# Physics Articles, Guides, and Tutorials

## An Alternative Approach to Solving Collision Problems

Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles of conservation of momentum and energy for solving simple collision problems in one dimension. In this article we will be examining a very common type of collision problem: the inelastic or…

## Why We Don’t Discuss Perpetual Motion Machines (PMM)

Authorship Contributions From: Anorlunda You may want to believe the article you read, or the video you saw, or you may be very proud of your PMM invention.   It can be very difficult to analyze what is inside the box to find the flaw. Maybe we can’t find it. Maybe nobody can find it.  If…

## Accurate Fluid Dynamics By Video Analysis

Introduction Providing accurate fluid dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility, simplicity, and accessibility to introductory students.  The data from many introductory experiments, for example, is not sufficiently accurate to test whether a linear or a quadratic relationship more appropriately models the dependence of drag force on velocity.  An optimal…

## Fundamentals of the Diffraction Grating Spectrometer

Introduction In this article we will discuss the fundamentals of the diffraction grating spectrometer.  The operation of the instrument is based upon the textbook equations for the far-field interference (Fraunhofer case) that results from a plane wave incident on a diffraction grating.   It is rather remarkable how the standard textbook equations can be used to…

## Ionization Energy of Atomic Hydrogen

Introduction In previous articles relating to various transition energies in Hydrogen, Helium and Deuterium we have employed the following formula for electron energy given a particular primary quantum number n: $$E_{n}=\mu c^2\sqrt{1-\frac{Z^2\alpha^2}{n^2}}$$ where ## \alpha ## is the fine structure constant and ## \mu ## the reduced electron mass for a single electron…

## Answering Mermin’s Challenge with Wilczek’s Challenge

Nearly four decades ago, Mermin revealed the conundrum of quantum entanglement for a general audience  using his “simple device,” which I will refer to as the “Mermin device” (Figure 1). To understand the conundrum of the device required no knowledge of physics, just some simple probability theory, which made the presentation all the more…

## Bell States and Conservation of Spin Angular Momentum

In a recent thread, I outlined how to compute the correlation function for the Bell basis states \begin{equation}\begin{split}|\psi_-\rangle &= \frac{|ud\rangle \,- |du\rangle}{\sqrt{2}}\\ |\psi_+\rangle &= \frac{|ud\rangle + |du\rangle}{\sqrt{2}}\\ |\phi_-\rangle &= \frac{|uu\rangle \,- |dd\rangle}{\sqrt{2}}\\ |\phi_+\rangle &= \frac{|uu\rangle + |dd\rangle}{\sqrt{2}} \end{split}\label{BellStates}\end{equation} when they represent spin states. The first state ##|\psi_-\rangle## is called the “spin singlet state” and it…

## Modern Physics Understood as an Unrecognized Kuhnian Revolution

People often claim on Physics Forums and in the foundations community proper that quantum mechanics is “incomplete.” Indeed, Lee Smolin recently wrote [1, p. xvii]: I hope to convince you that the conceptual problems and raging disagreements that have bedeviled quantum mechanics since its inception are unsolved and unsolvable, for the simple reason that the…