Showing papers in "American Journal of Physics in 2013"

Observation of PT phase transition in a simple mechanical system

Abstract: If a quantum-mechanical Hamiltonian is PT symmetric, there are two possibilities: either all of the eigenvalues are real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else some of the eigenvalues are real and some are complex, in which case the Hamiltonian is said to be in a broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one can pass through the phase transition that separates the unbroken and broken phases. This transition has recently been observed in a variety of laboratory experiments. This paper explains the phase transition in a simple and intuitive fashion and then describes an elementary experiment in which the phase transition is easily observed.

Simulation of a Brownian particle in an optical trap

Abstract: An optically trapped Brownian particle is a sensitive probe of molecular and nanoscopic forces. An understanding of its motion, which is caused by the interplay of random and deterministic contributions, can lead to greater physical insight into the behavior of stochastic phenomena. The modeling of realistic stochastic processes typically requires advanced mathematical tools. We discuss a finite difference algorithm to compute the motion of an optically trapped particle and the numerical treatment of the white noise term. We then treat the transition from the ballistic to the diffusive regime due to the presence of inertial effects on short time scales and examine the effect of an optical trap on the motion of the particle. We also outline how to use simulations of optically trapped Brownian particles to gain understanding of nanoscale force and torque measurements, and of more complex phenomena, such as Kramers transitions, stochastic resonant damping, and stochastic resonance.

Radiometry and the Friis transmission equation

Abstract: To more effectively tailor courses involving antennas, wireless communications, optics, and applied electromagnetics to a mixed audience of engineering and physics students, the Friis transmission equation—which quantifies the power received in a free-space communication link—is developed from principles of optical radiometry and scalar diffraction. This approach places more emphasis on the physics and conceptual understanding of the Friis equation than is provided by the traditional derivation based on antenna impedance. Specifically, it shows that the wavelength-squared dependence can be attributed to diffraction at the antenna aperture and illustrates the important difference between the throughput (product of area and solid angle) of a single antenna or telescope and the throughput of a transmitter-receiver pair.

About photon correlations

Abstract: Some general properties of photon correlations are discussed in a simple way through an analysis of the two-detector measurement scheme It is shown that the assumption of the discreteness of the random process leads directly to the conclusion that the zero-delay value of the correlation function is only bound to be non-negative The adopted approach allows discussing in a more intuitive way the photon correlation properties of different optical fields, including non-classical fields presenting an apparent violation of the Cauchy-Schwarz inequality The comparison between the two- and the single-detector experiment clarifies the role of the operator ordering in the definition of the correlation function

There are no particles, there are only fields

Abstract: Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply that unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying that it's also true of nonrelativistic systems. Particles are epiphenomena arising from fields. Thus, the Schrodinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the two-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the two-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories.

The process of transforming an advanced lab course: Goals, curriculum, and assessments

Abstract: A thoughtful approach to designing and improving labs, particularly at the advanced level, is critical for the effective preparation of physics majors for professional work in industry or graduate school. With that in mind, physics education researchers in partnership with the physics faculty at the University of Colorado Boulder have overhauled the senior-level Advanced Physics Lab course. The transformation followed a three part process of establishing learning goals, designing curricula that align with the goals, and assessment. Similar efforts have been carried out in physics lecture courses at the University of Colorado Boulder, but this is the first systematic research-based revision of one of our laboratory courses. The outcomes of this effort include a set of learning goals, a suite of new lab-skill activities and transformed optics labs, and a set of assessments specifically tailored for a laboratory environment. While the particular selection of advanced lab experiments varies widely between institutions, the overall transformation process, the learning goals, and the assessments are broadly applicable to the instructional lab community.

Using a mobile phone acceleration sensor in physics experiments on free and damped harmonic oscillations

Abstract: We have used a mobile phone acceleration sensor, and the Accelerometer Monitor application for Android, to collect data in physics experiments on free and damped oscillations. Results for the period, frequency, spring constant, and damping constant agree very well with measurements obtained by other methods. These widely available sensors are likely to find increased use in instructional laboratories.

