Narrow Results

In his 1972 book Science At the Crossroads, Helbert Dingle attacked the consistency of special relativity through a fallacious argument championed by the crank community even to this day. Dingle’s affair is a curious chapter in the history of physics and, more generally, science. We briefly review Dingle’s case from a historical and didactic perspective.

Based on some important properties of dS space, we present a Beltrami model ℬ_Λ that may shed light on the observable puzzle of dS space and the paradox between the special relativity principle and cosmological principle. In ℬ_Λ, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson–Walker-like metric. It is of positive spatial curvature of order Λ. This has already been shown by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.

We define new coordinates using the family of accelerated Rindler observers in Minkowski space–time and study the spatial sections (hypersurfaces of simultaneity) adapted to the noninertial frame that arises from our definition. We show that the geometry of the spatial sections is not Euclidean. Owing to this feature, the new noninertial frame can be employed to illustrate, in a simple way, the connection between acceleration and non-Euclidean geometry in the relativistic context.

By means of the rotational transformations of octonion coordinate systems, the paper aims to explore the physical properties of conserved quantities relevant to the vectorial magnitudes within the material media, revealing the simultaneity of some conserved quantities in the electromagnetic and gravitational fields. Maxwell first utilized the algebra of quaternions to describe the electromagnetic theory. The subsequent scholars studied the physical properties of electromagnetic and gravitational fields simultaneously, including the octonion linear momentum, angular momentum, torque and force within the material media. According to the algebra of octonions, the scalar parts of octonion physical quantities remain unchanged, while the vectorial parts may alter, in the rotational transformations of octonion coordinate systems. From the octonion characteristics, it is able to deduce a few conserved quantities related to the vectorial magnitudes in the octonion space $𝕆$, including the magnitudes of linear momentum, angular momentum, torque and force. Similarly, it is capable of inferring several conserved quantities relevant to the vectorial magnitudes in the transformed octonion space ${𝕆}_u$, including the magnitudes of electric current, magnetic moment and electric moment. Through the analysis and comparison, it is concluded that some conserved quantities, relevant to the vectorial magnitudes, are unable to be established simultaneously, from the point of view of the octonion spaces. This is helpful to deepen the further understanding of some conserved quantities related to the vectorial magnitudes.

A simple method to objectively and simultaneously measure eye’s longitudinal and transverse chromatic aberrations was proposed. A dual-wavelength wavefront measurement system using two Hartmann–Shack wavefront sensors was developed. The wavefronts of the red (639.1nm) and near-infrared (786.0nm) lights were measured simultaneously for different positions in the model eye. The chromatic wavefronts were converted into Zernike polynomials. The Zernike tilt coefficient (first term) was used to calculate the transverse chromatic aberration along the $x$-direction, while the Zernike defocus coefficient (fourth term) was used to calculate the longitudinal chromatic aberration. The measurement and simulation data were consistent.

In the present paper, we propose a heuristic and intuitive approach to visualize how force fields “move” when their source moves at a constant velocity $v$ or accelerates with acceleration $a$ relative to a stationary observer. Our approach is based on the application of the principle of relativity and the principle of equivalence and holds regardless of the nature of the force field. The results presented here have been derived in the nonrelativistic approximation ($v\ll c$ and $a\mathrm{\Delta }t\ll c$, $\mathrm{\Delta }t$ being the interval of time within which we observe the field). We shall show that in both cases of uniform and accelerated motion of the source, the field moves rigidly with the source. Namely, for every observer, however distant from the source, the field is always directed away from (or points towards) the present, instantaneous position of the source. We also show that these results are in agreement with what we know from experimental evidence and full-fledged physical theories (of electromagnetism and gravitation) beyond the nonrelativistic approximation. The proposed approach may be considered as a tool to facilitate students in graduate and undergraduate courses to familiarize themselves with (and self convince of) such a counter-intuitive feature of the force fields.

Research has often focused on how foreign direct investment (FDI) transfers technology from developed economies to less developed economies. Most FDI occurs between developed economies, however, and the country receiving the greatest inflow of FDI is the United States. This paper examines whether such FDI inflows have stimulated growth of the U.S. economy. We apply time-series data to a simultaneous-equation model (SEM) that explicitly captures the bi-directional relationship between FDI and U.S. economic growth. FDI is found to have a significant, positive, and economically important impact on U.S. growth. Also, our SEM estimates reveal that FDI growth is income inelastic. These results imply that: (1) even a technologically advanced country such as the U.S. benefits from FDI, (2) the gains from FDI are very substantial in the long run, and (3) the sustainability of the U.S. current account deficit is enhanced by FDI's positive effect on productivity but undermined by the income inelasticity of FDI. Overall, the results suggest that U.S. policies should focus on keeping the country attractive to foreign direct investors.

This paper investigates the effects of health indicators such as adult survival rates (ASR) on GDP growth rates at 5-year intervals in several countries. Panel data were analyzed on GDP series based on purchasing power adjustments and on exchange rates. First, we developed a framework for modeling the inter-relationships between GDP growth rates and explanatory variables by re-examining the life expectancy–income relationship. Second, models for growth rates were estimated taking into account the interaction between ASR and lagged GDP level; issues of endogeneity and reverse causality were addressed. Lastly, we computed confidence intervals for the effect of ASR on growth rate and applied a test for parameter stability. The results showed positive effects of ASR on GDP growth rates in low-income countries.

This paper modeled the proximate determinants of infant survival using the National Family Health Survey data on 11,500 women from the most populous Indian state Uttar Pradesh in the period 1982–1992. A methodological framework was developed for analyzing the interrelationships between high fertility and infant mortality, gender differences in mortality, and for modeling the effects of health care and family planning variables. Probit models were estimated by maximum likelihood taking into account simultaneity of regressors and unobserved household differences. The proximate determinants of infant survival included maternal education and age at first birth, birth interval, the number of children before family planning was first used, maternal tetanus vaccination, and child's vaccinations. Indicator variables for a boy (girl) born at a birth order higher than the "ideal" number showed that unwanted births exacerbated female mortality.