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Here is an alphabetical list of all Physics Forums Insights grouped by format and then discipline. It is auto updated as new Insights are published. Enjoy!
Articles
Physics Articles
- 11d Gravity From Just the Torsion Constraint
- 15 of the Best PF 2017 Eclipse Photos
- It Was 20 Years Ago Today — the M-theory Conjecture
- Why Uranus Spins on Its Side: Spin–Orbit Resonance
- 9 Reasons Quantum Mechanics is Incomplete
- A Beginner Physics Guide to Baryon Particles
- A Classical View of the Qubit
- A First Idea of Quantum Field Theory – 20 Part Series
- A Numerical Insight for the Fundamental Theorem of Calculus
- A Physics Misconception with Gauss’ Law
- A Principle Explanation of the “Mysteries” of Modern Physics
- A Black Hole Problem From Greg Egan’s “Incandescence”
- Intro to AC Power Analysis: Learn System Basics
- Intro to AC Power Analysis: Network Analysis
- AC Power Analysis: The 4 Levels of Cyber Resilience
- Video Analysis of Spheres Falling Through Two Liquids
- Acoustic ‘beats’ from Mismatched Musical Frequencies
- Addition of Velocities (Velocity Composition) in Special Relativity
- How to Manage TCP/IP In Automation or Measurement Networks
- Against “interpretation”
- Learn All About Earth’s Gravity
- An Example of An Accurate Hooke’s Law Laboratory
- Why Road Capacity Is Almost Independent of the Speed Limit
- Exploring the Anatomy of Compton Scattering
- Answering Mermin’s Challenge with the Relativity Principle
- Learn The Main Conceptual Ideas of Anyon Particles
- Approximate LCDM Expansion in Simplified Math
- Approximate LCDM Expansion in Simplified Math (Part 2)
- Approximate LCDM Expansion in Simplified Math (Part 4)
- Are Electromagnetic Waves Always Transverse? Full Explanation
- Are Magnetic Field Lines Real?
- Aspects Behind the Concept of Dimension in Various Fields
- Assessing the Physics in Edmond Hamilton’s “The Second Satellite”
- Balloon Analogy Explained: Cosmology, Expansion & Limits
- Learn the Basics of Positron Emission Tomography (PET)
- Exploring Bell States and Conservation of Spin Angular Momentum
- Intro to the Big Bang and Infinity Concepts
- Radial Infall into a Static Mass: Equations & Guide
- VHE Gamma Rays from Sgr A*: Black Holes and CTA Observations
- The Block Universe – Refuting a Common Argument
- Blockworld and Its Foundational Implications: Time Dilation and Length Contraction
- Blockworld and Its Foundational Implications: The Relativity of Simultaneity and Blockworld
- Blockworld and its Foundational Implications: General Relativity and the Big Bang
- Blockworld and its Foundational Implications: General Relativity and Closed Timelike Curves
- Blockworld and its Foundational Implications: Delayed Choice and No Counterfactual Definiteness
- Big Bang, Inflation & Dark Energy — FLRW Cosmology
- Calculating the Balmer Alpha Line: Atomic Hydrogen
- Can We See an Atom?
- Can We Do Better Than Mechanical Energy Conservation?
- Introduction to Causal Perturbation Theory
- Intro to Centrifugal Force Reversal in Kerr Spacetime
- The What and Why of Circuit Analysis Assumptions
- Clarifying Common Issues with Indistinguishable Particles
- Addressing the “Classical Physics Is Wrong” Fallacy
- Thoughts on the Complexity of Modern Science
- Explore Coordinate Dependent Statements in an Expanding Universe
- Learn Damped Motion in Classical and Quantum Mechanics
- Dark Energy Part 1: Einstein-deSitter Cosmology
- Dark Energy Part 2: LCDM Cosmology
- Dark Energy Part 3: Fitting the SCP Union 2.1 Supernova Data
- Demystifying the Often Misunderstood Bernoulli’s Equation
- Differential Equation Systems and Nature
- The Diffraction Limited Spot Size with Perfect Focusing
- Direct Echo-Based Measurement of the Speed of Sound
- Does the Block Universe of Physics Mean Time is an Illusion?
- Either the Sun Is Getting Smaller or Gravity Is Getting Weaker
- Emergence From the Superpoint
- Lesson on Entanglement Entropy in Quantum Field Theory
- Learn Entanglement Entropy in Quantum Mechanics
- Epsilontic – Limits and Continuity
- Equations of State for Photon Gas and Relativistic Electron Gas
- Examples of Prequantum Field Theories I: Gauge Fields
- Examples of Prequantum Field Theories II: Higher Gauge Fields
- Examples of Prequantum Field Theories III: Chern-Simons-type Theories
- Examples of Prequantum Field Theories IV: Wess-Zumino-Witten-type Theories
- Exploring the Spectral Paradox in Physics
- LHC Relativistic Energies and Time Dilation at 3.5–14 TeV
- Killing Vector Field & Surface Gravity in Kerr BH Explained
- Explosion-Generated Collapsing Vacuum Bubbles Reach 20,000 Kelvin
- Frames of Reference: A Skateboarder’s View
- Learn Frenet Equations in 2-D Which Result in the Cornu Spiral
- Fun with Self-Avoiding Walks Simulations
- The Fundamental Difference in Interpretations of Quantum Mechanics
- Learn the Fundamentals of the Diffraction Grating Spectrometer
- Gaia Astrometry: Detecting Gravitational Waves Effectively
- Exploring General Relativity as a Gauge Theory
- Does Gravity Gravitate? Part 2
- Does Gravity Gravitate: The Wave
- Learn About the Greenberger-Horne-Zeilinger Experiment
- What Planck Length Is and It’s Common Misconceptions
- High Temperature and Low Duality for the Ising Model on an Infinite Regular Tree
- Why Higher Category Theory in Physics?
