Here I offer some teaching materials for learning Special and General relativity that I developed as an undergraduate, during an independent study with Professor Emeritus John Stachel.
First, I include a webpage, inspired by Hermann Bondi's 'Relativity and Common Sense', that seeks to explain the postulates of Special Relativity and their basic consequences, including three user-interactive, visual Java apps, introduced and explained throughout the lesson, and also made available for download.
Second, I offer a paper and accompanying visualization on the frame-dragging effects of GR. The paper builds on work of Professor Stachel's
on the logical independence of the Gravitational Equivalence Principle (EP) from the postulates of Special Relativity (SR), introducing mathematical objects fundamental to GR but only constructed in response to the conceptual requirements of the equivalence principle, and using the resulting mathematical apparatus to predict a near-field, low-velocity limit of a General-Relativistic spacetime in which a simplified model of the Earth is embedded. This solution includes the frame-dragging, or gravitomagnetic, effects of GR. I also include a user-interactive, visual simulation to help in intuitively understanding this effect. What is shown is the rotation that ideal rods would undergo for a uniform sphere of the mass and radius of Earth rotating at the rate at which Earth does rotate. The relative rotation rate of Earth to the rods shown is sped up by a rate of about 3 million as compared with the solution found. You can move your perspective by clicking and dragging with the mouse, and, if you have a mouse with a rolling wheel, can zoom in and out with that.
Numerous other calculations are presented, including a derivation of the centrifugal and Coriolis forces in terms of an affine-flat spacetime, the amount of splitting between the equatorial radii at which there are stable orbits for orbits in the direction of Earth's rotation versus in the opposite direction owing to the frame-dragging effects (this is analogous to the Zeeman effect) and an order-of-magnitude estimate of the amount of rotation undergone by Stanford's Gravity Probe B due to these effects.