Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our...
We introduce a series of activities to help students understand the partial derivatives that arise in thermodynamics. Students construct thought experiments that would allow them to measure given partial derivatives. These activities are constructed with a number of learning goals in mind, beginning with helping students to learn to think...
Representations of SO(4,2;R) are constructed using 4 x 4 and 2 x 2 matrices with elements in H' ⊗ C . Using 2 x 2 matrix representations of C and H', the 4 x 4 representation is interpreted in terms of 16 x 16 real matrices. Finally, the known isomorphism...
Physics problems that require integration, such as finding the center of mass of an object or finding the electric field from a continuous distribution of charge, are one type of problem that is difficult for introductory physics students to solve. These problems require students to define a coordinate system in...
Physicists seek to understand the world and often use mathematics to aid in attaining that goal. Thus when doing mathematics they often interrogate their results in order to ensure that they align with their expectations and to gain new insight into how the world works. This seeking of coherence between...
In this dissertation we study the electromagnetic properties of planar waveguides
with non-magnetic strongly anisotropic dielectric cores. We develop an analytical
description of the mode propagation in these systems and show that the index
of refraction can be either positive or negative depending on the specific material
parameters. Propagating modes...
Several studies in recent years have demonstrated that upper-division students struggle with partial derivatives
and the complicated chain rules ubiquitous in thermodynamics. We asked several experts (primarily faculty who teach
thermodynamics) to solve a challenging and novel thermodynamics problem in order to understand how they navigate through
this maze. What...
Several studies in recent years have demonstrated that upper-division students struggle with the
mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts
to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold.
First, we highlight the importance of cognitive task...
We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...
We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and
compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to
their motion. Applications involving possible violations of the second law of thermodynamics are briefly
addressed.