A quantum theory of gravitation is constructed, by considering the gravitational field in the linear approximation to be a rank II tensor field, which has imposed upon it the auxiliary conditions of symmetry, transversality, and tracelessness. Extensive use is made of the close analogy between the electromagnetic field as a special case of a vector field, and the gravitational field as a special case of a tensor field. This analogy includes the necessity of introducing an indefinite metric in order to make the auxiliary conditions compatible with the commutation relations. A complete theory of gravitation must take into account the gravitating nature of gravitation and hence must be a nonlinear theory. A method proposed by Gupta of iterating the linear field equations for this purpose is investigated, and it is shown that this method fails, because the Lagrangian for the second order equations does not exist. An alternative method of iteration is proposed which avoids this problem, and which yields a functional equation for the Lagrangian of the full nonlinear theory. Finally, the problem of photon-photon scattering due to the gravitational interaction is investigated. This is done by constructing an interaction Hamiltonian by using the principle of the compensating field and then applying the standard methods of quantum electrodynamics. It is found that for sufficiently high frequencies this process dominates the purely electrodynamic scattering of photons by photons. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

It has long been presumed that any consistent nonlinear theory of a spin-two field must be generally covariant. Using Wald's consistency criteria, we exhibit classes of nonlinear theories of a spin-two field that do not have general covariance. We consider four alternative formulations of the spin-two equations. As a first example, we consider a conformally invariant theory of a spin-two field coupled to a scalar field. In the next two cases, the usual symmetric rank-two tensor field, γab, is chosen as the potential. In the fourth case, a traceless symmetric rank-two tensor field is used as the potential. We find that consistent nonlinear generalization of these different formulations leads to theories of a spin-two field that are not generally covariant. In particular, we find types of theories which, when interpreted in terms of a metric, are invariant under the infinitesimal gauge transformation γab→γab + ∇ (a∇[symbol omitted]K[symbol omitted]), where Kab is an arbitrary two-form field. In addition, we find classes of theories that are conformally invariant. As a related problem, we compare the types of theories obtained from the nonlinear extension of a divergence- and curl-free vector field when it is described in terms of two of its equivalent formulations. We find that nonlinear extension of the theory is quite different in each case. Moreover, the resulting types of nonlinear theories may not necessarily be equivalent. A similar analysis is carried out for three-dimensional electromagnetism. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

An invariant formalism is developed for a two-body system in a flat spacetime interacting by the exchange of particles of zero proper mass. A solution, to second order, of the equations of motion is obtained. The principle of equivalence is applied to study the motion of a system of particles in a uniform gravitational field. The equations of motion are then generalized to a Riemannian spacetime and the acceleration of non-spinning point-particles in a gravitational field is briefly discussed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This dissertation identified and addressed four of the unresolved issues pertaining to the proposition that nonabsolute/ relativistic (N/R) thinking is one of the possible unifying commonalities underlying the selected models of postformal reasoning, namely Problem Finding, Dialectical Reasoning, Relativistic Operations and Reflective Judgment. A total of 254 participants aged 10 to 48 and attending Grade 5 to doctoral studies were involved. Each participant was administered eight tests in pencil-and-paper format to measure eight different constructs of thinking. Different specific hypotheses were evaluated through different statistical approaches. The four identified issues were addressed as follows: Firstly, nonabsolute/ relativistic thinking was reconceptualized and operationally defined as a multidimensional and multilevel construct. Two dimensions were proposed: the basic form and the epistemic view. Within the basic form dimension, two levels were proposed: the formal and the postformal forms. Secondly, a battery of three tests was specifically designed by Arlin and the author to measure the different dimensions and levels of nonabsolute/ relativistic thinking. Thirdly, strong empirical evidence was obtained supporting the general hypothesis that nonabsolute/ relativistic thinking is a possible unifying commonality underlying the four selected postformal models. Within the construct of nonabsolute/ relativistic thinking, two dimensions, the basic form and the epistemic view, can be differentiated as hypothesized. Fourthly, empirical evidence was also obtained supporting the general hypothesis that nonabsolute/ relativistic thinking is an instance of both formal and postformal reasoning. Specifically within the basic form dimension, two qualitatively different forms, the formal and the postformal, can be differentiated as hypothesized. Findings also suggested that the development of a nonabsolute epistemic view might play a crucial role in the development of the postformal form. Therefore, the emergence of the postformal form can be explained by a paradigm shift from an absolute to a nonabsolute epistemic view. Performances in the tests of the postformal form and of the epistemic view in combination were found to be good predictors of performances in the selected postformal tests. Significant implications of the findings are that nonabsolute/ relativistic thinking represents a form of metamorphosis from closed-system to open-system thinking and it might serve as a potential springboard in the development of higher order thinking. / Education, Faculty of / Educational and Counselling Psychology, and Special Education (ECPS), Department of / Graduate

No description available.