Using the Xbox Kinect Sensor for Positional Data Acquisition

Abstract: The Kinect sensor was introduced in November 2010 by Microsoft for the Xbox 360 video game system. It is designed to be positioned above or below a video display to track player body and hand movements in three dimensions (3D). The sensor contains a red, green, and blue (RGB) camera, a depth sensor, an infrared (IR) light source, a three-axis accelerometer, and a multi-array microphone, as well as hardware required to transmit sensor information to an external receiver. In this article, we evaluate the capabilities of the Kinect sensor as a 3D data-acquisition platform for use in physics experiments. Data obtained for a simple pendulum, a spherical pendulum, projectile motion, and a bouncing basketball are presented. Overall, the Kinect sensor is found to be a useful data-acquisition tool for motion studies in the physics laboratory.

On the universality of free fall, the equivalence principle, and the gravitational redshift

Abstract: Through the contributions of Galileo, Newton, and Einstein, we recall the universality of free fall (UFF), the weak equivalence principle (WEP), and the strong equivalence principle (SEP), in order to stress that general relativity requires all test masses to be equally accelerated in a gravitational field; that is, it requires UFF and WEP to hold. The possibility of testing this crucial fact with null, highly sensitive experiments makes these the most powerful tests of the theory. Following Schiff, we derive the gravitational redshift from the WEP and special relativity and show that, as long as clocks are affected by a gravitating body like normal matter, measurement of the redshift is a test of UFF/WEP but cannot compete with direct null tests. A new measurement of the gravitational redshift based on free-falling cold atoms and an absolute gravimeter is not competitive either. Finally, we compare UFF/WEP experiments using macroscopic masses as test bodies in one case and cold atoms in the other. We conclude that there is no difference in the nature of the test and that the merit of any such experiment rests on the accuracy it can achieve and on the physical differences between the elements it can test, macroscopic proof masses being superior in both respects.

Improving the quantification of Brownian motion

Abstract: Brownian motion experiments have become a staple of the undergraduate advanced laboratory, yet quantification of these experiments is difficult, typically producing errors of 10%–15% or more. Here, we discuss the individual sources of error in the experiment: sampling error, uncertainty in the diffusion coefficient, tracking error, vibration, and microscope drift. We model each source of error using theoretical and computational methods and compare the model to our experimental data. Finally, we describe various ways to reduce each source of error to less than 1%, improving the quantification of Brownian motion.

New insights into student understanding of complete circuits and the conservation of current

Abstract: The research reported in this paper represents an in-depth examination of the finding from an earlier investigation that university students often do not develop a functional understanding of the concept of a complete circuit. Participants in this study included undergraduates in introductory and upper-division physics courses as well as graduate teaching assistants. Although the concept of a complete circuit is covered in the standard undergraduate curriculum, students in all three groups had difficulty in applying this concept to single-loop, resistive circuits. Students frequently did not apply the conservation of current when analyzing circuits containing more than one battery. Certain basic conceptual difficulties spanned all of the populations and even persisted after instruction in upper-division courses that involved analog electronics.

Mansuripur's paradox

Abstract: A recent article by Mansuripur claims that the Lorentz force law is incompatible with special relativity. We discuss the “paradox” on which this claim is based. The resolution depends on whether one assumes a “Gilbert” model for the magnetic dipole (separated monopoles) or the standard “Ampere” model (a current loop). The former case was treated in these pages many years ago; the latter, as several authors have noted, constitutes an interesting manifestation of “hidden momentum.”

Kinetic exchange models: From molecular physics to social science

Abstract: We discuss several multi-agent models that have their origin in the kinetic exchange theory of statistical mechanics and have been recently applied to a variety of problems in the social sciences. This class of models can be easily adapted for simulations in areas other than physics, such as the modeling of income and wealth distributions in economics and opinion dynamics in sociology.

