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Growing explanations
Historical Perspectives on Recent Science
By M. Norton Wise Duke University Press
ISBN: 0-8223-3319-8
Chapter One
Mirror symmetry: persons, values, and objects
Peter Galison
At the millennium, there was much talk about "the end of physics." Many physicists believed that their enterprise was coming to a final phase of its history, but they interpreted "the end" in numerous ways. At the end of the cold war some made dire predictions about the discipline because military research and development were downsized, the $15 billion superconducting supercollider was canceled in 1993, the National Science Foundation offered less to physics, and the Department of Energy budget was significantly reallocated. These same words-"the end of physics"-took on a second meaning in the 1980s and 1990s, when some high-energy particle physicists turned against a small but growing minority of theorists who embraced string theory. For these critics string theory appeared a false salvation, a mathematical chimera that abandoned experiment, tempted the young, distorted pedagogy, and ultimately threatened the existence of physics as science. A third meaning of the "end of physics" emerged within string theorists' own ambitions: many argued that a remarkable series of discoveries within the mathematical physics of strings provided grounds, the best ever, for an account of all the known forces including gravity, completing the historicalmission of fundamental physics. It would be, its most enthusiastic backers argued, a "theory of everything."
Physics at the millennium
Hopes and fears for finality in physics are not new. Distinctive is the string-theoretical vision in which mathematics itself came to stand where experiment once was: the view that the powerful constraints of mathematical self-consistency would hem theory in so tightly that, at the end, only one theory would stand, and that an elegant, compact theory would cover the world by predicting all the basic forces and masses that constitute and bind matter. Theoretical physics would end, in this third sense, because the ancient search for physical explanation in terms of basic building blocks had reached its last station.
Rejecting the doomsayers, the new alliance between physics and mathematics saw the opportunity to restructure the bounds of both fields, opening a window on twenty-first century mathematics that might, imminently, produce a unified account of gravity and particle physics. But the optimism came with warnings from some quarters of both math and physics-what would be the proper standards of demonstration in this new interzone between disciplines? Would this new "speculative mathematics" sacrifice experiment on the physics side and intrude physical argumentation into the heartland of mathematics on the other? Would it compromise both the physicists' demand for laboratory confirmation and the mathematicians' historical insistence on rigor?
These discussions over the place of string theory are enormously instructive. They over a glimpse into theoretical physics during a remarkable period of transition, for in the realignment of theory toward mathematics the meaning of both theory and theorist were in flux: First, in the 1990s a new category of theorist was coming into being, part mathematician and part physicist. Second, theorists ushered a new set of conceptual objects onto the stage, not exactly physical entities and yet not quite (or not yet) fully mathematical objects, either. Finally, alongside the shift in theorist and theory, there arose, in the trading zone between physics and mathematics, a style of demonstration that did not conform either to older forms of physical argumentation familiar to particle physicists or to canonical proofs recognizable to "pure" mathematicians.
By introducing new categories of persons, objects, and demonstrations, string theory made manifest conflicts over the values that propel and restrict the conduct of research. These debates, joined explicitly by both mathematicians and physicists, focused on the values that ought to guide research, and the disagreements were consequential. At stake were the principles according to which students should be trained, how credit for demonstrations should be partitioned, what research programs ought be funded, and what would count as a demonstration. For all these reasons, the status of claims and counterclaims about string theory mattered. They were not "just rhetoric" constructed after the fact; they were, in part, struggles over the present and future of physics. Values, in the conjoint moral and technical sense I have in mind, were not, as one historian derisively called them, mere "graffiti." Nor is it the case that these values respected a distinction between "inside" and "outside" science. These were not values in the sense of "propriety," such as whether or not honorary authorship would be countenanced on a group paper. Rather, I will argue that the "values" in debate crosscut through the central, guiding commitments of physics and mathematics into the wider, everyday sense of the term. For this reason, dismissing the role of values in shaping theoretical research makes it impossible to understand both the moral passion behind these debates over demonstrative standards, the participants' own understanding of their distinctive scientific cultures, and ultimately, the scientific persona of the physicist.
