breaking of this symmetry as something more superficial? Or is the symmetry itself superficial, being an apparent (and merely approximate) phenomenon emerging out of underlying ingredients that do not actually possess this symmetry.

It should be made clear that the latter view, though not the conventional one, is perfectly consistent with the experimental facts and with generally accepted quantum-mechanical principles. Why, then, do particle physicists seem almost universally to take the view that symmetry is indeed fundamental? I believe that the reason is largely historical, and perhaps also cultural. The historical point is that by taking symmetry as fundamental, Weinberg, Glashow, Salam, and others have followed a valuable route to an electroweak theory with all the required consistency (finiteness) properties. However, it is now known that there are other routes which would have led to effectively the same theory but where the symmetry is taken as superficial, not fundamental. The cultural point is that theories with symmetry are regarded as simple and beautiful, and therefore more likely to lead to the secrets of nature’s ways.

One of the strengths of Weinberg’s Dreams is that he is honest and explicit about the important role of aesthetic considerations in the judgment of physical theories. He argues, with special reference to Einstein’s general theory of relativity (the theory that explains gravitation in terms of curved space-time), that beauty is an indispensable ingredient of a successful physical theory—and I agree with him. The ways that we might differ, in certain respects, would be in relation to which particular features of a theory we regard as beautiful. To Weinberg, the symmetry aspects of the standard model of particle physics are important ingredients of its beauty. I have to confess that I do not feel the same way about symmetry as such. In certain respects, symmetry can represent an ugly complication in a theory rather than a simple and elegant feature. To me, the fact that there are at least seventeen undetermined parameters in this standard model outweighs whatever beauty may be imparted by its own particular collection of symmetries!

Weinberg has interesting things to say in relation to the use of the word “beauty” in this context. He refers to a racehorse trainer talking about a “beautiful horse” as one that the trainer expects to win races. In a similar way, a physicist might sometimes merely mean by a “beautiful theory” one that that physicist expects to be successful—for various reasons of logical judgment or experience. It is clear that Weinberg believes that there is something deeper to the issue of beauty in scientific theory than just this, however, and he discusses this matter at some length. He also emphasizes the important point that science is an objective quest for truth, strongly defending the activities of science against attacks by those who regard science as an essentially social activity.

It is simply a logical fallacy to go from the observation that science is a social process to the conclusion that the final product, our scientific theories, is what it is because of social and historical forces acting in this process. A party of mountain climbers may argue over the best path to the peak, and these arguments may be conditioned by the history and social structure of the expedition, but in the end, either they find a good path to the peak or they do not, and when they get there they know it.

There is, no doubt, a certain arrogance that scientists—and particularly physicists—may sometimes exhibit, believing that their understanding of the truths of the world are deeper and more unshakable than those in other fields of endeavor. This arrogance is often unintentional, but it may upset those who are less versed in scientific procedures. Despite his conscious efforts to counteract such tendencies, Weinberg’s confidence in the supremacy of the particular area of elementary particle physics does sometimes get the better of him. I expect that some people will have difficulties with his statement: “The reason we give the impression that we think that elementary particle physics is more fundamental than other branches of physics is because it is.”

I have difficulty with that statement myself. I do not myself believe that elementary particle physics is the most fundamental area of physics. Einstein’s general relativity is not part of particle physics; yet it is concerned with the very nature of the space-time within which all the particles of nature must reside. Perhaps someday Einstein’s theory will be brought into accordance with quantum theory and thus become, in some sense, a particle theory also. But that day has not arrived. Moreover, it is my opinion that quantum theory itself will someday undergo important changes. The study of how this theory might indeed change is, in a significant sense, also more fundamental than particle physics.

The issue of possible changes in the nature of quantum theory is a fascinating one. Might such changes be part of Weinberg’s “Final Theory”? He seems to believe otherwise. For he states: “If there is anything in our present understanding of nature likely to survive in a final theory, it is quantum mechanics.” In fact, a few years ago Weinberg himself put forward an interesting proposal for the modification of the rules of quantum theory. It did not work—which is perhaps why he is reluctant to countenance other possible changes. In my own opinion, no theory could have a chance of being “final” if it did not incorporate important changes from the present framework of quantum theory.

Is it likely that the ssc, if it is completed, will lead the way to the discovery of the “Final Theory”? What is the chance that such a Final Theory even exists? In my own opinion there is very little chance that SSC could, in itself, get us much closer to such a theory. It is very likely, on the other hand, that it could tell us something important about the nature of electroweak interactions. Perhaps what it may tell us will shock those who most strongly support the continuation of the ssc project. Perhaps the symmetry of the current electroweak theory is not fundamental, and there is no proper Higgs particle. I would myself hope that this is the case. A fundamental nature for electroweak and other particle symmetries raises very awkward problems in relation to the early universe. In order to resolve problems of this kind, some particle physicist/cosmologists have introduced the picture of the early universe known as “inflation”—a picture that has become quite fashionable but which, for various reasons, I myself find unpleasant and unsatisfactory.