- Higher Prequantum Geometry II: The Principle of Extremal Action – Comonadically
- Higher Prequantum Geometry III: The Global Action Functional – Cohomologically
- Higher Prequantum Geometry IV: The Covariant Phase Space – Transgressively
- Higher Prequantum Geometry I: The Need for Prequantum Geometry
- Higher Prequantum Geometry V: The Local Observables – Lie Theoretically
- What is the Homopolar Generator: An Analytical Example
- Homotopy Lie-n Algebras in Supergravity
- How Can We Jump When the Ground Does No Work?
- How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics
- How Quantum Information Theory Solves “the only mystery” of Quantum Mechanics
- How to Better Define Information in Physics
- How to Create a Universe: Instructions for an Apprentice God
- The Essential Guide to Self Study Mathematics
- How to Zip Through a Rotating Tunnel Without Bumping Into the Walls
- I Know the Math Says so, but Is It Really True?
- Independent Research: Thinking Outside The Box Versus Knowing What’s In The Box
- Spatial Curvature in Cosmological Models
- Inflationary Misconceptions and the Basics of Cosmological Horizons
- Initiating Physics PhD Research: Getting Started Effectively
- The Interaction of Sound and Light
- Electric Vector Potential: Detect Non-Conservative Fields
- Introduction to Pitot-Static Systems in Gliders
- Intro to the Ionization Energy of Atomic Hydrogen
- Is Mechanical Energy Conservation Free of Ambiguity?
- Is Pressure A Source Of Gravity?
- Is Science an Authority? How to View Announcements from Scientists
- Learn About the FLRW Metric and The Friedmann Equation
- Learn About the Friedmann Equation and the Cosmos
- Learn About Knut Lundmark and the Prehistory of Dark Matter
- The LCDM Cosmological Model in Simplified Math (Part 3)
- Lessons From the Bizzaro Universe
- LHC Part 2: Commissioning
- LHC Part 3: Protons as Large as a Barn
- LHC Part 4: Searching for New Particles and Decays
- Massive Meets Massless: Compton Scattering Revisited
- Maxwell’s Equations in a Static, Spherically Symmetric Spacetime
- How to Scientifically Measure How Many Days Are in a Year
- Can You Measure Quantum Entanglement?
- Learn a Misconception of the Heisenberg Uncertainty Principle
- Top Misconceptions about Virtual Particles
- Modern Physics Understood as an Unrecognized Kuhnian Revolution
- Mixing vs Beating: Superheterodyne & Beat Frequency
- Why the Need of Infinity in Physics
- Negative Absolute Temperatures: Explanation & Examples
- Learn About Neutrino Masses and Speed
- Learn the Fields of Mathematical Quantum Field Theory
- Learn Field Variations in Mathematical Quantum Field Theory
- Learn Free Quantum Fields in Mathematical Quantum Field Theory
- Learn Gauge Fixing in Mathematical Quantum Field Theory
- Learn Gauge Symmetries in Mathematical Quantum Field Theory
- Learn the Geometry of Mathematical Quantum Field Theory
- Learn Interacting Quantum Fields in Mathematical Quantum Field Theory
- Learn Lagrangians in Mathematical Quantum Field Theory
- Learn Observables in Mathematical Quantum Field Theory
- Learn Phase Space in Mathematical Quantum Field Theory
- Learn Propagators in Mathematical Quantum Field Theory
- Learn Quantization in Mathematical Quantum Field Theory
- Learn Reduced Phase Space in Mathematical Quantum Field Theory
- Learn Renormalization in Mathematical Quantum Field Theory
- Learn Spacetime in Mathematical Quantum Field Theory
- Learn Symmetries in Mathematical Quantum Field Theory
- Learn Why Ohm’s Law Is Not a Law
- What Thermodynamics and Entropy Means
- When Pro Scientists Explain Using Pop Science
- Oppenheimer-Snyder Model of Gravitational Collapse: Implications
- Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details
- Introduction to Perturbative Quantum Field Theory
- PBS Video Comment: “What If Physics IS NOT Describing Reality”
- Permanent Magnets Explained by Magnetic Surface Currents
- Hand-to-Hand Combat Physics — Force, Momentum, Speed
- Learn the Physics of Virtual Particles in Quantum Mechanics
- Plus/minus What? How to Interpret Error Bars
- A Poor Man’s CMB Primer: Orientation of the Universe
- A Poor Man’s CMB Primer: The Birth of a Cosmic Background Radiation
- A Poor Man’s CMB Primer: Bumps on a Blackbody
- A Poor Man’s CMB Primer: Cosmic Acoustics
- A Poor Man’s CMB Primer: Quantum Seeds
- Posterior Predictive Distributions in Bayesian Statistics
- Learn About Quantum Amplitudes, Probabilities and EPR
- Quantum Computing for Beginners
- Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect
- The Quantum Liar Experiment: An Instantiation of the Mermin Device
- Quantum Mechanics and the Famous Double-slit Experiment
- Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics
- Infinity in Mathematics: Limits and Cardinality FAQ
- Exploration into the Physics of Rainbows
- Relativator (Circular Slide-Rule) – Simulated with Desmos
- Relativistic Treatment of the DC Conducting Straight Wire
- Learn the Relativistic Work-Kinetic Energy Theorem
- Relativity on Rotated Graph Paper (a graphical motivation)
- When Renewable Energy Meets Power Grid Operations
- How Representative is the Night Sky?
