We show how to embed spacelike slices of the Schwarzschild wormhole (or Einstein-Rosen bridge) in 3. Graphical images of embeddings are given, including depictions of the dynamics of this nontraversable wormhole at constant Kruskal times up to and beyond the “pinching off” at Kruskal times ±1.

The phase shift that occurs upon reflection from a dielectric surface is an interesting yet elusive topic in undergraduate and graduate level optics courses. Many students learn the Fresnel equations, which describe the theory of reflection-induced phase shifts, but there are few experiments which enable direct measurements of these phase shifts. We describe several experiments based on polarimetry to measure the differential phase shifts which occur upon reflection from dielectric–dielectric interfaces. Comparison of the experimental results with the theory given in optics textbooks reveals apparent inconsistencies, which can be resolved by taking into account various conventions.

We have developed a senior undergraduate experiment that illustrates frequency stabilization techniques using radio-frequency electronics. The primary objective is to frequency stabilize a voltage controlled oscillator to a cavity resonance at 800 MHz using the Pound-Drever-Hall method. This technique is commonly applied to stabilize lasers at optical frequencies. By using only radio-frequency equipment, it is possible to systematically study aspects of the technique more thoroughly, inexpensively, and free from eye hazards. Students also learn about modular radio-frequency electronics and basic feedback control loops. By varying the temperature of the resonator, students can determine the thermal expansion coefficients of copper, aluminum, and super invar.