Young's double-slit experiment with single photons and quantum eraser

Abstract: An apparatus for a double-slit interference experiment in the single-photon regime is described. The apparatus includes a which-path marker that destroys the interference as well as a quantum eraser that restores it. We present data taken with several light sources, coherent and incoherent and discuss the efficacy of these as sources of single photons.

A simple proof of Bell's inequality

Abstract: Bell’s theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an extremely simple proof of Bell's inequality; a single figure suffices. This simplicity may be useful in the unending debate over what exactly the Bell inequality means, because the hypotheses underlying the proof become transparent. It is also a useful didactic tool, as the Bell inequality can be explained in a single intuitive lecture.

A thermoacoustic oscillator powered by vaporized water and ethanol

Abstract: We measure the temperature difference required to drive a thermoacoustic oscillator containing air, water vapor, and liquid water as the working fluids. The oscillator is composed of a large tube containing an array of narrow tubes connected at one end to a tank of liquid water. When the water is heated, the temperature difference across the tube array increases until thermoacoustic oscillations occur. The temperature difference at the onset of oscillation is measured to be 56 °C, significantly smaller (by ∼200 °C) than the temperature measured when the tank is filled with dry air instead of water. The temperature difference can be further reduced to 47 °C by using ethanol instead of water.

The Pilot-Wave Perspective on Quantum Scattering and Tunneling

Abstract: The de Broglie-Bohm “pilot-wave” theory replaces the paradoxical wave-particle duality of ordinary quantum theory with a more mundane and literal kind of duality: each individual photon or electron comprises a quantum wave (evolving in accordance with the usual quantum mechanical wave equation) and a particle that, under the influence of the wave, traces out a definite trajectory. The definite particle trajectory allows the theory to account for the results of experiments without the usual recourse to additional dynamical axioms about measurements. Instead, one need simply assume that particle detectors click when particles arrive at them. This alternative understanding of quantum phenomena is illustrated here for two elementary textbook examples of one-dimensional scattering and tunneling. We introduce a novel approach to reconcile standard textbook calculations (made using unphysical plane-wave states) with the need to treat such phenomena in terms of normalizable wave packets. This approach allows for a simple but illuminating analysis of the pilot-wave theory's particle trajectories and an explicit demonstration of the equivalence of the pilot-wave theory predictions with those of ordinary quantum theory.

A cost-efficient frequency-domain photoacoustic imaging system.

Abstract: Photoacoustic (PA) imaging techniques have recently attracted much attention and can be used for noninvasive imaging of biological tissues. Most PA imaging systems in research laboratories use the time domain method with expensive nanosecond pulsed lasers that are not affordable for most educational laboratories. Using an intensity modulated light source to excite PA signals is an alternative technique, known as the frequency domain method, with a much lower cost. In this paper, we describe a simple frequency domain PA system and demonstrate its imaging capability. The system provides opportunities not only to observe PA signals in tissue phantoms but also to acquire hands-on skills in PA signal detection. It also provides opportunities to explore the underlying mechanisms of the PA effect.

Response times to conceptual questions

Abstract: We measured the time taken by students to respond to individual Force Concept Inventory (FCI) questions We examine response time differences between correct and incorrect answers, both before and after instruction We also determine the relation between response time and expressed confidence Our data reveal three results of interest First, response times are longer for incorrect answers than for correct ones, indicating that distractors are not automatic choices Second, response times increase after instruction for both correct and incorrect answers, supporting the notion that instruction changes students' approach to conceptual questions Third, response times are inversely related to students' expressed confidence; the lower their confidence, the longer it takes to respond

Quasicrystals: A Primer (2nd ed.).

Abstract: This article reviews Quasicrystals: A Primer (2nd ed.). by Christian Janot 426 pp. , Oxford, UK, 2013. Price: $74.99 (paper) ISBN 978-0-19-965740-7.