During the first stages of planet formation small particles (~0.1 – 1 µm) in the protoplanetary disk collide at low relative velocities (less than 1 m/s) and tend to aggregate into cm-size "pebbles" through a combination of electrostatic interactions and gravitational streaming instabilities. Particles in this size regime also compose a layer of regolith on small, airless bodies that evolves under conditions very different than those on Earth. Characterizing the response of regolith to low-energy impacts in a microgravity environment is therefore critical to our understanding of the processes that lead to the formation of these objects and our ability to develop safe operation procedures on their surfaces. Flight-based microgravity experiments investigating low-velocity collisions of cm-size projectiles into regolith have revealed that certain impact events result in mass transfer from the target regolith onto the surface of the projectile. Characterizing the key parameters and their interactions that produce these events have important implications for the role of energy dissipation and accretion in planet formation processes and understanding the mechanical behavior of granular media composing the surfaces of small bodies. I carried out experimental and numerical campaigns designed to investigate these mass transfer events and found that accretion outcomes differ significantly depending on whether the projectile is launched into granular material or initially at rest before pulling away from the granular bed. I found that interaction effects between various parameters and the balance of the experiment design significantly influence mass transfer outcomes and must be taken into account for future experiment designs. I also present my contributions to a CubeSat mission that will provide the opportunity to observe tens of thousands of collisions between particles in the velocity and size regime relevant to the earliest stages of planet formation.

The spirit of the Latin 'classicus' as a broad ideology has in one sense existed through every age of modern human history. It could begin to be described as an attitude that is resistant to sudden change and is not interested in dramatic breaks with tradition or the avant garde. It embraces the methodical evolution of aesthetic and artistic values that are connected at their origin to a cosmography which is conceived within every given age. This large-scale conception of existence which encompasses all of what is known in the cosmos is a primary manifestation of every culture. Several systems of ideas are given by 20th century theoretical physics. They are the foundation of our science and provide an explicit basis for all branches of scientific endeavor. Taken as a whole, they constitute the current understanding of our universe--our world. What emerges from the ideas given by relativity theory, quantum physics, string theory, and the mathematics of astro-physics is a profound and far reaching cosmography resembling nothing like that of the Renaissance or of classical Greece. Non-Euclidean geometry and the math of higher dimensional space begin to break free of their abstract character as these symbolic disciplines now inform and reconcile the reality of cosmic space. It is therefore appropriate to understand the cosmography of today in relation to the new science paradigm. As cosmic space and conceptual space have always been intimately connected in architecture of the classical spirit, this new cosmography then becomes a viable basis for reestablishing a classical expression. / Master of Architecture

Doppelt defends the key elements of Kuhn's thesis that scientific revolutions occur when one paradigm is replaced by another and that crucial aspects of competing paradigms are incommensurable. He concedes the merits in the views of those positivist critics of Kuhn who contend that for paradigms to be comparable their proponents must be able to communicate with one another, to agree on a common core of meaning for basic concepts and to deal with shared data and problems. However, he maintains that in identifying the problems which are held to be of fundamental importance and in adopting the standards by which explanatory adequacy is to be evaluated, rival paradigms do not overlap sufficiently for them to have genuine commensurability. This leads Doppelt to accept Kuhn's version of epistemological relativism which maintains that the rationality of the acceptance of new paradigms by the scientific community, at least in the short-run, has an irreducible normative dimension that is strongly conditioned by subjective factors. Doppelt also accepts Kuhn's views with respect to the loss of data, and the question of cumulative progress. The absence of paradigm-neutral external standards allegedly allows each paradigm to assign priority to its own internal standards, thus providing persuasive grounds for the incommensurability of competing paradigms and for epistemological relativism. Nevertheless, he acknowledges that the validity of these arguments over the long term is a contingent issue which can only be resolved by a careful examination of the historical evidence. A chemical revolution took place in the latter part of the eighteenth century when the oxygen theory replaced that based on hypothetical phlogiston. This transition is frequently cited as a typical example of a paradigm - one that illustrates Kuhn's claims for a shift in standards and a loss of data as central features of scientific revolutions. The phlogiston theory held that phlogiston was a normal constituent of air. It explained smelting as the transfer of phlogiston from the air (or from phlogiston-rich charcoal) to the earthy components of the ore, and held that the similar properties of the metallic products could be attributed to their phlogiston content. Combustion, including the calcination of metals and the respiration of living organisms, was viewed as a process involving the release of phlogiston to the atmosphere. The development of improved techniques for collecting gases and for measuring their volume and weight lead to emphasis on precise quantitative methods for evaluating chemical data as distinct from those based on simple quantitative descriptive observations. These developments soon posed difficulties for the phlogiston theory (eg.,the anomalous weight loss during combustion). Eventually, clarification of the composition of water and the use of the 'nitrous air1 test for the ability of a gas to support combustion and respiration (its 'goodness') led to the discovery of oxygen as a component of air and the demonstration that combustion involved combination with an exact quantity of this gas. Within a relatively short period of time, the oxygen theory gained general acceptance and the phlogiston theory was abandoned by most chemists. A critical examination of the events which culminated in the chemical revolution fails to bear out the claim that it was accompanied by a significant loss of empirical data or that it did not represent genuine cumulative progress in scientific knowledge. Instead the history of this revolution indicates that paradigm-neutral external standards for evaluating explanatory adequacy (conservatism, modesty, simplicity, generality, internal and external coherence, refutability, precision, successful predictions) were available and played a crucial role in bringing about this transition. Accumulating evidential warrant played the decisive role in the triumph of the oxygen theory. / Arts, Faculty of / Philosophy, Department of / Graduate

A new method for generating initial data for simulations of neutron stars in binary systems. The construction of physically relevant initial data is crucial to accurate assessment of gravitational wave signals relative to theoretical predictions. This method builds upon the Bowen-York curvature for puncture black holes. This data is evolved and compared against simulations in the literature with respect to orbital eccentricity, merger and collapse times, and emitted energy and angular momentum. The data exhibits some defects, including large central density oscillations in stars and center of mass drift in unequal-mass systems. Some approaches for improvements in potential future work are discussed.

No description available.