Physics

Velocity Time Function

Revisiting the Velocity-Time Function

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Kinematics: The Velocity-Time FunctionAuthor's Preface: A Collaborative Approach to Lesson Development The intention behind what I hope will be…
Entangled Photon Polarization Qubits

Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality per Quantum Information Theory

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In her YouTube video Bell's Theorem Experiments on Entangled Photons, Dr. Fugate shows how polarization-entangled photons violate Bell's inequality. In…
relativator

Relativator (Circular Slide-Rule) – Simulated with Desmos

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The Relativator (revisited) This is an update of my 2006 post (reconstructed in 2014) Relativator: The circular slide-rule for physicists. This is a…
quantum entanglement

Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

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Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and…
no tidal bulge

Why the Tidal Bulge Doesn’t Exist – Tidal Theory Explained

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Introduction Overview That there is no tidal bulge is the key premise of this article. Upper-level oceanography undergraduates and above know this. Yet…
physics of reality

Quantum Reconstruction & Bell Correlations Explained

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Comment on PBS Space Time video PBS Space Time produces some very good videos on the foundations of quantum mechanics (QM), so let me comment on their…

Addition of Velocities (Velocity Composition) in Special Relativity

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The "Addition of Velocities" formula (more correctly, the "Composition of Velocities" formula) in Special Relativity[tex]\frac{v_{AC}}{c}=\frac{ \frac{v_{AB}}{c}+\frac{v_{BC}}{c}…
Schrodinger's cat

Schrödinger’s Cat and the Qbit

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The concept of quantum superposition (or superposition for short) is very counterintuitive, as Schr##\ddot{\text{o}}##dinger noted in 1935 writing [1],…
slinky drop experiment

The Slinky Drop Experiment Analysed

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The slinky drop is a rather simple experiment. In its most basic form, it requires only a popular toy for children, a stable hand, and a keen eye.…
einstein field equations

Einstein Field Equations – Definition and Fast Facts

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Definition/Summary The Einstein Field Equations (EFE) are a set of ten interrelated differential equations that form the core of Einstein's general theory…
Multi-Atwood Machine Assembly

How to Solve a Multi-Atwood Machine Assembly

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IntroductionThe figure on the right shows a "double-double" Atwood machine with three ideal pulleys and four masses.  All pulleys are released from…
Variable Mass Systems

How to Apply Newton’s Second Law to Variable Mass Systems

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Introduction The applicability of Newton's second law in the oft-quoted "general form"  $$\begin{align}\frac{d\mathbf{P}}{dt}=\mathbf{F}_{\text{ext}}\end{align}$$…
quantum information

How Quantum Information Theory Solves “the only mystery” of Quantum Mechanics

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In Chapter 37 of "The Feynman Lectures on Physics Volume 1," Richard Feynman famously wrote that the mystery of wave-particle duality in the double-slit…
Measure Internal Resistance of Battery

How to Measure Internal Resistance of a Battery

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Introduction A commonly encountered school-level Physics practical is the determination of the internal resistance of a battery - typically an AA or D…
gravity collapse

Oppenheimer-Snyder Model of Gravitational Collapse: Implications

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Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsIn the last article in this series, we finished up with a metric for the Oppenheimer-Snyder…
tensors relativity

Tensors Explained: Beginner’s Essentials for Relativity

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If you try learning general relativity, and sometimes special relativity, on your own, you will undoubtedly run into tensors. This article will outline…
gravity collapse

Oppenheimer-Snyder Model of Gravitational Collapse: Mathematical Details

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Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsIn a previous article, I described in general terms the model of gravitational…
twin paradox

Twin Paradox Guide: Spacetime Geometry Explained Clearly

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Introduction This article is intended for anyone who wants to start a thread here at Physics Forums on the twin paradox. There are already many, many threads…
gravity collapse

The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview

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Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsMost people who have spent any time at all studying GR are familiar with the…
object slide down ramp physics

Subtleties Overlooked in Friction Questions: Object Slides Down Ramp

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Problem statement (simplified) An object slides down a ramp at angle θ to encounter level ground. Both surfaces have kinetic friction: μ' on the ramp,…
quantum computers 101

Quantum Computing Explained: Qubits, Algorithms & Applications

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Overview This article provides an accessible introduction to quantum computing, a cutting-edge technology that processes certain types of information…
gauss law misconceptions

A Physics Misconception with Gauss’ Law

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Introduction It is relatively common to see the following type of argument: The surface area is ##A## and the enclosed charge is ##Q##. The electric…
model magnet

How to Model a Magnet Falling Through a Conducting Pipe

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Introduction In an earlier article, we examined a magnet falling through a solenoid. We argued that the point dipole model can account for the basic features…
model magnet

How to Model a Magnet Falling Through a Solenoid

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Introduction Modeling a magnet realistically is a task best done numerically.  Even the simplified model of two separated disks with uniform surface…
why can we jump

How Can We Jump When the Ground Does No Work?