The argument will follow this order: section two tracks the reaction by particle physicists to the shift by string theorists away from the constant interplay between theory and experiment. Sections three through five home in on the creation during the late 1980s and early 1990s of a striking "trading zone" between physicists and mathematicians around a variety of developments including that of "mirror symmetry," a remarkable development at once physical and mathematical. Mirror symmetry offered insight both into the shape of string theory after the higher dimensions curled up and provided new ways of understanding not only fundamental features of algebraic geometry, but also reshaped the status of geometry itself. By following the ways mathematicians and physicists saw one another in the episode of mirror symmetry-and the ways each side came to understand aspects of the other's theoretical culture-it becomes possible to characterize the broad features of a new place for theory in the world. Finally, in light of the tremendous impact of this hybrid physics-mathematics, section six analyzes the mathematicians' sometimes conflicted reaction: a response mixing enormous enthusiasm with grave reservations about the loss of rigor that accompanied the mathematicians' collaboration with the physicists. In a sense the physicists' and mathematicians' anxieties mirrored one another: both saw danger in parting from historically established modes of demonstrations that gave identity to their fields. These discussions were hard fought and explicit: in the midst of remarkable new results, claims, and critics, string theorists never had the luxury of being unself-conscious: the purpose, standards, and foundation of their budding discipline were always on the table.
At the end of the millennium, string theory resided, both powerfully and precariously, in the hybrid center between fields, bounded on one side by the continent of physics under the flag of experiment and on the other side by the continent of mathematics under the flag of rigor. To understand the aspirations and anxieties of this turbulent territory is to grasp a great deal of where theory stood at the end of the twentieth century.
Theory without experiment
In 1989, David Gross, from Princeton, chose physicists' favorite site for metaphors (the romantic mountains) on which to erect a new relation between theory and experiment, one far different from the close cooperation that had marked the mid-1970s. "One of the important tasks of theorists is to accompany our experimental friends down the road of discovery; walk hand in hand with them, trying to figure out new phenomena and suggesting new things that they might explore." Burnt into the collective memory both of pro- and antistring theorists was the example of the J/psi and other "charm" discoveries of November 1974. During the frenetic days of that late fall, and the months that followed, experimentalists tossed new particles into the ring, so to speak, and theorists worked furiously to explain them; theorists postulated new particles, new effects, and new theories-experimentalists responded with tests that could be prosecuted almost immediately. At the time Gross was writing, in the late 1980s, that highly responsive dialogue had fallen into silence-few experimental results were coming out of the accelerators, and the discoveries that were being reported had a wickedly short life: the neutrino oscillations (indicating that the neutrino might have a mass) came and went; proton decays were reported and retracted; monojets spurted momentarily from CERN, then vanished; the fifth force grabbed attention for a while and then loosened its hold. Under these circumstances some theorists-Gross included-were less and less inclined to theorize furiously after each new sighting. These were no longer the days of new, hot experimental news and papers written on airplanes returning from the accelerator laboratories, of quick phenomenological calculations using a couple of Feynman diagrams and Lie group calculations that could be done on one's fingers. Looking back in 1989, Gross put it this way:
It used to be that as we were climbing the mountain of nature the experimentalists would lead the way. We lazy theorists would lag behind. Every once in a while they would kick down an experimental stone which would bounce off our heads. Eventually we would get the idea and we would follow the path that was broken by the experimentalists. Once we joined our friends we would explain to them what the view was and how they got there. That was the old and easy way (at least for theorists) to climb the mountain. We all long for the return of those days. But now we theorists might have to take the lead. This is a much more lonely enterprise.
Without knowing the location of the summit, or how far it was, the theorists could promise little reassurance to themselves or to the experimentalists. In the meantime, experimentalists were not only left behind; they were left out altogether.
Not surprisingly, many experimentalists were shocked by the theorists' string ambition, not so much by the idea of theorists leading the way on an uncertain trek up an uncharted mountain, but because the experimentalists did not see how they could even gain a toehold in the foothills. Carlo Rubbia, who only a few years before had taken home a Nobel Prize for his team's 1983 discovery of the intermediate vector bosons, the W and the Z, lamented the loss of contact between experiment and theory at a meeting on supersymmetry and string theory:
I am afraid I am one of the few experimentalists here. In fact, I can see we are really getting fewer and fewer. I feel like an endangered species in the middle of this theoretical orgy. I am truly amazed. The theories are inventing particle after particle and now for every particle we have there is a particle we do not have, and of course we are supposed to find them. It is like living in a house where half the walls are missing and the floor only half finished.
