Physics, Math and Science Articles

Independent Research: Thinking Outside The Box Versus Knowing What’s In The Box

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In Memory of Dr. Thomas J. LeCompte (1964-2025), Detector Designer and Champion of Education and Science. Prologue Someone who shows interest in science is initially a welcome development. So are fresh ideas from unexpected quarters. In contrast, there is a scientific community that is meticulously organized down to the last detail, allowing little to no…

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Split Electric Fields

Es vs Em Fields in Electrodynamics: Capacitor & Antenna

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Abstract The analysis of the two kinds of electric fields, namely the irrotational and non-conservative, is extended to electrodynamics, as exemplified…
bayesian statistics

How to Get Started with Bayesian Statistics

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Confessions of a moderate Bayesian, part 1 Bayesian statistics by and for non-statisticianshttps://www.cafepress.com/physicsforums.13265286 Background I…
projectile motion

How to Master Projectile Motion Without Quadratics

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Introduction In a homework thread a while back a PF member expressed dismay along the lines of "Oh no, not another boring projectile motion problem."…
electric potential

Electric Vector Potential: Detect Non-Conservative Fields

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Main Point The electric vector potential offers a means of determining the non-conservative component of a mixed stationary or quasi-stationary electric…
Learn the Math

I Know the Math Says so, but Is It Really True?

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104 Comments
I'm sure anyone who has hung out long enough here on Physics Forums has encountered threads that go something like this (I'll use an example based on threads…
block universe time illusion

Does the Block Universe of Physics Mean Time is an Illusion?

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29 Comments
I have written many Insights (and coauthored an entire book) explaining how the puzzles, problems, and paradoxes of modern physics can be attributed to…
flight simulator

Introduction to Pitot-Static Systems in Gliders

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Like many others, I have been seeking new and fun things to do during a pandemic.   I decided on the new Microsoft Flight Simulator 2020, but the Condor…
mechanical conservation of energy

Why Bother Teaching Mechanical Energy Conservation?

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Note: It is assumed that the reader has read part I and part II of the series.Is Mechanical Energy Conservation Free of Ambiguity? Can We Do Better…
kerr spacetime centrifugal force

Intro to Centrifugal Force Reversal in Kerr Spacetime

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In this article, we will analyze "centrifugal force reversal" in Kerr spacetime, similar to what was done for Schwarzschild spacetime in a previous Insights…
strings waves

Intro to Physically Reasonable Waves on a String

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Introduction Physics teachers who are either writing physics questions that deal with waves on a string or setting up equipment for a class lab or demo…
Physics Olympiad Corrections

Corrections to the Australian Physics Olympiad Questions and Solutions

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ref: asi.edu.au/programs/past-exams/physics-olympiad-past-exams/ Classification of issues: [1*] Quibble regarding the solution. [2*] Clearer problem…
physics mysteries

A Principle Explanation of the “Mysteries” of Modern Physics

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All undergraduate physics majors are shown how the counterintuitive aspects ("mysteries") of time dilation and length contraction in special relativity…
Compton Scattering

Exploring the Anatomy of Compton Scattering

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Introduction In this article, we take as our starting point the original equations which Compton drew up and solved in his ground-breaking 1925 article:  From…
Twins Paradox

Learning the Twin Paradox for Freely-falling Observers

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The "twin paradox" is often discussed in the introductory treatment of special relativity. Under "twin paradox" we understand the fact that if two twins…
android ringtone

Create an Android Ringtone Picker with Ringtonemanager Class

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3 Comments
In this article, I will show you how to create a ringtone picker using the RingtoneManager class in Android. You will be able to get the list of tones,…
artificial intelligence

AI and Learning: How It Impact Our Future

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PF Advisors: How AI Will Affect STEM — Part 3We asked our PF Advisors, "How do you see the rise in AI affecting STEM in the lab, classroom, industry,…
artificial intelligence

How AI Is Changing STEM Labs, Classrooms & Industry

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We asked our PF Advisors: “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry, or in everyday society?” We received so…
artificial intelligence

How the Rise of AI Is Transforming STEM: Labs to Classrooms

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1 Comment
We asked our Physics Forums (PF) Advisors: "How do you see the rise of AI affecting STEM in the lab, classroom, industry, and everyday society?" We received…
jrmichler engineer interview

Interview with Engineer jrmichler

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Today we get to know a little more about Engineering Mentor jrmichler! Tell us a bit about your education and academic years Two years college (UW-Madison)…
electromagentic waves traverse

Are Electromagnetic Waves Always Transverse? Full Explanation

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In this insight, we will explore classical electrodynamics and examine whether electromagnetic (EM) waves are always transverse. We use Jefimenko's equations…
calculus

How to Solve Second-Order Partial Derivatives

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Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…
pressure is a source of gravity

Is Pressure A Source Of Gravity?