- Find Out the Results Shown at 2017 CERN EPS Conference
- Understanding Retrocausality and Blockworld
- Retrocausality: How Fundamental is the Arrow of Time?
- Reversible vs Irreversible Gas Compression and Expansion Work
- The Revival of Newton-Cartan Theory in General Relativity
- Roger Babson’s Anti-Gravity Contest and Modern Physics
- Animal Speed Scaling: Body-Lengths per Second Across Sizes
- Schrödinger’s Cat and the Qbit
- The Schwarzschild Geometry: Spacetime Diagrams
- The Schwarzschild Metric: GPS Satellites
- The Schwarzschild Metric: The Photon Sphere
- The Schwarzschild Metric: A Newtonian Comparison
- Should You Do Science for Love or for Money
- Scientific Inference: Logical Induction Ain’t Logical
- Scientific Inference: Do We Really Need Induction?
- Introduction to the Secondary Forces in Physics
- Have Scientists Seen an Electron? How We Detect Them
- Math Self-Study Roadmap: Topics & Book Recommendations
- Signature of the Sun: Analyzing the Solar Balmer Series Lines
- Explore Some Sins in Physics Didactics
- Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime
- Learn About Spacetime Diagrams of Light Clocks
- Spectral Standard Model and String Compactifications
- Learn About the Speed of Light and Galilean Relativity
- Learn Statistical Mechanics: The Ideal Gas
- How the EPR Paradox Fits Between Entanglement and Nonlocality
- How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics
- Struggles with the Continuum: Spacetime Conclusion
- Struggles With the Continuum: Is Spacetime Really a Continuum?
- Struggles With The Continuum: Quantum Mechanics of Charged Particles
- Struggles With the Continuum: Point Particles and the Electromagnetic Field
- Struggles with the Continuum – Relativity and Quantum
- Struggles with the Continuum: Quantum Electrodynamics
- Struggles with the Continuum – Freeman Dyson and QED
- Struggles with the Continuum: General Relativity
- Super p-Brane Theory Emerging from Super Homotopy Theory
- Superdeterminism and the Mermin Device
- Garrett Lisi’s Superparticle Bet With Frank Wilczek
- Learn About Supersymmetry and Deligne’s Theorem
- Symmetry Arguments and the Infinite Wire with a Current
- The 10 Commandments of Index Expressions and Tensor Calculus
- The 7 Basic Rules of Quantum Mechanics
- Revisiting The Deuterium Lyman Alpha Line Experiment
- The Einstein Field Equation in a Static, Spherically Symmetric Spacetime
- Cosmic Web Connectivity: Galaxy Evolution and Quenching
- Star Fate: From Nebulae to White Dwarfs and Black Holes
- Apollo Program: Moon Missions & Last Moonwalk 1972
- The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview
- The Poor Man’s Milli-Ohm Meter
- Supernova Refsdal: Multiply-Imaged Supernova Explained
- The Slinky Drop Experiment Analysed
- Learning the Twin Paradox for Freely-falling Observers
- The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations
- Beyond the Tidal Bulge
- Time Dilation & Redshift of Schwarzschild Black Holes
- Learn Time Synchronization Across Switched Ethernets
- Tolman Law in a Nutshell
- Tools to Enrich our Quantum Mechanics Interpretations Discourse
- Understanding Bohr’s Helium Lines
- Understanding Buoyancy: The Limits of Archimedes
- Understanding the General Relativity View of Gravity on Earth
- Understanding Superposition Physically and Mathematically
- Some Useful Integrals In Quantum Field Theory
- How to Use the Spaghetti-Twist Method to Align DNA
- Explore The Vacuum Fluctuation Myth in Quantum Theory
- Learn About Vacuum Fluctuations in Experimental Practice
- “Violating” Einstein’s Photoelectric Effect Model
- Weak Values Part 1: Asking Photons Where They Have Been
- Weak Values Part 2: The Quantum Cheshire Cat Experiment
- What Are Tensors and Why Are They Used in Relativity?
- What Happens When You Flip the Light Switch: From Zero Seconds to 20 Years
- A Definition and Controversy of Energy
- When Discussing the Twin Paradox: Read This First
- When Science is Not Enough: Legal and Health Implications of Questions
- When Vehicle Power Dictates Acceleration
- Why Bother Teaching Mechanical Energy Conservation?
- Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality per Quantum Information Theory
- Why the Quantum | A Response to Wheeler’s 1986 Paper
- Why There Are Maximum Mass Limits for Compact Objects
- The Quantum Mystery of Wigner’s Friend
- Yardsticks to Metric Tensor Fields
Math Articles
- 10 Math Things We All Learnt Wrong At School
- A Pure Hamiltonian Proof of the Maupertuis Principle
- Intuitive Black‑Scholes Options Pricing Explained Simply
- Is Zero a Natural Number?
- An Overview of Complex Differentiation and Integration
- Peano Axioms: Construction of Natural Numbers and Properties
- Brachistochrone Subway Tunnel: Fastest Tunnel Shape Explained
- Brownian Motions and Quantifying Randomness in Physical Systems
- Can Angles be Assigned a Dimension?
- Hear the Case for Learning Complex Math
- Classification of Mathematics by 42 Branches
- Counting to p-adic Calculus: All Number Systems That We Have
- Differential Equation Systems and Nature
- Fermat’s Last Theorem
- Fixing Things Which Can Go Wrong With Complex Numbers
- Set-Theoretic Foundations of Numbers and Functions
- Exploring Frequentist Probability vs Bayesian Probability
- Ramsey Theory: Foundations, Generalizations, Key Results
- Klein’s Erlangen Program: Groups Define Geometry
- Learn the Basics of Hilbert Spaces and Their Relatives: Definitions
- Learn the Basics of Hilbert Spaces and Their Relatives: Operators
- How Bayesian Inference Works in the Context of Science
- How to Write a Math Proof and Their Structure
- How to Get Started with Bayesian Statistics
- Learn About Intransitive Dice with a Twist
- Évariste Galois and His Theory
- Introduction to the World of Algebras
- A Journey to The Manifold SU(2): Differentiation, Spheres, and Fiber Bundles
- Learn Lie Algebras: A Walkthrough – The Basics
- Learn Lie Algebras: A Walkthrough – The Representations
- Learn Lie Algebras: A Walkthrough – The Structures
- Mary Somerville: Scottish Polymath & RAS Honorary Member
- Teaching Math as Obvious Thinking | Make Math Click
- Intro to the Millennium Prize Problems
- The Monographic Substitution Cipher: From Julius Caesar to the KGB
- P vs. NP and what is a Turing Machine (TM)?
- Is It Possible to Design an Unbreakable Cipher?
- Beginners Guide to Precalculus, Calculus and Infinitesimals
- Probabilistic Factors Involved in Disease and Virus Testing
- Linear Representations and Why Precision is Important in Math
- Scientific Inference: Balancing Predictive Success with Falsifiability
- Series in Mathematics: From Zeno to Quantum Theory
- When Simple Geometry Unveils Deep Math
- How to Tell Operations, Operators, Functionals, and Representations Apart
- The Amazing Relationship Between Integration And Euler’s Number
- The History and Importance of the Riemann Hypothesis
- The Lambert W Function in Finance
- The Many Faces of Topology
- The Sum of Geometric Series from Probability Theory
- Things Which Can Go Wrong with Complex Numbers
- Trials and Tribulations of a Physicist who Became a Math Geek
- Views On Complex Numbers
- What Are Infinitesimals – Advanced Version
- What Are Numbers?
- What Exactly is Dirac’s Delta Function?
- Formal Syntax and WFFs in Set Theory (Hrbacek-Jech)
- When Lie Groups Became Physics
- Why Division by Zero is a Bad Idea
- Why Vector Spaces Explain The World: A Historical Perspective
- Yardsticks to Metric Tensor Fields
Engineering Articles
Other Science Articles
- 5 Pieces of Evidence that Support Theory of Evolution
- Atomic Positioning with DNA Hinges
- Can Gene Editing Eliminate Alzheimer’s Disease?
- What Causes Cancer: Bad Luck or Bad Lifestyles?
- Differential Equation Systems and Nature
- Why CRISPR Technologies Won’t Lead to Designer Babies
- Frequently Made Errors in Climate Science – The Greenhouse Effect
- Learn About History’s First Science Experiments
- Tell One Wood from Another: Basic Wood Anatomy
- Ultra-Wide Lenses: Field of View, Design & Tips for Photographers
- Learn the Amazing New Research on Untying Knots in Polymers
- Probabilistic Factors Involved in Disease and Virus Testing
- Why Your Software is Never Perfect
- Bioethics & Genetic Engineering: Ethics and Policy
- Introduction to Evolution: Key Concepts & FAQs Guide
- Polymer Physics and Genetic Sequencing
- When did Mitochondria Evolve?
Education Articles
- Suanpan & Soroban Abacus: History, Use, How-To Guide
- Blaming Government for Teacher and Scientist Failures in Integrity
- Spotting Fake Science News: Wendelstein 7‑X & Media
- False Physics Major Dichotomy: Theorist or Experimentalist?
- Why Imagination Without Knowledge Is Ignorance Waiting to Happen
- What Is The Most Important Thing That You Learned?
- How to Ask Questions Effectively and Avoid Cold Questions
- Finding Niches for Publishable Undergraduate Research
- When Pro Scientists Explain Using Pop Science
- Why Quantum Mechanics Feels Difficult — Mathematical Bridge
- Real Research in Unexpected Places: Backyards, Barns, Bayous
- Real Research in Unexpected Places; Boat Ramps
- Revamping Undergraduate Introductory Physics Laboratory
- Why Study Physics? A Bit Goes a Long Way!
