Insights and disclosures: a study of the philosophical theology of Bernard Lonergan and Ian Ramsey

The thesis compares and contrasts some aspects of the philosophical theology of Canadian Jesuit Bernard Lonergan (1904 - 1984) and Anglican Bishop Ian Ramsey (1915 - 1972). We ask whether the views of two theologians from very different backgrounds can be compatible. Lonergan and Ramsey both thought that modern science was a key resource for examining how intentional cognitive activity in humans is undertaken and hence science and scientific method give a strong indication of how we think and talk about God, theology and theological method. We therefore start with the authors’ views of science and scientific method, noting similarities alongside a crucial difference: Ramsey emphasises the scientific use of models, while Lonergan emphasises the precision of mathematics. We then argue that their descriptions of cognitive processes are similar, albeit with some differences. The differences in the views of models are emphasised in our comparison of their understandings of language and meaning. We suggest that while the views are different they are compatible and we propose a hybrid model for religious language based on an integration and synthesis of both authors’ views. The discussion draws together around theological method. Lonergan proposed several methods in his work and we discuss two. Ramsey did not describe an explicit method, but a consistent approach can be found in his theological writings. These methods are then compared with the authors’ theological writings in a case study, the atonement. We argue that Lonergan follows neither of his methods and that both he and Ramsey have a flexible approach to the process of doing theology. The discussions of theological method, supplemented by earlier considerations of models and method are used to suggest a hybrid theological method. This generalises Lonergan’s method, includes Ramsey’s process and yields a model whereby we can discuss how theology is done

Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step, square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a future publication.Comment: 18 pages, 8 figure

Two state scattering problem to Multi-channel scattering problem: Analytically solvable model

Starting from few simple examples we have proposed a general method for finding an exact analytical solution for the two state scattering problem in presence of a delta function coupling. We have also extended our model to deal with general one dimensional multi-channel scattering problems

The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses

Particle production due to external fields (electric, chromo-electric or gravitational) requires evolving an initial state through an interaction with a time-dependent background, with the rate being computed from a Bogoliubov transformation between the in and out vacua. When the background fields have temporal profiles with sub-structure, a semiclassical analysis of this problem confronts the full subtlety of the Stokes phenomenon: WKB solutions are only local, while the production rate requires global information. Incorporating the Stokes phenomenon, we give a simple quantitative explanation of the recently computed [Phys. Rev. Lett. 102, 150404 (2009)] oscillatory momentum spectrum of e+e- pairs produced from vacuum subjected to a time-dependent electric field with sub-cycle laser pulse structure. This approach also explains naturally why for spinor and scalar QED these oscillations are out of phase.Comment: 5 pages, 4 figs.; v2 sign typo corrected, version to appear in PR

Clinical and economic evaluation of laparoscopic surgery compared with medical management for gastro-oesophageal reflux disease : 5-year follow-up of multicentre randomised trial (the REFLUX trial)

Peer reviewedPublisher PD

Reconciling Semiclassical and Bohmian Mechanics: III. Scattering states for continuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. A modification for discontinuous potential stationary stattering states was presented in a second paper [J. Chem. Phys. 124 034115 (2006)], whose generalization for continuous potentials is given here. The result is an exact quantum scattering methodology using classical trajectories. For additional convenience in handling the tunneling case, a constant velocity trajectory version is also developed.Comment: 16 pages and 14 figure

Low-energy fusion caused by an interference

Fusion of two deuterons of room temperature energy is studied. The nuclei are in vacuum with no connection to any external source (electric or magnetic field, illumination, surrounding matter, traps, etc.) which may accelerate them. The energy of the two nuclei is conserved and remains small during the motion through the Coulomb barrier. The penetration through this barrier, which is the main obstacle for low-energy fusion, strongly depends on a form of the incident flux on the Coulomb center at large distances from it. In contrast to the usual scattering, the incident wave is not a single plane wave but the certain superposition of plane waves of the same energy and various directions, for example, a convergent conical wave. As a result of interference, the wave function close to the Coulomb center is determined by a cusp caustic which is probed by de Broglie waves. The particle flux gets away from the cusp and moves to the Coulomb center providing a not small probability of fusion (cusp driven tunneling). Getting away from a caustic cusp also occurs in optics and acoustics

A Gravitational Redshift Determination of the Mean Mass of White Dwarfs. DBA and DB Stars

We measure apparent velocities (v_app) of absorption lines for 36 white dwarfs (WDs) with helium-dominated atmospheres -- 16 DBAs and 20 DBs -- using optical spectra taken for the European Southern Observatory SN Ia progenitor survey (SPY). We find a difference of 6.9+/-6.9 km/s in the average apparent velocity of the H-alpha lines versus that of the HeI 5876AA for our DBAs. This is a measure of the blueshift of this He line due to pressure effects. By using this as a correction, we extend the gravitational redshift method employed by Falcon et al. (2010) to use the apparent velocity of the HeI 5876AA line and conduct the first gravitational redshift investigation of a group of WDs without visible hydrogen lines. We use biweight estimators to find an average apparent velocity, _BI, (and hence average gravitational redshift, _BI) for our WDs; from that we derive an average mass, _BI. For the DBAs, we find _BI = 40.8+/-4.7 km/s and derive _BI = 0.71 +0.04 -0.05 Msun. Though different from of DAs (32.57 km/s) at the 91% confidence level and suggestive of a larger DBA mean mass than that for normal DAs derived using the same method (0.647 +0.013 -0.014 Msun; Falcon et al. 2010), we do not claim this as a stringent detection. Rather, we emphasize that the difference between _BI of the DBAs and of normal DAs is no larger than 9.2 km/s, at the 95% confidence level; this corresponds to roughly 0.10 Msun. For the DBs, we find ^He_BI = 42.9+/-8.49 km/s after applying the blueshift correction and determine _BI = 0.74 +0.08 -0.09 Msun. The difference between ^He_BI of the DBs and of DAs is less than or equal to 11.5 km/s (~0.12 Msun), at the 95% confidence level. The gravitational redshift method indicates much larger mean masses than the spectroscopic determinations of the same sample by Voss et al. (2007)...Comment: Accepted to the Astrophysical Journal, 10 pages double-column, 3 figures, 5 table

Euclidean resonance in a magnetic field

An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed regions, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. Such phenomenon, which occurs at the certain magnetic field, is called Euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance a long distance underbarrier motion is possible.Comment: 7 pages, 4 figure

Landau-Zener problem for energies close to potential crossing points

We examine one overlooked in previous investigations aspect of well - known Landau - Zener (LZ) problem, namely, the behavior in the intermediate, i.e. close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4 x 4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy, and continously matching those in the corresponding energy regions.Comment: 5 pages, 1 figur