# Science and Math Articles

Here is the collection of expert science and math articles that span all the sciences and mathematics. Some examples include physics, mathematics, biology, chemistry, cosmology and earth sciences. For math we cover algebra to advanced calculus.

### Are Electromagnetic Waves Always Transverse?

/
In this insight we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko's…

### Is Pressure A Source Of Gravity?

/
In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…

### Massive Meets Massless: Compton Scattering Revisited

/
Introduction In a previous article entitled "Alternate Approach to 2D Collisions" we analysed collisions between a moving and stationary object by defining…

### Is Science An Authority?

/
In a previous article, I discussed why scientists (among others) are almost never interested in considering a new theory proposed by a non-scientist: because…

### Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data

/
In Part 1 of this 3-part series, I explained kinematics in Einstien-deSitter (EdS) cosmology and in Part 2, I explained kinematics in ##\Lambda##CDM cosmology…

### Dark Energy Part 2: LCDM Cosmology

/
This is Part 2 of a 3-part series explaining evidence for so-called “dark energy” leading to a current positive cosmological acceleration. The evidence…

### A Beginner's Guide to Baryons

/
Introduction At the beginning of the 20th century it was thought that all matter consisted of only three particles: the electron, the neutron and the…

### Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

/
In the first two articles in this series, we looked at the Einstein Field Equation and Maxwell's Equations in a static, spherically symmetric spacetime.…

### The Reappearance of Supernova (SN) Refsdal

/
Space is always changing. Over thousands of years, astronomers have attempted to understand the workings. Trying to explain astronomical events offers…

### Dark Energy Part 1: Einstein-deSitter Cosmology

/
In this 3-part series, I want to motivate the (re)introduction of the cosmological constant ##\Lambda## into Einstein's equations of general relativity…

### The Evolution of the Universe, Cosmic Web and Connections

/
The universe was not perfectly uniform when it started, some areas had higher density than others. During the evolution of the universe, these areas of…

### Gaia and the Race to Detect More Gravitational Waves

/
Gravitational waves (GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most…

### 3 Possible Models For Why Uranus Spins on Its Side

/
Uranus spins on its side. Uranus has an obliquity (tilt) of 98º, making its axis of rotation closer to the ecliptic plane than any other planet. It is…

### Black Holes Are Not Empty Voids. A Black Hole at the Heart!

/
Black Holes (BH’s) are curious because of their mysterious nature and unknown properties. BH’s are not empty voids. They are astronomical objects…

### Can We Do Better Than Mechanical Energy Conservation?

/
Note: It is assumed that the reader has read part I of the series. Introduction The ambiguity and flaws discussed in part I can be resolved using the…

### Is Mechanical Energy Conservation Free of Ambiguity?

Introduction "Close to any question that is in the textbook, there is another question that has never been answered that is interesting." [Stephen Wolfram,…

### What is Evolution: A Beginner's Guide

/
Introduction to Evolution The study of evolution has dominated the field of biology for over a century. Explaining why the life we see is as it is fascinates…

### Mathematician Mary Somerville Features in Google Doodle

/
The Google Doodle for 2 February 2020 celebrated Mary Somerville, the Scottish polymath and science writer, and with Caroline Herschel, the joint first…

### Accurate Fluid Dynamics By Video Analysis

/
IntroductionProviding accurate fluid dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility,…

### Want to Tell One Wood from Another? Learn Basic Wood Anatomy

/
As a long-time woodworker I have an interest in being able to tell one wood from another and in the process of learning how to do that, I've developed…

### 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…

### 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…

### Answering Mermin's Challenge with Wilczek's Challenge

/
Nearly four decades ago, Mermin revealed the conundrum of quantum entanglement for a general audience [1] using his "simple device," which I will refer…

### 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{split}|\psi_-\rangle &=…

### 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…

### Relativistic Treatment of the DC Conducting Straight Wire

/
Introduction The direct-current-conducting infinitely long wire is often discussed in the context of relativistic electrodynamics. It is of course a completely…

### Revisiting The Deuterium Lyman Alpha Line Experiment

/
Introduction In this article we will be revisiting a somewhat understudied (and seemingly unrepeated) experiment to measure the Deuterium Lyman Alpha…

### Signature of the Sun: Analyzing the Solar Balmer Series Lines

/
Introduction We are in many ways a fortunate generation having so many wonderful tools at our disposal on account of the "silicon revolution" . The advent…

### Understanding Bohr's Helium Lines

/
Introduction In a previous article "Calculating the Balmer Alpha Line" we mentioned how accurate predictions of the spectral lines of singly ionized Helium…

### How to Zip Through a Rotating Tunnel Without Bumping Into the Walls

/
Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below.  For the reader's convenience,…

### Calculating the Balmer Alpha Line: Atomic Hydrogen

/
Introduction Most readers acquainted with the hydrogen spectrum  will be familiar with the set of lines in the visible spectrum representing transitions…