The rise and fall of spinning tops

Abstract: The motion of four different spinning tops was filmed with a high-speed video camera. Unlike pointed tops, tops with a rounded peg precess initially about a vertical axis that lies well outside the top, and then spiral inward until the precession axis passes through a point close to the center-of-mass. The center-of-mass of a top with a rounded peg can rise as a result of rolling rather than sliding friction, contrary to the explanation normally given for the rise of spinning tops. A tippe top was also filmed and was observed to jump vertically off a horizontal surface several times while the center-of-mass was rising, contrary to the usual assumption that the normal reaction force on a tippe top remains approximately equal to its weight. It was found that the center-of-mass of a tippe top rises as a result of rolling friction at low spin frequencies and as a result of sliding friction at high spin frequencies. It was also found that, at low spin frequencies, a tippe top can precess at two different frequencies simultaneously.

Synchronization of a thermoacoustic oscillator by an external sound source

Abstract: Since the pioneering work of Christiaan Huygens on the sympathy of pendulum clocks, synchronization phenomena have been widely observed in nature and science. In this paper, we describe a simple experiment, with a thermoacoustic oscillator driven by a loudspeaker, which exhibits several aspects of synchronization. Both the synchronization region of leading order around the oscillator's natural frequency f0 and regions of higher order (around f0∕2 and f0∕3) are measured as functions of the loudspeaker voltage and frequency. We also show that increasing the coupling between the loudspeaker and the oscillator gives rise under some circumstances to the death of self-sustained oscillations (quenching). Moreover, two additional set of experiments are performed: the first investigates a feedback loop in which the signal captured by the microphone is delivered to the loudspeaker through a phase-shifter; the second investigates the nontrivial interaction between the loudspeaker and the oscillator when the latter a...

Bound charges and currents

Abstract: Bound charges and currents are among the conceptually challenging topics in advanced courses on electricity and magnetism. It may be tempting for students to believe that they are merely computational tools for calculating electric and magnetic fields in matter, particularly because they are usually introduced through abstract manipulation of integral identities, with the physical interpretation provided a posteriori. Yet these charges and currents are no less real than free charges and currents and can be measured experimentally. A simpler and more direct approach to introducing this topic, suggested by the ideas in the classic book by Purcell and emphasizing the physical origin of these phenomena, is proposed.

The symplectic egg in classical and quantum mechanics

Abstract: Symplectic geometry is the language of Classical Mechanics in its Hamiltonian formulation, and it also plays a crucial role in Quantum Mechanics. Symplectic geometry seemed to be well understood until 1985, when the mathematician Gromov discovered a surprising and unexpected property of canonical transformations: the non-squeezing theorem. Gromov's result, nicknamed the “principle of the symplectic camel,” seems at first sight to be an abstruse piece of pure mathematics. It turns out that it has fundamental—and unsuspected—consequences in the interpretations of both Classical and Quantum Mechanics, because it is essentially a classical form of the uncertainty principle. We invite the reader to a journey taking us from Gromov's non-squeezing theorem and its dynamical interpretation to the quantum uncertainty principle, opening the way to new insights.

A simple optics experiment to engage students in scientific inquiry

Abstract: A cone of light appears in a tank of water when a laser pointer shines through the water onto a white piece of paper upon which the tank is sitting. We describe how students can understand the origins of this cone by constructing multiple explanations, then proposing and designing experiments to test their explanations. This process is the foundation of the Investigative Science Learning Environment (ISLE) framework, designed to engage students in the reasoning activities similar to those that physicists use to construct and apply new knowledge. We describe typical student ideas and provide a list of equipment and suggestions for facilitating student exploration relating to optics. We also explain the formal physics behind the phenomena that are involved in the experiment. Finally, we suggest how the ISLE framework can be used to help instructors find problems and experiments that engage students in devising and testing multiple explanations.

