Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists' language encodes different varieties of analogical models through the use of grammar and conceptual metaphor. We hypothesize that students categorize concepts into ontological categories based on the grammatical structure of physicists' language. We also hypothesize that students over-extend and misapply conceptual metaphors in physicists' speech and writing. Using our theory, we will show how, in some cases, we can explain student difficulties in quantum mechanics as difficulties with language.Comment: Accepted for publication in Phys. Rev. ST:PE

Uses and Abuses of Effective Lagrangians

Motivated by past and recent analyses we critically re-examine the use of effective lagrangians in the literature to constrain new physics and to determine the `physics reach' of future experiments. We demonstrate that many calculations, such as those involving anomalous trilinear gauge-boson couplings, either considerably overestimate loop-induced effects, or give ambiguous answers. The source of these problems is the use of cutoffs to evaluate the size of such operators in loop diagrams. In contrast to other critics of these loop estimates, we prove that the inclusion of nonlinearly-realized gauge invariance into the low-energy lagrangian is irrelevant to this conclusion. We use an explicit example using known multi-Higgs physics above the weak scale to underline these points. We show how to draw conclusions regarding the nature of the unknown high-energy physics without making reference to low-energy cutoffs.Comment: 36 page

From General Relativity to Quantum Gravity

In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades.Comment: To appear in \emph{General Relativity and Gravitation: A Centennial Survey}, commissioned by the International Society for General Relativity and Gravitation and to be published by Cambridge University Press. Abhay Ashtekar served as the `coordinating author' and combined the three contribution

Learning with multiple representations: An example of a revision lesson in mechanics

We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion using various representations: motion diagrams, vector diagrams, free-body diagrams, verbal description, equations and graphs, drawn against time as well as against displacement. Overall, feedback from students about the lesson was positive. We further discuss the benefits of using computer simulation to support and extend student learning.Comment: 10 pages, 5 figures, 2 tables http://iopscience.iop.org/0031-912