We describe an experimental technique that allows for the direct determination of the motion (i.e., the momentum) of electrons in atoms, molecules, and solids. This ($e$, $2e$) technique centers on a fast electron's ejecting a second electron from a target. Precise spectroscopy of both electrons' final energies and momenta provides very significant information on the second electron's initial state. Decades of past ($e$, $2e$) studies on single-molecule states have now progressed into studies of condensed matter. The interpretation of these experiments is mediated in this colloquium by analysis of intermediate models in the form of chainlike molecules.

The development of different analytical and approximate numerical methods for calculations of shock-wave propagation in the inhomogeneous interstellar medium is reviewed. The models of ultracompact H II regions, nonspherical supernova remnants, bubbles produced by stellar winds of hot stars, and expanding supershells are discussed on the basis of these calculations.

Although thermodynamic fluctuation theory originated from statistical mechanics, it may be put on a completely thermodynamic basis, in no essential need of any microscopic foundation. This review views the theory from the macroscopic perspective, emphasizing, in particular, notions of covariance and consistency, expressed naturally using the language of Riemannian geometry. Coupled with these concepts is an extension of the basic structure of thermodynamic fluctuation theory beyond the classical one of a subsystem in contact with an infinite uniform reservoir. Used here is a hierarchy of concentric subsystems, each of which samples only the thermodynamic state of the subsystem immediately larger than it. The result is a covariant thermodynamic fluctuation theory which is plausible beyond the standard second-order entropy expansion. It includes the conservation laws and is mathematically consistent when applied to fluctuations inside subsystems. Tests on known models show improvements. Perhaps most significantly, the covariant theory offers a qualitatively new tool for the study of fluctuation phenomena: the Riemannian thermodynamic curvature. The thermodynamic curvature gives, for any given thermodynamic state, a lower bound for the length scale where the classical thermodynamic fluctuation theory based on a uniform environment could conceivably hold. Straightforward computation near the critical point reveals that the curvature equals the correlation volume, a physically appealing finding. The combination of the interpretation of curvature with a well-known proportionality between the free energy and the inverse of the correlation volume yields a purely thermodynamic theory of the critical point. The scaled equation of state follows from the values of the critical exponents. The thermodynamic Riemannian metric may be put into the broader context of information theory.

Irreversible fractal-growth models like diffusion-limited aggregation (DLA) and the dielectric breakdown model (DBM) have confronted us with theoretical problems of a new type for which standard concepts like field theory and renormalization group do not seem to be suitable. The fixed-scale transformation (FST) is a theoretical scheme of a novel type that can deal with such problems in a reasonably systematic way. The main idea is to focus on the irreversible dynamics at a given scale and to compute accurately the nearest-neighbor correlations at this scale by suitable lattice path integrals. The next basic step is to identify the scale-invariant dynamics that refers to coarse-grained variables of arbitrary scale. The use of scale-invariant growth rules allows us to generalize these correlations to coarse-grained cells of any size and therefore to compute the fractal dimension. The basic point is to split the long-time limit ($t\to \infty$) for the dynamical process at a given scale that produces the asymptotically frozen structure, from the large-scale limit ($r\to \infty$) which defines the scale-invariant dynamics. In addition, by working at a fixed scale with respect to dynamical evolution, it is possible to include the fluctuations of boundary conditions and to reach a remarkable level of accuracy for a real-space method. This new framework is able to explain the self-organized critical nature and the origin of fractal structures in irreversible-fractal-growth models. It also provides a rather systematic procedure for the analytical calculation of the fractal dimension and other critical exponents. The FST method can be naturally extended to a variety of equilibrium and nonequilibrium models that generate fractal structures.

Understanding the mechanism responsible for superconductivity in the high-temperature cuprates has been one of the major goals of condensed-matter physicists since the discovery of these exciting materials in 1986. Experimental evidence suggests that the pairing state may be unconventional, featuring an anisotropic order parameter for which a wide range of theoretical models for the superconducting pairing have been proposed. Recently, a new class of experiments has been presented that are sensitive to the phase of the superconducting order parameter, allowing an unambiguous determination of the symmetry of the pairing state. These experiments, based on the interference of the quantum-mechanical phases in Josephson tunnel junctions and dc SQUID devices, give strong evidence for pairing in a channel with $d$--wave symmetry in the most widely studied cuprate, $Y{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$. Confirmation of this pairing state will focus efforts to develop a microscopic theory for the high-temperature superconductors and to apply them in power transmission and electronic device technologies.