- The Most Important Thing You Can Learn from Physics Forums
- Why Bother Teaching Mechanical Energy Conservation?
- Why ChatGPT AI Is Not Reliable
- Why You Should Not Use Wikipedia As Your Primary Source
- Why Work Ethic Is a Key to Success for Science Majors
FAQs
Physics FAQs
- Space Law Explained — Outer Space Treaty & Satellite Rules
- How Does an Airplane Wing Work? A Primer on Lift
- Did the Big Bang Have a Center? Explaining Cosmology
- Do Black Holes Really Exist?
- Why Rigid Rods Can’t Send Faster-Than-Light Signals
- Is the Universe Rotating? Evidence, Tests & Limits
- Do Photons have Mass?
- Do Photons Move Slower in a Solid Medium?
- Does Gravity Gravitate?
- Does Heisenberg Uncertainty Violate Energy Conservation?
- Why Electrons Don’t Crash Into the Nucleus — Quantum View
- Was the Early Universe in a Disordered State?
- Learn About Energy Gained by Charge in an Electrostatic Field
- Evidence for the Big Bang: CMB, Hubble’s Law, FAQ Guide
- A Geometrical View of Time Dilation and the Twin Paradox
- How Fast Do Changes in the Gravitational Field Propagate?
- Lenses and Pinholes: What Does “In Focus” Mean?
- PF’s policy on Lorentz Ether Theory and Block Universe
- Why the Observable Universe Radius Exceeds Its Age
- Evidence that Galaxy and Quasar Redshifts Are Cosmological
- Why Is the Speed of Light the Same in All Frames of Reference?
- What Is the Steady-state Model and Why It’s No Longer Viable
- Why the Early Big Bang Universe Didn’t Form a Black Hole
- At What Velocity Does the Universe Expand and Can It Be Faster than Light?
- What Are Tensors and Why Are They Used in Relativity?
- Black Hole Thermodynamics: Four Laws Explained — Guide
- Virtual Particles Explained — Quantum Field Theory
- What Is Heat? Definition in Thermodynamics Explained
- Impedance in AC Circuits: Definition & Key Equations
- Mass Inflation Inside Black Holes — Explanation & Equations
- Potential Energy Explained — Definitions & Formulas
- What is relativistic mass and why it is not used much?
- Bell Spaceship Paradox: Why the String Breaks in SR
- What is the Double Slit? A 5 Minute Introduction
- Moment of Inertia: Definitions, Formulas & Tensor Guide
- Why Does C Have a Particular Value, and Can It Change?
- Why Is Acceleration Due to Gravity a Constant?
- Why We Don’t Discuss Perpetual Motion Machines (PMM)
- Will All Matter Be Converted to Photons?
- Why Won’t You Look at My New Theory?
- Why You Can’t Quantum Tunnel Through a Wall
Math FAQs
- How to Find a Potential Function of a Vector Field
- Mathematical Proofs: How to Understand and Write Them
- Understanding Zero: History, Division, Exponents, 0!
- Significant Figures: Rounding Rules & Examples for Science
- Fibre Bundle: Definition, Examples & Intuitive Guide
- Limits of Functions for Calculus: Definition & Examples
- First-Order Linear Equation: Definition & Solutions
- Parabola: Definition, Equations & Applications — 5-Min Guide
- Real Numbers: Definition, Properties & Axioms — Explained
- Tangent to a Curve: Definition, Equations & Examples
- What Is a Tensor? The mathematical point of view.
- What is Integration By Parts? A 5 Minute Introduction
- Lie Algebra Basics: Definitions, Equations & Examples
- Why Division by Zero is a Bad Idea
- Why 1 Equals 0.999… — Explanations & Rigorous Proofs
Guides
Physics Guides
- How to Spot Pseudoscience: A Practical Science Guide
- Astrophotography Mounts, Tracking & Post-Processing Tips
- An Accurate Simple Harmonic Oscillator Laboratory
- Astrophotography Level 2: Camera Setup & Techniques
- Corrections to the Australian Physics Olympiad Questions and Solutions
- Solar System Imaging Guide: Planets, Moon & Sun Tips
- Beginner Telescope Buyer’s Guide: Choose the Right Scope
- Avoid Breaking Physics: Ask Better ‘What If’ Questions
- Astrophotography Guide for Beginners — Essential Tips
- Physics Blogs You Need to Be Reading
- The Science Crackpot Index and Bingo Game
- Solar Eclipse Viewing & Safety Guide — What to Expect
- What Are Your Favorite Science or Math Blogs?
