Entries by stevendaryl

Rindler Motion in Special Relativity, Part 1: Hyperbolic Trajectories

Introduction: Why Rindler Motion? When students learn relativity, it’s usually taught using inertial (constant velocity) motion. There are lots of reasons for this, but mainly it’s because it’s the easiest kind of motion for deriving the results of relativity, and historically, thinking about inertial motion is what led to Einstein’s theory.  An unfortunate side-effect of…

Lenses and Pinholes: What Does “In Focus” Mean?

In introductory physics, the optics unit often teaches about virtual and real images, focal lengths, indexes of refraction, etc. Some questions that are sometimes glossed over in the rush to present the mathematical formulas and definitions is: What does it mean for an image to form at a particular location? What does it mean for…

Quantum Amplitudes, Probabilities and EPR

This is a little note about quantum amplitudes. Even though quantum probabilities seem very mysterious, with weird interference effects and seemingly nonlocal effects, the mathematics of quantum amplitudes are completely straight-forward. (The amplitude squared gives the probability.) As a matter of fact, the rules for computing amplitudes are almost exactly the same as the classical…

Solving the Cubic Equation for Dummies

Everybody learns the “quadratic formula” for solving equations of the form [itex]A x^2 + B x + C = 0[/itex], even though you don’t really need such a formula, because you can solve for [itex]x[/itex] through the technique of “completing the square”. What you need a formula for is the solution to the cubic equation:…