Stamatis Vokos

Student understanding of time in special relativity: Simultaneity and reference frames

This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of relativity was probed. The results indicate that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames. Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co-exist.

The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems

The issue of how to assess learning is addressed in the context of an investigation of student understanding of the work-energy and impulse-momentum theorems. Evidence is presented that conceptual and reasoning difficulties with this material extend from the introductory to the graduate level and beyond. A description is given of the development of an instructional sequence designed to help students improve their ability to apply the theorems to real motions. Two types of assessment are compared. The results demonstrate that responses to multiple-choice questions often do not give an accurate indication of the level of understanding and that questions that require students to explain their reasoning are necessary. Implications for the preparation of teaching assistants are discussed.

The Challenge of Changing Deeply Held Student Beliefs about the Relativity of Simultaneity.

Previous research indicates that after standard instruction, students at all levels often construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity co-exist. We describe the development and assessment of instructional materials intended to improve student understanding of the concept of time in special relativity, the relativity of simultaneity, and the role of observers in inertial reference frames. Results from pretests and post-tests are presented to demonstrate the effect of the curriculum in helping students deepen their understanding of these topics. Excerpts from taped interviews and classroom interactions help illustrate the intense cognitive conflict that students encounter as they are led to confront the incompatibility of their deeply held beliefs about simultaneity with the results of special relativity.

Student understanding of light as an electromagnetic wave: Relating the formalism to physical phenomena

During an investigation of student understanding of physical optics, we found that some serious difficulties that students have with this topic may be due, at least in part, to a lack of understanding of the nature of light as an electromagnetic wave. We therefore decided to look carefully at how students interpret the diagrammatic and mathematical formalism commonly used to represent a plane EM wave. The results of this research have guided the development and modification of tutorials that address some of the difficulties that we identified. These instructional materials are an example of how, within a relatively short time allotment, a curriculum developed on the basis of research can help students relate the concepts and formal representations associated with EM waves to physical phenomena.

Student understanding of the wave nature of matter: Diffraction and interference of particles

This paper reports on a study of student understanding of the wave nature of matter in the context of the pattern produced by the diffraction and interference of particles. Students in first-year, second-year, and third-year physics courses were asked to predict and explain how a single change in an experimental setup would affect the pattern produced when electrons or other particles are incident on a single slit, double slit, or crystal lattice. The errors made by students after standard instruction indicated the presence of similar conceptual and reasoning difficulties at all levels. Among the most serious was an inability to interpret diffraction and interference in terms of a basic wave model. Other errors revealed a lack of a functional understanding of the de Broglie wavelength. Students often treated it as a fixed property of a particle, not as a function of the momentum. An important goal of this investigation was to provide a research base for the design of instruction to help students develop a...

Long range forces in quantum gravity.

We calculate the leading quantum and semi-classical corrections to the Newtonian potential energy of two widely separated static masses. In this largedistance, static limit, the quantum behaviour of the sources does not contribute to the quantum corrections of the potential. These arise exclusively from the propagation of massless degrees of freedom. Our one-loop result is based on Modanese’s formulation and is in disagreement with Donoghue’s recent calculation. Also, we compare and contrast the structural similarities of our approach to scattering at ultra-high energy and large impact parameter. We connect our approach to results from string perturbation theory.

Thermodynamic q distributions that aren't

Bosonic q-oscillators commute with themselves and so their free distribution is Planckian. In a cavity, their emission and absorption rates may grow or shrink – and even diverge – but they nevertheless balance to yield the Planck distribution via Einstein’s equilibrium method, (a careless application of which might produce spurious q-dependent distribution functions). This drives home the point that the black-body energy distribution is not a handle for distinguishing q-excitations from plain oscillators. A maximum cavity size is suggested by the inverse critical frequency of such emission/absorption rates at a given temperature, or a maximum temperature at a given frequency. To remedy fragmentation of opinion on the subject, we provide some discussion, context, and references.

Conserving energy in physics and society: Creating an integrated model of energy and the second law of thermodynamics

The second law of thermodynamics is typically not a central focus either in introductory university physics textbooks or in national standards for secondary education. However, the second law is a key part of a strong conceptual model of energy, especially for connecting energy conservation to energy degradation and the irreversibility of processes. We present the beginnings of a conceptual model of the second law as it relates to energy, with the aim of creating models and representations that link energy degradation, the second law, and entropy in a meaningful way for learners analyzing real-life energy scenarios. Our goal is to develop tools for use with elementary and secondary teachers and secondary and university students.

Goals for teacher learning about energy degradation and usefulness

The Next Generation Science Standards (NGSS) require teachers to understand aspects of energy degradation and the second law of thermodynamics, including energys availability and usefulness, changes in energy concentration, and the tendency of energy to spread uniformly. In an effort to develop learning goals that support teachers in building robust understandings of energy from their existing knowledge, we studied teachers impromptu conversations about these topics during professional development courses about energy. Many of these teachers ideas appear to align with statements from the NGSS, including the intuition that energy can be present but inaccessible, that energy can change in its usefulness as it transforms within a system, and that energy can lose its usefulness as it disperses, often ending up as thermal energy. Some teachers ideas about energy degradation go beyond what is articulated in the NGSS, including the idea that thermal energy can be useful in some situations and the idea that energys usefulness depends on the objects included in a scenario. Based on these observations, we introduce learning goals for energy degradation and the second law of thermodynamics that (1) represent a sophisticated physics understanding of these concepts, (2) originate in ideas that teachers already use, and (3) align with the NGSS. I. Introduction

Analytic structure of the self-energy for massive gauge bosons at finite temperature.

We show that the one-loop self-energy at finite temperature has a unique limit as the external momentum [ital p][sub [mu]][r arrow]0 [ital if] the loop involves propagators with distinct masses. This naturally arises in theories involving particles with different masses as is demonstrated for a toy model of two scalars as well as in a U(1) Higgs theory. We show that, in spontaneously broken gauge theories, this observation nonetheless does not affect the difference between the Debye and plasmon masses, which are often thought of as the ([ital p][sub 0]=0,[bold p][r arrow]0) and ([ital p][sub 0][r arrow]0,[bold p]=0) limits of the self-energy.