This colloquium reviews some unusual paramagnetic phenomena in granular high-temperature superconductors. These are consistently explained by assuming that there is frustration in the coupling patterns between the neighboring grains. Such frustration effects occur in a natural way in a multiply connected superconductor with Josephson junctions if the order parameter has unconventional symmetry due to Cooper pairing in a higher angular momentum channel, e.g., $d$- wave pairing. A simple model is introduced to describe the magnetic properties of a frustrated granular superconductor. Large orbital magnetic moments are spontaneously created, leading to superparamagnetic behavior. These results suggest that the unusual paramagnetic phenomena are a consequence of unconventional symmetry of the pairing state in the high-temperature superconductors.

The first-order phase transition between the $A$ and $B$ phases of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ has remained an outstanding mystery in helium physics for nearly 20 years. The small difference in bulk free energies between the two phases, combined with the relatively large surface energy associated with the $\mathrm{AB}$ interface, leads to an anomalously large critical radius for nucleation, of order 1 μm, suggesting a lifetime for the super-cooled $A$ phase against homogeneous nucleation far beyond the age of the universe. Yet anisotropy of the high-temperature phase minimizes the depairing effects of surfaces, thus making conventional heterogeneous nucleation unlikely. Recent experiments have been reported that lend support to one of the more exotic nucleation mechanisms ever proposed: Leggett's "baked Alaska" model, in which the $B$ phase is nucleated by cosmic rays penetrating the supercooled $A$ phase. The results of these experiments are discussed, along with the prospects for future work.

It is a fact of life in empirical science that experiments often give discordant results. This is nowhere better illustrated than in the recent history of experiments concerning the existence of a heavy, 17-keV neutrino. The 17-keV neutrino was first "discovered" by Simpson in 1985. The initial replications of the experiment all gave negative results, and suggestions were made that attempted to explain Simpson's result using accepted physics, without the need for a heavy neutrino. Subsequent positive results by Simpson and others led to further investigation. Several of these later experiments found evidence supporting that claim, whereas others found no evidence for such a particle. Some theorists attempted to explain away the result, and others tried to explain it and to incorporate it within existing theory without the need for a new particle, or to look for the further implications of such a particle, or to propose a new theory that would incorporate the new particle. The question of the existence of such a heavy neutrino remained for several years. Recently, doubt has been cast on the two most convincing positive experimental results, and errors have been found in those experiments. In addition, recent, extremely sensitive experiments have found no evidence for the 17-keV neutrino. The consensus is that it does not exist. The discord has been resolved by a combination of finding errors in one set of experiments and a preponderance of evidence.

A survey is offered of applications to fundamental physical research, in the years immediately following World War II, of the instrumentalities developed for radar during that war. Attention is given to radar astronomy and radio astronomy, linear and cyclical accelerators, microwave spectroscopy, molecular beams, nuclear magnetic resonance, electron paramagnetic and ferromagnetic resonance, measurements of resistivity at high frequencies in metals and of second sound in helium II, and to the concepts of information and signal-to-noise ratio as basic to the design and analysis of experiments. In conjunction with this survey, consideration is given to the autonomy of physics as a knowledge-producing enterprise, framed as a question of continuity in research directions. As that question implies a baseline, the survey of postwar applications is preceded by a survey of those prewar directions of physical research requiring the highest available radio frequencies. Some 500 references are given.

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields, the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.

