Introduction to Measurement with Theory.

This paper is the introduction to the forthcoming Macroeconomic Dynamics Special Issue on Measurement with Theory. The Guest Editors of the special issue are William A. Barnett, W. Erwin Diewert, Shigeru Iwata, and Arnold Zellner. The authors of this detailed introduction and commentary are William A. Barnett, W. Erwin Diewert, and Arnold Zellner. The included papers are part of a larger initiative to promote measurement with theory in economics.Measurement; index number theory; aggregation theory.

Angular EPR paradox

The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum correlations for the conjugate variables of orbital angular momentum and angular position. We determine an experimentally testable criterion for the demonstration of an angular version of the EPR paradox. For the interpretation of future experimental results from our proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. For this measurement angular apertures are used to determine the probability density of the angle. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected.Comment: 21 pages, 9 figures, to be published in J. Mod. Opt. special issue on quantum imagin

Master of Science

thesisEmigration Canyon is situated in the portion of the Wasatch Mountains that are in the eastern part of Salt Lake County in north central Utah. A significant amount of ground-water development has taken place in the canyon in recent years to satisfy domestic water needs. This hydrologic investigation was undertaken to learn more about the ground-water aquifers in the canyon and their interrelationship so that the effects of past and future water development can be better understood. The area under study comprises about 29 square miles in the Rocky Mountain physiographic province and ranges in altitude from 4,870 feet to 8,954 feet. The rocks in the canyon have been folded into the Emigration Canyon syncline. The axis of the syncline is near to the stream channel and roughly parallel to it. The syncline plunges to the northeast, which is opposite to the direction of flow of Emigration Creek. More than half of the nearly 120 drilled wells in the canyon divert water from bedrock formations; others divert water from the alluvial, valley-fill material overlying the bedrock. The bedrock aquifers in the canyon are almost entirely in the Twin Creek Limestone, the Preuss Sandstone, and the Kelvin Formation. For this ground-water study, the area is referred to as the Emigration Canyon district of Salt Lake County and divided into four sub-districts--the Twin Creek, Preuss, Kelvin, and the Pinecrest. There are about 37 drilled wells in the Twin Creek sub-district, 12 in the Preuss sub-district, 65 in the Kelvin sub-district, and 4 in the Pinecrest sub-district. The water in the aquifers is under artesian pressures, and the pressures fluctuate annually as does the stream flow. The wells generally produce only a few gallons per minute, and their specific capacities are low. The rights to divert water from the stream date back as early as 1847, but most of the well rights have been established within the last 20 years. The majority of the estimated 660 persons that live in the canyon on a fu11- or part-time basis depend on drilled wells for their water supply. Over the past 65 years the stream flow of Emigration Creek has averaged about 4,350 acre-feet of water annually and has ranged from 13,500 acre-feet to 234 acre-feet. A thick alluvial cover over most of the canyon absorbs a large amount of the 20 to 35 inches of annual precipitation and influences the total annual stream flow. A seepage run, which was conducted in the late summer of 1965, indicates that some reaches of the stream are effluent, while other reaches are influent. The chemical quality of the stream and all but two of the wells sampled is of a calcium bicarbonate type. The water is very hard, but it is suitable for culinary use. Two wells sampled produce waters that are very high in total dissolved solids and are unfit for culinary use. The stream is highly contaminated with coliform bacteria. Coliform bacterial contamination was found in the shallow ground water, but tests indicate that deeper sources are probably uncontaminated. During the period of study, stream temperatures varied almost 30 degrees, while temperatures of water from individual wells varied only 3 or 4 degrees and remained near the average annual air temperature of the canyon. The annual ground-water pumpage is about 100 acre-feet of water, which is only about one-fortieth of the average annual flow of the stream. It is unlikely that present ground-water development has influenced surface- or ground-water rights, and additional drilling of small culinary wells could probably be allowed. Large wells or additional surface-water development could influence already established surface- and ground-water rights in both quantity and quality

Introduction to Measurement with Theory

This working paper is the first draft of an overview and commentary on the papers to appear in a Macroeconomic Dynamics Special Issue on Measurement with Theory. The included papers in the special issue are part of a larger initiative to promote "measurement with theory" in economics and planned to appear as special issues of other journals. A later revised draft of this initial commentary is planned to appear as the introduction to the Macroeconomic Dynamics special issue, expected to appear in 2010.Measurement; index number theory; aggregation theory.

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying ``diamagnetic'' angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields

Fourier relationship between angular position and optical orbital angular momentum

We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.Comment: 4 pages, 4 figure

How Effective Is Security Screening of Airline Passengers?

With a simple mathematical model, we explored the antiterrorist effectiveness of airport passenger prescreening systems. Supporters of these systems often emphasize the need to identify the most suspicious passengers, but they ignore the point that such identification does little good unless dangerous items can actually be detected. Critics often focus on terrorists\u27 ability to probe the system and thereby thwart it, but ignore the possibility that the very act of probing can deter attempts at sabotage that would have succeeded. Using the model to make some preliminary assessments about security policy, we find that an improved baseline level of screening for all passengers might lower the likelihood of attack more than would improved profiling of high-risk passengers

Spatially dependent electromagnetically induced transparency

Recent years have seen vast progress in the generation and detection of structured light, with potential applications in high capacity optical data storage and continuous variable quantum technologies. Here we measure the transmission of structured light through cold rubidium atoms and observe regions of electromagnetically induced transparency (EIT). We use q-plates to generate a probe beam with azimuthally varying phase and polarisation structure, and its right and left circular polarisation components provide the probe and control of an EIT transition. We observe an azimuthal modulation of the absorption profile that is dictated by the phase and polarisation structure of the probe laser. Conventional EIT systems do not exhibit phase sensitivity. We show, however, that a weak transverse magnetic field closes the EIT transitions, thereby generating phase dependent dark states which in turn lead to phase dependent transparency, in agreement with our measurements.Comment: 5 Pages, 5 Figure

Violation of Leggett inequalities in orbital angular momentum subspaces

We report an experimental test of Leggett's non-local hidden variable theory in an orbital angular momentum (OAM) state space of light. We show that the correlations we observe are in conflict with Leggett's model, thus excluding a particular class of non-local hidden variable theories for the first time in a non-polarization state space. It is known that the violation of the Leggett inequality becomes stronger as more detection settings are used. The required measurements become feasible in an OAM subspace, and we demonstrate this by testing the inequality using three and four settings. We observe excellent agreement with quantum predictions and a violation of five and six standard deviations, respectively, compared to Leggett's non-local hidden variable theory

Large-uncertainty intelligent states for angular momentum and angle

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.Comment: 20 pages, 9 figures, submitted to J. Opt. B special issue in connection with ICSSUR 2005 conferenc