What are these awkward problems? What is inflation? The problems are not specific to the symmetries of electroweak theory; they occur also with other aspects of modern theories of particle physics. The difficulty is that in the standard model of the “big bang,” there is no “communication” between different spatial regions of the universe in its early stages. Thus, when the temperature drops below the value relevant to symmetry breaking (some 10¹⁸ degrees, in the case of electroweak theory), the breaking is likely to be different in different regions of the universe. When we look, with our telescopes, into a distant region in which the breaking is different from what it is here, serious problems may arise. It would seem that a particle emitted as a photon in that distant region would have to be received here, instead, as some combination of photon, Z, and W particles. This kind of situation leads to all sorts of cosmic horrors, such as those referred to as “monopoles,” “cosmic strings,” and “domain walls”—vast fractures in the vacuum of space—and there could be serious conflict with observation if such things were at all prevalent.

To remove this danger of observational conflict, the “device” of “inflationary cosmology” is resorted to, according to which the universe is supposed to have expanded by a stupendous factor—perhaps by something like ’10⁶⁰ or more, in its early stages, over and above what the standard model of cosmology demands. The idea of this would be to push all these horrors to such enormous distances away from us that that observational conflict disappears. It is not appropriate for me to enter into a discussion of these matters here, except to say that the issues are controversial, that there is no direct observation specifically supporting inflation, and that many kinds of further dramatic ideas of differing degrees of believability need to be introduced. Some people are favorably disposed to these implications of spontaneous symmetry breaking; for my own part, I am not. The point that I am making is that these things are largely driven by the assumption that the symmetries of the various theories of particles physics are fundamental, with the consequent need for spontaneous symmetry breaking as an essential ingredient. There is thus a considerable importance in gaining information about the actual physical status of this ubiquitous, but yet-untested idea in modern particle physics.

I do not wish to enter the debate whether the SSC is worth the money—some $10¹⁰. Or should the matter be left to the Europeans, with their considerably cheaper and further-advanced alternative proposal, the Large Hadron Collider (LHC) at CERN in Switzerland? The energies available at LHC would be somewhat less than half those of SSC, however. Questions of this kind involve a difficult balance of one thing against another. The results of SSC would certainly be scientifically very important, but they cannot in themselves—without a further input from theory—bring us a great deal closer to a “Final Theory.” For one thing, the energies involved, stupendous as they are, are too ridiculously tiny! The fundamental energy, as Weinberg himself stresses, is the so-called Planck energy, where gravitation and particle physics come together. This energy is some 10¹⁴ times that which could be achieved by SSC—to attain it is a total absurdity, with foreseeable techniques and resources!

Important as foreseeable experiments are, therefore, they cannot by themselves point clearly toward anything that could stand a chance of being a Final Theory. To stand a chance, a putative such theory would, in my opinion, have to bear little manifest relation to anything that we have seen in physics so far. Certainly the ideas of the (super-)string theories, which enjoyed particular popularity a few years ago, could not in themselves supply anything that I could accept as “the answer.” Weinberg discusses these theories with favor (without mentioning the awkwardness that they require a number of spatial dimensions different from the three that we actually experience, or the fact that such theories are actually not finite, despite the fact that they are often claimed to be), and he regards them as providing the distinct possibility that the Final Theory might even already be within the physicists’ grasp.

In my view, if there is to be a Final Theory, it could only be a scheme of a very different nature. Rather than being a physical theory in the ordinary sense, it would have to be something more like a principle—a mathematical principle whose implementation might itself involve nonmechanical subtlety (and perhaps even creativity). Weinberg judges that there would be no role for morality in his Final Theory, and writes: “I would guess that, though we shall find beauty in the final laws of nature, we will find no special status for life or intelligence.” This is consistent with the sentiment that he “rashly” expressed earlier in The First Three Minutes: “The more the universe seems comprehensible, the more it seems pointless.” Perhaps, with the appropriate type of “principle” there could, on the other hand, be some scope for a “point” to our universe.

Whatever the status of such grandiose ideas, we are, at best, a very long way from any kind of ultimate understanding of the nature of our universe. For the moment, physics must progress by relatively small steps which allow us to move slowly forward, often in unexpected ways. Aesthetic judgments are always important for this, and Weinberg remarks: “In elementary particle physics aesthetic judgments seem to be working increasingly well. I take this as evidence that we are moving in the right direction, and perhaps not so far from our goal.”

Yet he views these aesthetic judgements as operating at a local rather than a global level: “In our hunt for the final theory, physicists are more like hounds than hawks; we have become good at sniffing around on the ground for traces of the beauty we expect in the laws of nature, but we do not seem able to see the path to the truth from the heights of philosophy.”

Without the kind of soaring global insights of an Einstein, I do not myself see how any real progress to anything approaching a Final Theory could be achieved. I fear, however, that there is something alarmingly appropriate about the image conjured up by a pack of impatient hounds. I hope I am wrong. I worry about the poor fox.