One of Feynman's early applications of path integrals was to superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. He showed that the thermodynamic properties of Bose systems are exactly equivalent to those of a peculiar type of interacting classical "ring polymer." Using this mapping, one can generalize Monte Carlo simulation techniques commonly used for classical systems to simulate boson systems. In this review, the author introduces this picture of a boson superfluid and shows how superfluidity and Bose condensation manifest themselves. He shows the excellent agreement between simulations and experimental measurements on liquid and solid helium for such quantities as pair correlations, the superfluid density, the energy, and the momentum distribution. Major aspects of computational techniques developed for a boson superfluid are discussed: the construction of more accurate approximate density matrices to reduce the number of points on the path integral, sampling techniques to move through the space of exchanges and paths quickly, and the construction of estimators for various properties such as the energy, the momentum distribution, the superfluid density, and the exchange frequency in a quantum crystal. Finally the path-integral Monte Carlo method is compared to other quantum Monte Carlo methods.

In recent years, major advances have taken place in our understanding of welding processes and welded materials. Because of the complexity of fusion welding processes, solution of many important contemporary problems in fusion welding requires an interdisciplinary approach. Current problems and issues in fusion welding are reviewed. Solution of these problems, apart from being a contribution to the advancement of science, is also necessary for science-based tailoring of composition, structure, and properties of the welded materials.

Superfluid turbulence in He II flows appears as a stochastic tangle of quantized vortex lines. Interest in this system extends beyond the field of superfluid helium to include the study of statistical physics of extended objects and classical turbulence. A wealth of information concerning the vortex tangle has been supplied by experiments, by phenomenological models, and by numerical simulation. In the restricted case of stationary homogeneous flows, a good correlation between theory and experiment has already been demonstrated. This review therefore concentrates on nonstationary and nonhomogeneous processes with the goal of understanding the dynamical properties of the vortex tangle. The first part of this paper reviews the concept of the stochastic vortex tangle with emphasis on the work of Vinen and Schwarz. Special attention is given to justifying Vinen's equation as a basis for the study of nonstationary processes. This analysis reveals that the interpretation of experimental results requires a careful account of the mutual influence of the vortex tangle and the flow of the supefluid. The second part of this paper reviews the development of the required hyrodynamic equations of superfluid turbulence. These equations are applied to a number of examples such as linear and nonlinear sound, heat pulses, and fluctuations. The role of stochastic vortices in the phase-transition problem is discussed. Attention is focused on the relation between hydrodynamic effects and the vortex tangle properties. Finally, the main results concerning the stochastic vortex tangle are resumed and some of the important questions are pointed out.

Recent initial experiments in magnetic resonance force microscopy (MRFM) have detected the magnetic force exerted by electrons and nuclei in microscopic samples. The experiments generate a force signal by modulating the sample magnetization with standard magnetic resonance techniques. Sample sizes of a few nanograms generate readily detected force signals of order ${10}^{-14\mathrm{}}$ to ${10}^{-16\mathrm{}}$ Newtons. This article describes the present status of MRFM technology, with particular attention to the feasibility of detecting single-electron magnetic moments, and the possible applications of MRFM in biological imaging.

The elements, theoretical basis, and experimental status of perturbative quantum chromodynamics are presented. Relevant field-theoretic methods are introduced at a nonspecialist level, along with a review of the basic ideas and methods of the parton model. This is followed by an account of the fundamental theorems of quantum chromodynamics, which generalize the parton model. Summaries of the theoretical and experimental status of the most important hard-scattering processes are then given, including electron-positron annihilation, deeply inelastic scattering, and hard hadron-hadron scattering, as induced both by electoweak interactions and by quantum chromodynamics directly. In addition, a discussion is presented of the global fitting approach to the determination of parton distributions in nucleons.

This article reviews the developments in the electrodynamics of direct interparticle action, emphasizing the achievements in quantum as well as classical electrodynamics. It is shown that the application of the Wheeler-Feynman absorber theory of radiation places stringent requirements on the asymptotic future and past light cones of the universe. All Friedmann cosmologies fail to meet these requirements, but the steady-state and the quasi-steady-state models have the right kind of structure to make the theory work. Further, it is shown that the working theory is free from the problems of divergence that trouble the classical and quantum field theory. In particular, no renormalization is needed: The bare mass and bare charge of an electron are finite. A few ideas relating to the response of the universe to a local microscopic experiment are presented as well as on possible clues to the outstanding issues of foundations of quantum theory.