After the bruising W and Z search, and a contentious struggle with the top quark, Rubbia had little appetite for a zoo of unknown particles as numerous as the known. Even one or two particles were terribly hard to find-Rubbia's UA1 collaboration had employed some 150 physicists for years at a cost of hundreds of millions of dollars to find the W and Z. Now this new breed of theorists was ordering a supersymmetric partner for every known entity: a selectron as partner to the electron, and so on all the way down the line.
Not only was this half-missing world overwhelming in its mandate for experimental discovery, but the very motivations cited by the theorists had moved ever further from the accelerator floor. Gosta Ekspong, a senior European experimentalist who often worked at CERN, addressed the purported aesthetic satisfactions of the string theorists:
I would like to address the question of truth and beauty; truth being experiment, beauty being theory.... The problem is that the latest [superstring] theories are so remote from experiment that they cannot even be tested. Therefore they don't play the same role as Dirac's equation.... I hope that this search for beauty does not drive theorists from experiments, because experiment has to be done at low energies, from one accelerator to the next and so on. Big jumps do not seem to be possible.
In the 1970s and 1980s, theory and experiment were categories (better: subcultures) with an intermediate trading zone of phenomenologists straddling the fence. Ahmed Ali was one of these, having worked at both DESY (Deutsches Elektronensynchrotron) and CERN, and he invoked the idiom of the fund-seeking experimentalist when he declaimed, "The present superstring theories are like letters of intent written by a lobby of theoretical physicists. They are very good in intent; but often what is said in the letter of intent and what is measured in the experiment are two very different things. The figure of merit of a theory is its predictive power which could be tested in an experiment in a laboratory."
In a sense, the discomfiture of experimentalists, and those working hand in glove with them, could be expected. New techniques in theory had left experimentalists ill at ease with gauge theories in their early stages, though by 1974 experimentalists had found the gauge theories suggestive of a wide range of predictions, tests, and directions for empirical work. The case of superstrings seemed much worse; there was no clear avenue for the accelerator laboratory to follow, and the theories themselves offered precious little to hold on to in the way of physically "intuitable" entities. Less expected, perhaps, was the vehement reaction against string theory from within the theoretical high-energy physics community.
I now turn to that part of the opposition that was certainly not grounded on a hostility to wide-ranging claims about unification, nor on a broad opposition to the disproportionate resources allocated to particle physics. (That is, I am not focusing here on criticisms mounted over the 1970s and 1980s by condensed-matter physicists such as Philip W. Anderson, who had in mind both a defense of emergent properties in many-body physics and an argument for a reallocation of human and material backing.) Far from being outsiders to the tradition of "fundamental" physics, Howard Georgi and Sheldon Glashow were as central to the gauge revolution of the 1970s as anyone. No, the dispute hinged on something even deeper, I believe, than the relative fundamentality of physical domains. It circled around differing visions of what theoretical physics should be.
Before the 1984 annus mirabilis of strings, Georgi opened the 1983 Fourth Workshop on Grand Unification with a transparency of a recent advertisement he had spotted:
HELP WANTED Young Particle theorist to work on Lattice Gauge Theories, Supergravity, and Kaluza-Klein Theories
Here, Georgi asserted, was a telling sign of the times, a position caught between "chemistry" (particle physicist nomenclature for a calculational activity in which fundamental principles were no longer at stake) and "metaphysics and mathematics" (particle physicist jargon for work without experiment). Superstrings had not yet emerged with the force it would a few years later, but the problem of choosing between truth as beauty and truth as experiment had, and Georgi sided squarely with those who demanded accessible measurements as a sine qua non of desirable theory.
The next years polarized the situation further. In 1986, Paul Ginsparg, who had himself contributed to the Alvarez-Gaume and Witten no-anomaly demonstration in superstrings, collaborated with his Harvard colleague Sheldon Glashow to bemoan the loss in superstrings of the historically productive conflict between experiment and theory:
In lieu of the traditional confrontation between theory and experiment, superstring theorists pursue an inner harmony where elegance, uniqueness and beauty define truth. The theory depends for its existence upon magical coincidences, miraculous cancellations and relations among seemingly unrelated (and possibly undiscovered) fields of mathematics. Are these properties reasons to accept the reality of superstrings? Do mathematics and aesthetics supplant and transcend mere experiment? Will the mundane phenomenological problems that we know as physics simply come out in the wash in some distant tomorrow? Is further experimental endeavor not only difficult and expensive but unnecessary and irrelevant?
(Continues...)
Excerpted from Growing explanations by M. Norton Wise Excerpted by permission.
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