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.

electromagentic waves traverse

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…
pressure is a source of gravity

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"…
Compton Scattering

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…
Science Authority

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 supernova

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 cosmology lcdm

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…
beginner guide to baryons

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…
symmetric spacetime

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.…
supernova refsdal

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 Cosmology Part 1

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…
Cosmic Web Connections

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 search for black holes

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…
energy conservation can we do better

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…
energy conservation ambiguity

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

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…
mary Somerville

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…
fluid dynamics experiment

Accurate Fluid Dynamics By Video Analysis

IntroductionProviding accurate fluid dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility,…
how to identify wood

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…
Diffraction Grating Spectrometer.

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…
quantum entanglement

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…
Conservation of Spin Angular Momentum

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 &=…
Kuhnian Revolution

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…
DC straight wire

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…
Deuterium Lyman Alpha Line

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…
Solar Balmer Lines

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…
Bohr’s Helium Lines

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…
rotating room

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,…
Balmer Alpha Line

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…
spacetime maxwell

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…
quantum superposition

Understanding Superposition

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

On the Meaning of Entropy

Introduction The intent of this article is to clarify the meaning of entropy and, while doing so, point out how a deeper analysis of entropy in classical…
Einstein Field Equation

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…
writing proofs

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…
Camera Lens Physics

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…
Star Equations

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…
rules of quantum mechanics

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…
Quantum Particles

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 Power Grid

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…
Maupertuis Principle

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…
create a universe story

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…
quantum qubit

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

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…
quantum mechanics is incomplete

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 quantum interpretations

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 algebra representations

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…
abacus introduction

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…
Hooke's Law Experiement

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 Algebra Structure

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…
lie algebra basics

Lie Algebras: A Walkthrough The Basics

  Part I: Basics 1. Introduction. This article is meant to provide a quick reference guide to Lie algebras: the terminology, important theorems,…
Bernoulli's equation

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.…
Magnetic Field Lines

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…
vehicle power

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…
Quantum Eraser

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]…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

The purpose of this article is not to provide some rigorous statement, neither a rigorous clever proof of the fundamental theorem of calculus. It is rather…
Super Quantum

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''…
killing Fields and Black Holes

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,…
LHC Energies

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…
Falling in Black Holes

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…