Field theory: why have some physicists abandoned it?

Our present-day theory for fundamental processes in Nature— and by this I mean our descriptions of elementary particles and forces—is phenomenally successful. Experimental data confirms theoretical prediction; where accurate calculations and experiments are attainable, agreement is achieved to many— six or seven—significant figures. Table 1 shows two examples. Of course mostly such precision cannot be achieved, neither theoretically nor experimentally. Yet no experiment has thus far contradicted our understanding of the gravitational interactions as described by Einstein’s general relativity, nor of the strong nuclear interactions, nor of the electromagnetic and radioactivity-producing weak interactions that are now collected into the Glashow–Weinberg–Salam ‘‘standard model.’’ (A hint of physical phenomena beyond the standard model has recently been provided by experimentalists announcing the discovery of a neutrino mass, which is not predicted by the standard model. But if this much-anticipated result is independently confirmed, it can then be fitted very easily into a straightforward extension of the present-day model.) The strong and electro-weak theories make use of a quantum mechanical description, whereas classical physics suffices to account for all known gravitational phenomena. The theoretical structure within which this success has been achieved is local field theory, which offers physicists a tremendously wide variety of applications; it is a language with which physical processes are discussed and it provides a model for fundamental physical reality, as described by our theories of strong, electro-weak, and gravitational processes. No other framework exists in which one can calculate ‘‘so many phenomena with such ease and accuracy’’ (L. P. Williams, personal communication). Arising from a mathematical account of the propagation of fluids (both ‘‘ponderable’’ and ‘‘imponderable’’), field theory emerged over 100 years ago in the discussion within classical physics of Faraday–Maxwell electromagnetism and soon thereafter of Einstein’s gravity theory. Schrödinger’s wave mechanics became a bridge between classical and quantum field theory: the quantum mechanical wave function is also a local field, which when ‘‘second’’ quantized gives rise to a true quantum field theory, albeit a nonrelativistic one. Quantization of electromagnetic waves produced the first relativistic quantum field theory, which when supplemented by the quantized Dirac field gave us quantum electrodynamics, whose further generalization to matrices of fields—the Yang–Mills construction—is the present-day standard model of elementary particles. This development carries with it an extrapolation over enormous scales: initial applications were at microscopic distances or at energies of a few electron volts, whereas contemporary studies of elementary particles involve 1011 electron volts or short distances of 10216 cm. The ‘‘quantization’’ procedure, which extended classical field theory’s range of validity, consists of expanding a classical field in normal modes and taking each mode to be a quantal oscillator. Field theoretic ideas also reach for the cosmos through the development of the ‘‘inflationary scenario’’—a speculative, but completely physical, analysis of the early universe, which appears to be consistent with available observations. Additionally, quantum field theories provide effective descriptions of many-body, condensed matter physics. Here the excitations are not elementary particles and fundamental interactions are not probed, but the collective phenomena that are described by many-body field theory exhibit many interesting effects, which in turn have been recognized as important for elementary particle theory. Such exchanges of ideas between different subfields of physics demonstrate vividly the vitality and flexibility of field theory. But in spite of these successes, today there is little confidence that field theory will advance our understanding of Nature at its fundamental workings, beyond what has been achieved. Although in principle all observed phenomena can be explained by present-day field theory (in terms of the quantal standard model for particle physics, perhaps slightly extended to incorporate massive neutrinos, and the classical Newton–Einstein model for gravity), these accounts are still imperfect. The particle physics model requires a list of ad hoc inputs that give rise to conceptual, general questions such as: Why is the dimensionality of space-time four? Why are there two types of elementary particles (bosons and fermions)? What determines the number of species of these particles? The standard model also leaves us with specific technical questions: What fixes the matrix structure, various mass parameters, mixing angles, and coupling strengths that must be specified for concrete prediction? Moreover, classical gravity theory has not been integrated into the quantum field description of nongravitational forces, again because of conceptual and technical obstacles: quantum theory makes use of a fixed space-time, so it is unclear how to quantize classical gravity, which allows space-time to fluctuate; even if this is ignored, quantizing the metric tensor of Einstein’s theory produces a quantum field theory beset by infinities that cannot be controlled. But these shortcomings are actually symptoms of a deeper lack of understanding that has to do with symmetry and symmetry breaking. Physicists mostly agree that ultimate laws of Nature enjoy a high degree of symmetry, that is, the © 1998 by The National Academy of Sciences 0027-8424y98y9512776-3$2.00y0 PNAS is available online at www.pnas.org. Table 1. Comparison between particle physics theory and experiment in two very favorable cases