Volume 72, Issue 2, February 2004
 PAPERS


Resource Letter PBGP1: Physics books for the general public
View Description Hide DescriptionThis Resource Letter is a checklist of popular books about physics and some of its allied sciences, grouped by subject and genre. Its principal purpose is to help physics teachers provide advice and guidance to their students and to the lay public.

The role of dynamics in the synchronization problem
View Description Hide DescriptionIs Einstein’s procedure for the synchronization of clocks in Special Relativity merely a convention about the oneway speed of light? This issue was first raised in the 1920s by H. Reichenbach, who argued that the standard synchronization involves circular reasoning, and that a nonstandard synchronization convention can be adopted, with unequal values of the speed of light in opposite directions. This “conventionalist thesis” has been widely discussed by physicists and philosophers in the context of kinematics, but not in the context of dynamics. We will show that an examination of the laws of dynamics resolves all ambiguities in synchronization. The nonstandard Reichenbach synchronization introduces pseudoforces into the equation of motion, and these pseudoforces are fingerprints of the nonstandard synchronization, just as the centrifugal and Coriolis pseudoforces are fingerprints of a rotating reference frame. In an inertial reference frame, the nonstandard synchronization is forbidden.

A laboratory on the fourpoint probe technique
View Description Hide DescriptionWe describe how a classic electrostaticsexperiment can be modified to be a fourpoint probe lab experiment. Students use the fourpoint probe technique to investigate how the measured resistance varies as a function of the position of the electrodes with respect to the edge of the sample. By using elementary electromagnetism concepts such as the superposition principle, the continuity equation, the relation between electric field and electric potential, and Ohm’s law, a simple model is derived to describe the fourpoint probe technique. Although the lab introduces the students to the ideas behind the Laplace equation and the methods of images, advanced mathematics is avoided so that the experiment can be done in trigonometry and algebra based physics courses. In addition, the experiment introduces the students to a standard measurement technique that is widely used in industry and thus provides them with useful handson experience.

Microwave Bragg diffraction in a model crystal lattice for the undergraduate laboratory
View Description Hide DescriptionWe describe an undergraduatelaboratory experiment in which Bragg diffraction is studied using microwavediffraction from a twodimensional crystal consisting of a square lattice of metal rods. This apparatus demonstrates the fundamental ideas of the Bragg theory of crystal diffraction using a macroscopic model. Thus, the geometrical relations between the crystal planes and the incoming and scattered wave directions are clearly visible. A key element of the apparatus is a computer interface that allows diffracted intensity measurements at all orientations of crystal and detector. No a priori assumptions need be made concerning the relation between the incident and refracted angles. We also present results of computer simulations of the scattering from our crystal. These simulations have been useful in understanding the differences between the simple Bragg theory and the results from our experiment on a small crystal with finite source and detector distances.

Resolution enhancement by dithering
View Description Hide DescriptionWe show that the uncertainty determined by the minimum division of a measuring instrument can be diminished by using dithering. We present a numerical example to introduce the technique and two experiments that show how the precision is enhanced.

Grading student problem solutions: The challenge of sending a consistent message
View Description Hide DescriptionGrading sends a direct message to students about what is expected in class. However, often there is a gap between the assigned grade and the goals of the instructor. In an interview study of faculty teaching calculusbased introductory physics, we verified that this gap exists and identified three themes that appear to shape grading decisions: (1) a desire to see student reasoning, (2) a reluctance to deduct points from a student solution that might be correct, and (3) a tendency to project correct thought processes onto a student solution. When all three themes were expressed by an instructor, the resulting conflict was resolved by placing the burden of proof on either the instructor or the student. The weighting of the themes with the burden of proof criterion explains our finding that although almost all instructors reported telling students to show their reasoning in problem solutions, about half graded problem solutions in a way that would likely discourage students from showing this reasoning.

A hint of renormalization
View Description Hide DescriptionAn elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what is specific to field theory and what is intrinsic to renormalization. We link the general arguments and results to real phenomena encountered in particle physics and statistical mechanics.

A wellknown boundary value problem requires unusual eigenfunctions
View Description Hide DescriptionThe Sturm–Liouville problem for the equation on a closed interval with general unmixed boundary conditions leads to periodic, linear, and exponential eigenfunctions. However, examples of physical situations where different types of these eigenfunctions are employed together in a general solution are difficult to find. We present a physical problem of this type.

Electrostatics in the presence of dielectrics: The benefits of treating the induced surface charge density directly
View Description Hide DescriptionA new method is presented for solving electrostaticboundary value problems with dielectrics or conductors and is applied to systems with spherical geometry. The strategy of the method is to treat the induced surface charge density as the variable of the boundary value problem. Because the potential is expressed directly in terms of the induced surface charge density, the potential is automatically continuous at the boundary. The remaining boundary condition produces an algebraic equation for the surface charge density, which when solved leads to the potential. The surface charge method requires the enforcement of only one boundary condition, and produces the induced surface charge in addition to the potential with no additional labor. The surface charge method also can be applied in nonspherical geometries and provides a starting place for efficient numerical solutions.