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11 Comments
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

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

Is Science an Authority? How to View Announcements from Scientists

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66 Comments
In a previous article, I discussed why scientists (among others) are rarely interested in considering a new theory proposed by a non-scientist: because…
lerch and zeta functions

The Analytic Continuation of the Lerch and the Zeta Functions

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Introduction In this brief Insight article the analytic continuations of the Lerch Transcendent and Riemann Zeta Functions are achieved via the Euler's…
dark energy supernova

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

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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

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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 Physics Guide to Baryon Particles

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

Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

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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

Supernova Refsdal: Multiply-Imaged Supernova Explained

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Supernova (SN) Refsdal — Key PointsAstronomers have been trying to understand space for thousands of years. Supernova Refsdal was the first…
Dark Energy Cosmology Part 1

Dark Energy Part 1: Einstein-deSitter Cosmology

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

Evidence for the Big Bang: CMB, Hubble’s Law, FAQ Guide

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Big Bang: Key PointsHubble's law (redshift of galaxies) and the Doppler effect provide direct evidence that the universe is expanding away from our…
Cosmic Web Connections

Cosmic Web Connectivity: Galaxy Evolution and Quenching

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The universe was not perfectly uniform at the beginning; some regions had higher density than others. Over time these higher-density regions attracted…
Gaia search for black holes

Gaia Astrometry: Detecting Gravitational Waves Effectively

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Gravitational waves (GWs) are disturbances in spacetime produced by massive objects moving asymmetrically. Only the most massive and most relativistic…
uranus spin

Why Uranus Spins on Its Side: Spin–Orbit Resonance

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Uranus spins on its side. It has an obliquity (tilt) of 98° — its rotation axis lies closer to the ecliptic plane than any other planet — and astronomers…
black holes are not empty

VHE Gamma Rays from Sgr A*: Black Holes and CTA Observations

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Black Hole Key PointsBlack holes (BHs) have a gravitational pull so strong that nothing, not even light, can escape. BHs can be divided into two…
Integral Representations of Some Special Functions

The Orin Fractional Calculus

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Introduction This bit is what new thing you can learn reading this:) As for original content, I only have hope that the method of using the sets $$C_N^n:…
energy conservation can we do better

Can We Do Better Than Mechanical Energy Conservation?

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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…
elastic ball collision

An Alternate Approach to Solving 2-Dimensional Elastic Collisions

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Introduction This article follows on from the previous on an alternate approach to solving collision problems. In that article, we determined the equal…
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,…

How to Recognize Split Electric Fields

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Introduction In a previous Insight, A New Interpretation of Dr. Walter Lewin’s Paradox, I introduced the fact that there are two kinds of E fields. …
Mass Generation

An Introduction to the Generation of Mass from Energy

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Introduction This article is essentially an addition to the previous one on (mainly) inelastic collisions to include the particular case of inelastic…
What is Evolution

Introduction to Evolution: Key Concepts & FAQs Guide

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Introduction to Evolution The study of evolution has dominated biology for over a century. Explaining why life is the way it is fascinates both scientists…
Collision problems

An Alternative Approach to Solving Collision Problems

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Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles…
mary Somerville

Mary Somerville: Scottish Polymath & RAS Honorary Member

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Google Doodle: Mary Somerville and Caroline Herschel The Google Doodle for 2 February 2020 celebrated Mary Somerville, the Scottish polymath and science…
perpetual motion machines

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

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Authorship Contributions From AnorlundaYou may want to believe the article you read, or the video you saw, or you may be very proud of your PMM invention.…
c++ guide for beginners

Beginner C++ Tutorial — Compiler, Types & I/O Basics

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ContentsGetting a C++ Compiler and Compiling Your First Program Simple Datatypes and Declarations Operators and Expressions Input and Output…
fluid dynamics experiment

Video Analysis of Spheres Falling Through Two Liquids

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

Tell One Wood from Another: Basic Wood Anatomy

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Introduction As a long-time woodworker, I enjoy being able to tell one wood from another. In the process of learning how to do that, I've developed some…
Odd Sums

Explore the Fascinating Sums of Odd Powers of 1/n

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The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is…
Diffraction Grating Spectrometer.

Learn the Fundamentals of the Diffraction Grating Spectrometer

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Introduction In this article, we will discuss the fundamentals of the diffraction grating spectrometer.  The operation of the instrument is based upon…
hydrogen

Intro to the Ionization Energy of Atomic Hydrogen

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Introduction In previous articles relating to various transition energies in Hydrogen, Helium, and Deuterium we have employed the following formula for…
grab bag science quiz

Grab Bag Science Quiz and Trivia

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16 Comments
Time to test your science knowledge with a fun 10 question quiz with random questions across all sciences. Difficulty is easy to medium. As always, post…
SOHCAHTOA

SOHCAHTOA: Seemingly Simple, Conceivably Complex

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8 Comments
What is SOHCAHTOA SOHCAHTOA is a mnemonic acronym used in trigonometry to remember the relationships between the sides and angles of right triangles.…
android rooting

An Intro to the Systemless Interface of Rooting Android Phones

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What you can learn from this article:What is meant by rooting an Android phone Steps to take before proceeding to root your phone Google’s…
quantum entanglement