Math Guides
- 10 Math Tips to Save Time and Avoid Mistakes
- 5 Common MATLAB Error Messages and How to Fix Them
- College-Level Math Options for High School Students
- Resources for High School Math at Home
- Linear Algebra Roadmap: Books & Resources for Students
- Abstract Algebra Self-Study Roadmap: Groups to Galois
- Advanced Analysis Study Guide: Measure & Functional
- Road Map for Self-Studying Mathematical Analysis Guide
- How to Self-Study Calculus: Topics, Order & Book Guide
- Pure Geometry Study Guide: Books & Roadmap for Students
- What Are Infinitesimals – Simple Version
Education Guides
- Learn 3 Tips For Cooling Off Hot Debates and Win The Argument
- A Lesson In Teaching Physics: You Can’t Give It Away
- Aiming High and Managing Distractions as Keys to Success for Science Majors
- Careers with a Physics Degree: Alternatives & Advice
- Physics Grad School: Senior-Year Application Guide
- What Academic Advice Would You Tell Your 18 Year Old Self?
- What’s Your Most Memorable Textbook?
- How to Become a Medical Physicist in 3653 Easy Steps
- Choosing a Physics Research Advisor in Graduate School
- Can You Succeed in Mathematics? Common Concerns Answered
- Doubt, Discouragement, and Perseverance in STEM Careers
- Early Physics Education in High Schools For Physics Majors
- Entering Physics Graduate School Without a Physics Degree
- Pass Physics Grad Qualifying Exams: Strategies & Plan
- Physics PhD Job Search: Start Well Before Graduation
- Guide to Publishing in Peer Reviewed Journals
- Avoid Breaking Physics: Ask Better ‘What If’ Questions
- So I Am Your Intro Physics Instructor
- Mathematical Prep for Physics Majors — Essential Guide
- Overcome Procrastination: Practical Student Strategies
- Presenting Physics Research: Conference Tips for Students
- APS March & April Meetings: Guide for Physics Grad Students
- Overcoming Challenges of Self-Studying Number Theory
- Postdoctoral Positions: How to Succeed as a Physicist
- Why Self-Studying Mathematics Often Fails and How to Persist
- How to Publish Your PhD Research in Physics Journals
- How to Publish in a Physics Journal (Addendum)
- Research Ethics for Physicists: Keep a Detailed Lab Notebook
- Resources for High School Physics at Home
- Learn the Secrets of Successful Science Projects
- Essential Guide: Surviving Your First Year in Physics
- The Birth of a Physics Textbook: An Author’s Journey
- Physics Major Guide: Succeed in Years 3–4 and Research
- Understanding the US Physics Graduate School System
- A Guide to Going Back to School For Math or Science
- Physics Graduate Assistantships: TA vs RA Explained
- How to Write a Master Degree Thesis As a Physics Major
- Writing Your Doctoral Thesis: Guide for Physics Grad
- CV Tips for Physicists: Secure Postdoc & Research Jobs
- Preparing for Your Physics PhD Thesis Defense Effectively
Other Science Guides
- An Intro to the Systemless Interface of Rooting Android Phones
- Debloating Android Phones: Risks and Best Practices
- Types of Programming Languages: Uses, Examples, Overview
- Create an Android Ringtone Picker with Ringtonemanager Class
- Introduction to Modern Digital Audio Concepts
- Ultimate Digital Camera Buyer’s Guide: Compacts, DSLR and Tripods
- DSLR Camera Guide: Lenses, Aberrations & Tips—Enthusiasts
- Digital Camera Buyer’s Guide — Choose the Best Camera
- Digital Camera Buyer’s Guide: Bridge Cameras
- Camera Tripod Guide: Choose Stable Tripods for Photos
- Digital Filtering and Exact Reconstruction of Digital Audio
- The LCEVC Coding Standard and 8K Television
- Evaluate Camera Lens Performance Using an LCD Display
- A Possible AI Modern Video Codec
- Programming an ATmega8A using Arduino
- Quantum Computing for Beginners
- Reflections on Technology Product Quality
- Studio in a Box: Learn About Digital Modeling Amplifiers
- AI and Learning: How It Impact Our Future
- How the Rise of AI Is Transforming STEM: Labs to Classrooms
- Revolutionary Technologies and Discoveries in 20 Years
- Why ChatGPT AI Is Not Reliable
Tutorials
Physics Tutorials
- A Formal Definition of Large-Scale Isotropy
- Lewin’s Circuit Paradox: Distinguishing E_s and E_m
- All About the Einstein Field Equations
- An Alternate Approach to Solving 2-Dimensional Elastic Collisions
- An Alternative Approach to Solving Collision Problems
- An Introduction to the Generation of Mass from Energy
- Learn Basic Kinematics in Classical Mechanics
- Calculate Sgr A* Spin from QPOs — Kerr Metric Derivation
- An Equation for the Centrifugal Force Reversal Near A Black Hole
- Corrections to MIT Open Courseware: Systems of Varying Mass
- Elementary Construction of the Angular Velocity
- Equations of Motion Revisited
- Learn The Basics of Rolling Motion
- Fabry-Perot and Michelson Interferometry: A Fundamental Approach
- Exploring Fermi-Walker Transport in Kerr Spacetime
- Learning Fermi-Walker Transport in Schwarzschild Spacetime
- Frames of Reference: Linear Acceleration View
- Frequently Made Errors in Equation Handling
- Frequently Made Errors in Heat: Elementary Level
- Frequently Made Errors in Mechanics: Forces
- Frequently Made Errors in Mechanics: Friction
- Frequently Made Errors in Mechanics: Hydrostatics
- Frequently Made Errors in Mechanics: Kinematics
- Frequently Made Errors in Mechanics: Moments