A demonstration of phonons that implements the linear theory
View Description Hide DescriptionBeads on a vibrating wire are used to simulate the discrete structure of a solidstate material. The novel idea of the experiment is to use very small oscillation amplitudes of the wire to avoid nonlinearities in the interaction. We achieve a good signaltonoise ratio using a lockin technique. We find quantitative agreement between theory and experiment for not only a mono and a diatomic chain, but also for the bare wire. The latter agreement is the crucial aspect that distinguishes our experiment from previous ones. This agreement assures that the fundamental assumption of the theory (Hooke’s law) is satisfied. We show that the properties of phonon dispersion curves are not special, and that the same band structures occur when the wavelength of any wave becomes comparable to the length scale of a discrete periodicity.

Operator domains and selfadjoint operators
View Description Hide DescriptionTo construct a selfadjoint operator the domain of the operator has to be specified by imposing an appropriate boundary condition or conditions on the wave functions on which the operator acts. We illustrate situations for which different boundary conditions lead to different operators and hence to different physics.

Physical time and physical space in general relativity
View Description Hide DescriptionThis paper comments on the physical meaning of the line element in general relativity. We emphasize that, generally speaking, physical spatial and temporal coordinates (those with direct metrical significance) exist only in the immediate neighborhood of a given observer, and that the physical coordinates in different reference frames are related by Lorentz transformations (as in special relativity) even though those frames are accelerating or exist in strong gravitational fields.

Nondegenerate normalmode doublets in vibrating flat circular plates
View Description Hide DescriptionThe vibrations of flat circular plates have been studied for hundreds of years and are well understood. However, when vibrating circular plates are discussed in textbooks, the relation between pairs of spatially orthogonal vibrational patterns that occur at each of the normalmode frequencies often is ignored. Usually these orthogonal solutions are presented to the student as being degenerate in frequency. However, in practice the degeneracy of the doublet often is broken, and the two spatially orthogonal solutions are separated in frequency. We show theoretically and experimentally that the degeneracy can be broken by small density perturbations in the plate, and we derive a formula for predicting the magnitude of the frequency splitting. We have used electronic speckle patterninterferometry to investigate the phenomenon of doublet splitting and have confirmed the validity of the theory.

A simple approach to Anderson localization in onedimensional disordered lattices
View Description Hide DescriptionWe present a simple approach to Anderson localization in onedimensional disordered lattices. We introduce the tightbinding model in which one orbital and a single random energy are assigned to each lattice site, and the hopping integrals are constant and restricted to nearestneighbor sites. The localization of eigenstates is explained by twoparameter scaling arguments. We compare the size scaling of the level spacing in the bare energy spectrum of the quasiparticle (in the ideal lattice) with the size scaling of the renormalized disorder seen by the quasiparticle. The former decreases faster than the latter with increasing system size, giving rise to mixing and to the localization of the bare quasiparticle wave functions in the thermodynamic limit. We also provide a selfconsistent calculation of the localization length and show how this length can be obtained from optical absorptionspectra for Frenkel excitons.

Perturbations of the excited quantum oscillator: From number states to statistical distributions
View Description Hide DescriptionWe discuss the transitions that an external timedependent perturbation can induce upon a quantum harmonic oscillator in an excited initial state. In particular, we show how to describe transitions of the oscillator from initial states characterized by statistical distributions. These results should be useful for interpretations of the properties of weakly dispersive bosonic excitations in quantum systems whose dynamics is investigated by time or energy resolved spectroscopies.

Determining a force law from a scattering experiment
View Description Hide DescriptionAn experiment is described in which a small permanent magnet is scattered by a second identical fixed magnet. The apparatus sits on an air table, so the scattered object can move with negligible friction. A ring of Hall effect switches surrounding the fixed magnet is used to determine the scattering angle. The experimental data are compared with numerical simulations and the form of the repulsive force between the two magnets is determined.

Why does a cylindrical permanent magnet rotate when levitated above a superconducting plate?
View Description Hide DescriptionStable levitation of a permanent magnet above a superconducting plate is a popular demonstration in physicslectures. If the magnet has a cylindrical shape and is axially magnetized, it can start to oscillate along the horizontal axis with increasing amplitude and might eventually rotate continuously. We present a mathematical model based on physical considerations and simulations of the stationary and transient rotation using a finite element method.

Tunneling ionization of atoms
View Description Hide DescriptionWe discuss the theory for the ionization of atoms by tunneling due to a strong external static electric field or an intense low frequency laser field.

Slow group velocity propagation of sound via defect coupling in a onedimensional acoustic band gap array
View Description Hide DescriptionA simple experimental system is presented in which the group velocity of acoustic wave packets traveling in an airfilled waveguide can be slowed to values much smaller than the speed of sound in air. The experiment is an acoustic analog of the muchstudied optical phenomenon of slow light propagation. Slow (or even stopped) light propagation has been observed in atomic vapors in the vicinity of strong dispersion, typically associated with electromagnetically induced transparency. In the acoustic experiment described here, strong dispersion is produced by the introduction of a defect in an otherwise perfectly periodic onedimensional acoustic band gap array. The defect produces a narrow transmission band within the forbidden acoustic band gap region resulting in strong dispersion. By tuning the carrier frequency of the acoustic wave packet to the peak transmission of the defect, the group velocity can be slowed to where is the speed of sound in air. These results are shown to be consistent with theoretical calculations.

Single light scattering: Bubbles versus droplets
View Description Hide DescriptionThe intensity and polarizationcharacteristics of scattered light beams are studied for bubbles in water and compared to the case of waterdroplets in air. The size distributions of the scatters in both systems are assumed to be the same. It is shown that spherical polydispersions of waterdroplets give generally larger depolarization effects than bubbles, leading to larger entropy production by droplets than bubbles.