Answering Mermin’s Challenge with the Relativity Principle

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Note: This Insight was previously titled, "Answering Mermin's Challenge with Wilczek's Challenge." While that version of this Insight did not involve any…
Conservation of Spin Angular Momentum

Exploring 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 wrote…
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

Debloating Android Phones: Risks and Best Practices

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

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

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Recursion is quite simple. It's a subroutine calling itself. It's surprising but some problems that look quite hard can be trivial using recursion - but…
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 are the black hole thermodynamics

Black Hole Thermodynamics: Four Laws Explained — Guide

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Overview Black hole thermodynamics is summarized by four laws that closely parallel the laws of ordinary thermodynamics. Below I present each law, the…
what is impedance

Impedance in AC Circuits: Definition & Key Equations

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Definition / Summary The impedance of a load (a combination of components) in an AC circuit is a complex number [itex]Z = R + jX[/itex], where [itex]R[/itex]…
what if physics questions

Avoid Breaking Physics: Ask Better ‘What If’ Questions

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We receive many "what if" questions here on Physics Forums. This article explores three common types and offers suggestions for students whose questions…
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…
What is Mass Inflation

Mass Inflation Inside Black Holes — Explanation & Equations

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Definition and summary Abstract from Poisson and Israel (1990), "Internal structure of black holes": "The gravitational effects associated with the radiative…
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…
What is potential energy

Potential Energy Explained — Definitions & Formulas

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Definition / Summary Potential energy is the negative of the work done by a conservative force. It represents stored mechanical energy associated with…
How to Find Potential Functions

How to Find a Potential Function of a Vector Field

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Definition and summary Given a vector field ##\vec F(x,y,z)## that has a potential function, how do you find it? Conditions and equations $$\nabla \phi(x,y,z)…
Moment of Inertia

Moment of Inertia: Definitions, Formulas & Tensor Guide

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Definition / Summary The moment of inertia is a property of a rigid body that relates torque (rotational force) to rotational acceleration in the same…
quantum superposition

Understanding Superposition Physically and Mathematically

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What is superposition Superposition is a fundamental concept in physics and mathematics, particularly in the fields of wave theory and quantum mechanics.…
What is Entropy

What Thermodynamics and Entropy Means

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Introduction The student of thermodynamics, as they consider pistons and ideal gasses and such, often begin to grasp the nature of entropy only to find…
What is a linear equation

First-Order Linear Equation: Definition & Solutions

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Definition / Summary This article summarizes the first-order (linear) polynomial equation in one variable, its solution, and natural extensions to matrices…
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 symmetric spacetimes. This is a…
What are significant figures

Significant Figures: Rounding Rules & Examples for Science

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Definition / Summary Significant figures (commonly called "sig figs") are the digits in a number that are considered when rounding a value to reflect…
writing proofs

How to Write a Math Proof and Their Structure

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Proofs in mathematics are what mathematics is all about. They are subject to entire books, created entire theories like Fermat's last theorem, are hard…
Camera Lens Physics

Evaluate Camera Lens Performance Using an LCD Display

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

Understanding Precession in Special and General Relativity

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16 Comments
The Absolute Derivative In relativity we typically deal with two types of quantities: fields, which are defined everywhere, and particle properties, which…
What is a fibre bundle

Fibre Bundle: Definition, Examples & Intuitive Guide

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Definition / Summary Fibre bundle — intuitively, a fibre bundle is a space E that locally looks like a product B × F but may have a different global…
What are real numbers

Real Numbers: Definition, Properties & Axioms — Explained

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Definition of real numbers Real numbers are the set of all values that can appear on the continuous number line. They include rational numbers (fractions…
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…
What is the double split

What is the Double Slit? A 5 Minute Introduction

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Definition/Summary The double-slit is a simple configuration used to demonstrate interference effects in waves.Equations At distances that are…
integration by parts

What is Integration By Parts? A 5 Minute Introduction

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Definition/Summary In this article, we shall learn a method for integrating the product of two functions. This method is derived from the 'product rule'…
rules of quantum mechanics

The 7 Basic Rules of Quantum Mechanics

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45 Comments
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…
What is a parabola

Parabola: Definition, Equations & Applications — 5-Min Guide

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What is a Parabola? A parabola is a U-shaped curve that appears frequently in mathematics, physics and engineering. It is a conic section defined by a…
Renewable Energy Power Grid

When Renewable Energy Meets Power Grid Operations

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

Limits of Functions for Calculus: Definition & Examples

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What is a limit? In mathematics, a limit describes the behavior of a function or sequence as its input approaches a particular value. Limits are a cornerstone…
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…
Lie Algebra Intro

Lie Algebra Basics: Definitions, Equations & Examples

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Definition / Summary A Lie algebra (pronounced "Lee") is the tangent-space algebra of a Lie group at its identity element. Concretely, it is a vector…
20 year tech predictions

Revolutionary Technologies and Discoveries in 20 Years

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Experts weigh in: Most revolutionary technologies and discoveries in the next 20 years We asked our Physics Forums science advisors, "What technology…
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 of the Lagrangian approach.The proof…