- Frequently Made Errors in Mechanics: Momentum and Impacts
- Frequently Made Errors in Mechanics: Springs
- Frequently Made Errors: Pseudo and Resultant Forces
- Frequently Made Errors in Vectors – Elementary Use
- Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes
- How to Determine the Change in Entropy
- How to Apply Newton’s Second Law to Variable Mass Systems
- How to Master Projectile Motion Without Quadratics
- How to Measure Internal Resistance of a Battery
- How to Model a Magnet Falling Through a Conducting Pipe
- How to Model a Magnet Falling Through a Solenoid
- How to Recognize Split Electric Fields
- How to Solve a Multi-Atwood Machine Assembly
- How to Solve Projectile Motion Problems in One or Two Lines
- Fermi-Walker Transport in Minkowski Spacetime
- How to Use Duality in Computational Electromagnetic Problems
- Learn an Integral Result from Parseval’s Theorem
- Learn the Basics of Dimensional Analysis
- LightCone 8 Tutorial Part III – How Things are Computed
- LightCone8 Tutorial Part I
- LightCone8 Tutorial Part II – Charts
- Maximizing Horizontal Range of a Projectile
- Maxwell’s Equations in Magnetostatics and Solving with the Curl Operator
- Mutual Inductance: When k≠1 and Two Coupling Coefficients
- A Numerical Electromagnetic Solver Using Duality
- Unity Orbital Mechanics and AR Scaling: Implementation Guide
- Learn Orbital Precession in the Schwarzschild and Kerr Metrics
- Derivation of Gauss’s Law: Coulomb to Flux Explained
- Intro to Physically Reasonable Waves on a String
- Understanding Precession in Special and General Relativity
- Quaternions in Projectile Motion
- Presenting a Rare Kinematic Formula
- Learn About Relativity on Rotated Graph Paper
- Learn Relativity Using the Bondi K-calculus
- Relativity Variables: Velocity, Doppler-Bondi k, and Rapidity
- Quantum Renormalisation Made Easy
- Why Renormalisation in Quantum Theory Needs a Cutoff
- Rindler Motion in Special Relativity: Hyperbolic Trajectories
- Rindler Motion in Special Relativity: Rindler Coordinates
- The Schwarzschild Geometry: Key Properties
- The Schwarzschild Geometry: Coordinates
- The Schwarzschild Geometry: Physically Reasonable?
- An Example of Servo-Constraints in Mechanics
- Learn A Short Proof of Birkhoff’s Theorem
- How to Solve Einstein’s Field Equations in Maxima
- Learn Statistical Mechanics: Equilibrium Systems
- Subtleties Overlooked in Friction Questions: Object Slides Down Ramp
- Learn About Tetrad Fields and Spacetime
- The Classical Limit of Quantum Mechanical Commutator
- The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors
- Understanding Entropy and the 2nd Law of Thermodynamics
- Valentine’s Reflections: Mathematical Matters of the Heart
- Particle in a Box: 1D & 2D Quantum Visualizations
Math Tutorials
- A Novel Technique of Calculating Unit Hypercube Integrals
- A Trick to Memorizing Trig Special Angle Values Table
- An Introduction to Theorema Primum
- Physical Applications of the “Tan Rule”
- Understanding Exponents: Real, Irrational & Imaginary
- Some Conceptual Difficulties in the Roles of Variables and Constants
- A Continuous, Nowhere Differentiable Function: Part 1
- A Continuous, Nowhere Differentiable Function: Part 2
- Demystifying the Chain Rule in Calculus
- Explore the Fascinating Sums of Odd Powers of 1/n
- Computing the Riemann Zeta Function Using Fourier Series
- Frequently Made Errors in Probability: Conditionals in Natural Language
- Explaining the General Brachistochrone Problem
- Ambiguous Case (SSA): When Triangles Are Impossible Explained
- Groups, The Path from a Simple Concept to Mysterious Results
- How to Solve Second-Order Partial Derivatives
- Informal Introduction to Cardinal Numbers
- Investigating Some Euler Sums
- Mathematical Irrationality for Dummies
- Rigorous Proof: Why 0.999… Equals 1 (Geometric Series)
- A Journey to The Manifold SU(2): Representations
- How to Make Units of Measurement Work for You
- Learn About Matrix Representations of Linear Transformations
- Integration Paradoxes: Indefinite Integrals and Constants
- Why the Gauge (Henstock-Kurzweil) Integral Matters
- The Pantheon of Derivatives – Manifolds And Vector Fields (II)
- The Pantheon of Derivatives – Sections, Pullbacks And Pushforwards (III)
- The Pantheon of Derivatives – Lie Derivatives And Others (IV)
- The Pantheon of Derivatives – Important Theorems (V)
- Demystifying Parameterization and Surface Integrals
- Learn Partial Differentiation Without Tears
- Introduction to Partial Fractions Decomposition
- Errors in Probability: Continuous and Discrete Distributions
- Python’s Sympy Module and the Cayley-Hamilton Theorem
- Reduction of Order For Recursions
- SOHCAHTOA: Seemingly Simple, Conceivably Complex
- Trick to Solving Integrals Involving Tangent and Secant
- Learn How to Solve the Cubic Equation for Dummies
- Solving Homogeneous Linear ODEs using Annihilators
- How to Solve Nonhomogeneous Linear ODEs using Annihilators
- Learn Further Sums Found Through Fourier Series
- The Analytic Continuation of the Lerch and the Zeta Functions
- The Art of Integration
- The Extended Riemann Hypothesis and Ramanujan’s Sum
- The Orin Fractional Calculus
- The Pantheon of Derivatives – The Direction (I)
- Using the Fourier Series To Find Some Interesting Sums
- What Are Eigenvectors and Eigenvalues in Math?