### Maxwell's Equations in a Static, Spherically Symmetric Spacetime

/
In the first article in this series, we looked at the Einstein Field Equations in a static, spherically symmetric spacetime. In this article, we are going…

### Understanding Superposition

/
IntroductionOne should first and foremost understand that superposition has both a mathematical an a physical meaning, or rather it originates as…

/

### The Einstein Field Equation in a Static, Spherically Symmetric Spacetime

/
This will be the first of several articles which will provide, for reference, useful equations for static, spherically symmeetric spacetimes. This is a…

### How Most Proofs Are Structured and How to Write Them

/
... or the answer to: "I have no idea where to start!" Proofs in mathematics are what mathematics is all about. They are subject to entire books, created…

### Lens Performance Testing: Evaluating a Camera Lens

/
I've done plenty of imaging performance testing on a variety of systems, from millimeter wave through UV. Until very recently, such testing required expensive…

### Equations of State for Photon Gas and Relativistic Electron Gas

/
This Insight develops equations of state that are useful in calculations about cosmology and about the insides of stars. The first calculation is for a…

### The 7 Basic Rules of Quantum Mechanics

/
For reference purposes and to help focus discussions on Physics Forums in interpretation questions on the real issues, there is a need for fixing the common…

### Clarifying Common Issues with Indistinguishable Particles

/
Commonly there is a lot of imprecision in talking about ''indistinguishable'' (or ''identical'') particles, even in serious work. This Insight article…

### Renewable Energy Meets Power Grid Operations

/
The electric power industry faces much turmoil in the coming decades.  The business model of of the electric utility company (public or private) may not…

### A Pure Hamiltonian Proof of the Maupertuis Principle

/
Here is another version of proof of Maupertuis's principle. This version is pure Hamiltonian and independent on the Lagrangian approach.The proof…

### How to Create a Universe - Instructions for an Apprentice God

/
(-: ##~~~## A fantasy to be read at leisure time ##~~~## :-) Written October 7, 1999 to relax from the strains of working on a new interpretation of quantum…

### A Classical View of the Qubit

/
This Insight article is part of my paper Foundations of quantum physics III. Measurement, featuring the thermal interpretation of quantum physics. See…

### The Sum of Geometric Series from Probability Theory

/
Here I present a simple (but to the best of my knowledge, new) derivation of the formula for the sum of the infinite geometric series. The derivation is…

### 9 Reasons Quantum Mechanics is Incomplete

/
I argue that all interpretations of quantum mechanics (QM) are incomplete, each for its own reason. I also point out that for some interpretations (those…

### Against "interpretation"

/
I am against "interpretations" of Quantum Mechanics (QM) in a sense in which John Bell [1] was against measurement in QM and Travis Norsen [2] is against…

### Lie Algebras: A Walkthrough The Representations

/
Part III: Representations  10. Sums and Products. Frobenius began in ##1896## to generalize Weber's group characters and soon investigated…

### An Introduction to the Traditional Abacus of China and Japan

/
Introduction Abacuses are commonly seen in ancient civilizations around the world as the convenient tool to do simple calculations. In this article, we…

### An Accurate Hooke's Law Laboratory

/
Learning Objectives * Gain confidence and experimental care in making accurate measurements. * Understand the relationship between force and spring stretch. *…

### Lie Algebras: A Walkthrough The Structures

/
Part II: Structures5. Decompositions.Lie algebra theory is to a large extend the classification of the semisimple Lie algebras…

/

### Demystifying the Often Misunderstood Bernoulli's Equation

/
Introduction Bernoulli's equation is one of the most useful equations in the field of fluid mechanics, owing to its simplicity and broad applicability.…

### Are Magnetic Field Lines Real?

/
We recently had a question in the relativity forums that mentioned the behavior of magnetic field lines, and reminded me of my own confusion at school…

### When Vehicle Power Dictates Acceleration

/
One interesting problem when dealing with a vehicle of a certain mass is to determine what is required in order to get the maximum acceleration while going…

### The Quantum Mystery of Wigner's Friend

/
In this Insight I will introduce the quantum mystery called Wigner's friend'' using Healey's version [1] of Frauchiger and Renner's (FR's) version [2]…

/

### The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

/
In this Insight, I will show how the Popescu-Rohrlich (superquantum) correlations provide an unreasonable advantage in a particular "quantum guessing game''…

### Exploring the Math in Killing Fields and Black Holes

/
Killing Vector Field The Killing vector field is a vector field on a differentiable manifold that preserves the metric over spacetime (from this I assume,…

### Exploring the Energies in the Large Hadron Collider

/
The Large Hadron Collider has produced collisions at 7 TeV. For collisions at 7 TeV, protons need to be ‘ramped’ to 3.5 TeV, the proton has a mass…

### Black Holes and the Properties of In-Falling Radial Plungers

/
From 'Exploring Black Holes' by John Wheeler and Edwin Taylor; can apply to any object falling radially towards a static spherical mass (where the mass…