Expert Math and Science Articles

Welcome to our 100% community authored science and math blog. All of our blog authors are experts in their respective STEM fields. You’ll find high quality, engaging and interesting math and science articles (physics, mathematics, engineering, chemistry, biology, technology…). Even better we have science and math tutorials, guides, quizzes and interviews too.

Conservation of Spin Angular Momentum

Bell States and Conservation of Spin Angular Momentum

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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

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People often claim on Physics Forums and in the foundations community proper that quantum mechanics is "incomplete." Indeed, Lee Smolin recently stated…
DC straight wire

Relativistic Treatment of the DC Conducting Straight Wire

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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

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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

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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…
bloatware android phones

Clearing Misconceptions and Some Tips on Debloating Android Phones

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What is bloatware? When you unbox your new phone, it comes with Android that is pre-installed by the manufacturer. This is termed as “stock firmware”.…
recursion in programming

Recursion in Programming and When to Use/Not to Use It

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Recursion is actually quite simple. It's a subroutine calling itself. Its surprising but some problems that look quite hard can be trivial using recursion…
Bohr’s Helium Lines

Understanding Bohr's Helium Lines

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

Maxwell's Equations in Magnetostatics and Solving with the Curl Operator

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Introduction: Maxwell's equation in differential form ## \nabla \times \vec{B}=\mu_o \vec{J}_{total}+\mu_o \epsilon_o \dot{\vec{E}}  ##  with ## \dot{\vec{E}}=0…
what if physics questions

How to Avoid Breaking Physics With Your "What If" Question

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We get a lot of "what if" questions here on Physics Forums. This article will explore three different types and then some suggestions for students who…
Learn Dimensional Analysis

Learn the Basics of Dimensional Analysis

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As a university teacher and as a PF member, I have often noted that students are largely unaware of or not using dimensional analysis to help them in their…
rotating room

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

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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

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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

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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

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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

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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

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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

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... 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

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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…
Quantum Mechanical Commutator

The Classical Limit of Quantum Mechanical Commutator

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The Classical Limit of Commutator (without fancy mathematics) Quantum mechanics occupies a very unusual place among physical theories: It contains classical…
Minkowski Spacetime

Precession in Special and General Relativity

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The Absolute Derivative In relativity we typically deal with two types of quantities: fields, which are defined everywhere, and particle properties, which…
Star Equations

Equations of State for Photon Gas and Relativistic Electron Gas

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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

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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

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

A Formal Definition of Large-Scale Isotropy

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This Insight is part of my attempt to develop a formal definition of 'large-scale isotropy', a concept that is fundamental to most cosmology, but that…
Renewable Energy Power Grid

Renewable Energy Meets Power Grid Operations

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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…
surface integral

Demystifying Parameterization and Surface Integrals

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Introduction This article will attempt to take the mystery out of setting up surface integrals. It will explain the basic ideas underlying surface integration…
20 year tech predictions

What Technology or Discovery Will Be the Most Revolutionary Within 20 Years?

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We asked our advisors "What technology or scientific discovery will be the most revolutionary within the next 20 years?" Here are their responses… Demystifier "Machine…
Maupertuis Principle

A Pure Hamiltonian Proof of the Maupertuis Principle

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

Fermi-Walker Transport in Kerr Spacetime

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In the last two posts in this series, we developed some tools for looking at Fermi-Walker transport in Minkowski spacetime and then applied them in Schwarzschild…
create a universe story

How to Create a Universe - Instructions for an Apprentice God

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(-: ##~~~## 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

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This Insight article is part of my paper Foundations of quantum physics III. Measurement, featuring the thermal interpretation of quantum physics. See…
Minkowski_Spacetime_2

Fermi-Walker Transport in Schwarzschild Spacetime

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In the first post in this series, we introduced the concepts of frame field, Fermi-Walker transport, and the "Fermi derivative" of a frame field, and developed…

Aiming High and Managing Distractions as Keys to Success for Science Majors

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Over the years, I've noticed some distinct trends among the physics and chemistry majors I've mentored and worked with.Those with GPAs in the 3.8-4.0…
AVX-512 Programming subtotals

AVX-512 Programming: Extracting Column Subtotals from a Table

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In this Insights article I'll present an example that shows how Intel® AVX-512 instructions can be used to read a whole row of data in a single operation,…
Minkowski Spacetime

Fermi-Walker Transport in Minkowski Spacetime

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This is the first of several posts that will develop some mathematical machinery for studying Fermi-Walker transport. In this first post, we focus on Minkowski…
The Sum of Geometric Series from Probability Theory

The Sum of Geometric Series from Probability Theory

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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

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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…
AVX-512 conclusion

AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Conclusion

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In the first part of this article (AVX-512 Assembly Programing - Opmask Registers for Conditional Arithmetic), we looked at how opmask registers can be…
AVX-512 registers

AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic

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This is the second installment in a continuing series of articles on Intel AVX-512 assembly programming. The first installment is An Intro to AVX-512 Assembly…
Simple Harmonic Oscillator Laboratory

An Accurate Simple Harmonic Oscillator Laboratory

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Learning Objectives * Execute a specific experimental procedure to test a specific hypothesis. * Use the Tracker video analysis software for a simple…
AVX-512 Assembly Programming

An Intro to AVX-512 Assembly Programming

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History In 1998, the Intel Corporation released processors that supported SIMD (single instruction, multiple data) instructions, enabling processors to…
against quantum interpretations

Against "interpretation"

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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

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  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

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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

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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

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  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

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  Part I: Basics 1. Introduction. This article is meant to provide a quick reference guide to Lie algebras: the terminology, important theorems,…
Data Structures Programming

Intro to Data Structures for Programming

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IntroductionIn the first part of this series, I talked about some fundamental notions in the world of algorithms. Beyond the definition of an algorithm,…
Bernoulli's equation

Demystifying the Often Misunderstood Bernoulli's Equation

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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?

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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…