Exploring the thermodynamics of a rubber band

Abstract: We describe an upper-division experiment in thermal physics where students measure the tension of a rubber band as a function of temperature and length and use a Maxwell relation to find the change in internal energy and entropy for an isothermal stretch. This allows students to experimentally check the predictions of the entropic spring model for elastomers and observe that the entropy does indeed decrease as a rubber band is stretched.

Why do bubbles in Guinness sink

Abstract: Stout beers show the counter-intuitive phenomena of sinking bubbles, while the beer is settling. Previous research suggests that this phenomenon is due to the small size of the bubbles in these beers and the presence of a circulatory current, directed downwards near the side of the wall and upwards in the interior of the glass. The mechanism by which such a circulation is established and the conditions under which it will occur has not been clarified. In this paper, we use simulations and experiments to demonstrate that the flow in a glass of stout beer depends on the shape of the glass. If it narrows downwards (as the traditional stout glass, the pint, does), the flow is directed downwards near the wall and upwards in the interior and sinking bubbles will be observed. If the container widens downwards, the flow is opposite to that described above and only rising bubbles will be seen.

Advance of perihelion

Abstract: The advance of perihelion, in particular for Mercury, is regarded as a classical test of general relativity, but a number of other (in some cases much larger) contributions to this phenomenon are seldom discussed in detail in textbooks. This paper presents a unified framework for evaluating the advance of perihelion due to (a) general relativity, (b) the solar quadrupole moment, and (c) planetary perturbations, the last in a ring model where the mass of each perturbing planet is “smeared out” into a coplanar circular orbit. The exact solution of the ring model agrees to within 4% with the usually quoted figure. Time-dependent contributions beyond the ring model contain some surprising features: they are not small, and some with long periods could mimic a secular advance.

On trajectories of rolling marbles in cones and other funnels

Abstract: We report on theoretical and experimental results for a ball that rolls without slipping on a surface of revolution, whose symmetry axis is aligned with a uniform gravitational field, particularly investigating both near-circular orbits and scattering-type orbits in cones. The experimental data give support for the theoretical treatment, a non-trivial application of Newton's second law that expands on our previous work and related work of others. Our findings refine those from a recent article in this journal, and largely replicate those obtained from an earlier Lagrangian approach, adding some new details and commentary. While the orbits of marbles rolling in cones do not match inverse-square-law orbits quantitatively (e.g., instead of Kepler's 3rd law, we have T2∝R), we argue that students should experience these qualitative phenomena—precession of orbits, escape velocity behavior, spin-orbit coupling, conservation laws for angular momentum, energy, and spin projection—as much for the fun and kinesthetic impressions as for the raw learning. We also report on a heretofore largely ignored variable in the exploration of rolling orbits in a gravity well: the marble's spin about its own axis as it rolls. Experimenters can, intentionally or not, vary this initial condition and produce different orbital periods for a given orbital radius—a distinctly non-celestial behavior. Careful selection of the initial spin direction and speed for a particular cone can result in marble orbits that mimic the planetary ellipses.

Collimated blue light generation in rubidium vapor

Abstract: We describe an experiment for generating and characterizing a beam of collimated blue light (CBL) in a rubidium vapor. Two low-power, grating-feedback diode lasers, operating at 780.2 nm (5S1/2→5P3/2) and 776.0 nm (5P3/2→5D5/2), respectively, provide step-wise excitation to the 5D excited state in rubidium. Under the right experimental conditions, cascade decay through the 6P excited state will yield a collimated blue (420-nm) beam of light with high temporal and spatial coherence. We investigate the production of a blue beam under a variety of experimental conditions and characterize the spatial coherence and spectral characteristics. This experiment provides advanced undergraduate students with a unique opportunity to investigate nonlinear optical phenomena in the laboratory and uses equipment that is commonly available in laboratories equipped to investigate diode-laser-based absorption spectroscopy in rubidium.