Other Science Tutorials
- An Intro to AVX-512 Assembly Programming
- AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic
- AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Conclusion
- AVX-512 Programming: Extracting Column Subtotals from a Table
- Why Can’t My Computer Do Simple Arithmetic?
- Create an Android Ringtone Picker with Ringtonemanager Class
- Beginner C++ Tutorial — Compiler, Types & I/O Basics
- How to Setup a Raspberry Pi Cluster
- Intro to Algorithms for Programming
- Intro to Data Structures for Programming
- Unity Orbital Mechanics and AR Scaling: Implementation Guide
- P vs. NP and what is a Turing Machine (TM)?
- Parallel Programming on a CPU with AVX-512
- Parallel Programming on an NVIDIA GPU
- Python’s Sympy Module and the Cayley-Hamilton Theorem
- Recursion in Programming and When to Use or Not to Use It
- Learn Simple Python Debugging with Pdb
- Simple Python Debugging with Pdb: Part 2
- The Joy of Processing
- How AI Is Changing STEM Labs, Classrooms & Industry
- Why ChatGPT AI Is Not Reliable
Interviews
Interviews
- Peter Krautzberger on MathJax — Accessibility & Future
- Pamela Gay Interview — Astronomy, Citizen Science & Outreach
- From Biology to Sysadmin: Career Insights & Advice
- Interview with a Biophysicist: Andy Resnick
- Interview with Chemical Physicist: DrClaude
- Interview with a Chemist: Borek
- Interview with an Electrical Engineer: Berkeman
- Russ Watters: Astrophotography & HVAC Engineer Mentor
- Jim Hardy: Nuclear Engineer — Energy Insights & Hobbies
- John Baez Interview — Mathematical Physicist & Networks
- John Baez Interview — Math, Climate & the Anthropocene
- David Hestenes on Geometric Algebra: Applications & Learning
- Arnold Neumaier Interview: QFT Foundations & Thermal
- Interview with a Mentor: Drakkith
- David J. Griffiths Interview: Teaching Quantum Mechanics
- Interview with a Physicist: Doc Al
- Sean Carroll Interview: Cosmology, Books & Insights
- Interview with a Physicist: ZapperZ
- Interview with Physics Mentor bhobba
- Interview with a Physics Mentor: Nugatory
- PeterDonis Interview – Physics Mentor on Science & Tech
- Interview with Physics Mentor: Stevendaryl
- Interview with Science Advisor DrChinese
- Carlo Rovelli Interview: Insights on Physics & Life
- Clifford V. Johnson: The Dialogues & Science Outreach
- Garrett Lisi: E8 Theory, Surfing & Physics Interview
- Sabine Hossenfelder: Dark Matter, Gravity & LIGO Interview
- Adam Becker — What Is Real? Quantum Foundations Explained
- Interview with Astrophysicist D H
- Interview with Biologist Ryan_m_b
- Meet Mentor Chestermiller — Chemical Engineering Profile
- Interview with Engineer jrmichler
- Interview with Engineer Mentor anorlunda
- Interview with Mathematician Mark44
- Interview with Mentor Evo
- Interview with Mentor Integral
- Interview with Mentor LisaB
- Interview: Niels Tuning — LHCb Run Coordinator at CERN
- Meet Mentor DaleSpam — Biomedical Engineer & Mentor
- Meet Mentor George Jones — UNBC Physicist & Educator
- Interview with Physicist jtbell
- Michio Kaku Interview — Physics, String Theory & Future
- Q&A With Universe Today’s Astronomer Fraser Cain
- Michio Kaku Interview — Peak Oil, String Theory & Space
Quizzes
Quizzes
- Ice Quiz: All About Ice Trivia
- Grab Bag Science Quiz and Trivia
- Albert Einstein Quiz: How Well Do You Know Albert Einstein?
- Inventions and Inventors Quiz and Trivia
- It’s Elemental! The Periodic Table Quiz
- Match the Scientist with the Story Quiz
- Name the Science Book Author Quiz
- Name the Science Photo Quiz
- Name the Scientist Quiz and Trivia
- PF Insight Scavenger Hunt 2
- PF Insights Scavenger Hunt
- NASA Quiz and Trivia: Test Your NASA Knowledge
- Isaac Newton Quiz: Test Yourself on Isaac Newton
- Moon Quiz: Test Yourself on the Moon
- Richard Feynman Quiz: Think You Know Richard Feynman?
- Stephen Hawking Quiz: Think You Know Stephen Hawking?
- LHC Quiz: Think You Know about the LHC?
- Pluto Quiz: Think You Know Pluto?
- Which Scientist Said What Quiz