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Common mistaken argument It is relatively common on Physics Forums to see arguments that are effectively similar to the following: When we jump off the…
magnetism current

Symmetry Arguments and the Infinite Wire with a Current

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Many people reading this will be familiar with symmetry arguments related to the use of Gauss law. Finding the electric field around a spherically symmetric…
mermin device quantum entanglement

Superdeterminism and the Mermin Device

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Superdeterminism as a way to resolve the mystery of quantum entanglement is generally not taken seriously in the foundations community, as explained in…
relativity rotated graph

Relativity on Rotated Graph Paper (a graphical motivation)

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(based on https://www.physicsforums.com/threads/teaching-sr-without-simultaneity.1011051/post-6588952 and https://physics.stackexchange.com/a/689291/148184…
quantum mechanics new approach

Quantum Physics via Quantum Tomography: A New Approach to Quantum Mechanics

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This Insight article presents the main features of a conceptual foundation of quantum physics with the same characteristic features as classical physics…
Kerr Spacetime

Geodesic Congruences in FRW, Schwarzschild and Kerr Spacetimes

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Introduction The theory of geodesic congruences is extensively covered in many textbooks (see References); what follows in the introduction is a brief…
MIT course corrections

Corrections to MIT Open Courseware: Systems of Varying Mass

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Corrections to MIT Open Courseware 8-01sc classical mechanics, fall 2016 Applying Newton's Laws to systems of Varying Mass PDF Course Link My concerns…
quantum information

How Quantum Information Theorists Revealed the Relativity Principle at the Foundation of Quantum Mechanics

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This Insight is a condensed version of No Preferred Reference Frame at the Foundation of Quantum Mechanics. Reference numbers here correspond to that paper.…
Quaternions in Projectile Motion

Quaternions in Projectile Motion

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Introduction In a previous Physics Forums article entitled “How to Master Projectile Motion Without Quadratics”, PF user @kuruman brought to our…
quantum double slit experiment

Quantum Mechanics and the Famous Double-slit Experiment

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Double-slit Key PointsQuantum mechanics is known for its strangeness, including phenomena like wave–particle duality, which allows particles to…
safety

Safety Factors: Why Forums Avoid Design Advice Online

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Forum Guidelines There are often questions on Physics Forums related to building machines or structures that are left unanswered because of this guideline…
solving projectile motion

How to Solve Projectile Motion Problems in One or Two Lines

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Introduction We show how one can solve most if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo…
tolman law beginner

Tolman Law in a Nutshell

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The Tolman law describes how the temperature in a fixed gravitational field depends on the position (see https://arxiv.org/abs/1803.04106 for a pedagogic…
physics cannonball projectile

Maximizing Horizontal Range of a Projectile

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Introduction A recent homework problem that appeared in the forums was concerned with maximizing the horizontal range of a projectile subject to the launch…
electromagnetic computations duality

Building a Numerical FEM Solver for Duality in EM Fields

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In the previous insights article (How to Use Duality in Computational Electromagnetic Problems), I covered some uniqueness theorems for the Riemann-Silberstein…
Electric Field Seen by an Observer

The Electric Field Seen by an Observer: A Relativistic Calculation with Tensors

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This Insight was inspired by the discussion in "electric field seen by an observer in motion", which tries to understand the relation between two expressions:…
electromagnetic computations

How to Use Duality in Computational Electromagnetic Problems

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Some weeks ago I happened across a post that caught my eye. Dale asked a question about the number of photons in an electromagnetic field. His question…
equations of motion

Equations of Motion Revisited

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Introduction In any school Physics course, the Newtonian equations of motion are very much a 'stock' item. Students learn the equations and are given…
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…
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…
flight simulator

Introduction to Pitot-Static Systems in Gliders

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Introduction 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,…
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 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…
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…
pressure is a source of gravity

Is Pressure A Source Of Gravity?

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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…
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.…
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 Overview The study of evolution has dominated biology for over a century. Explaining why life is the way it is fascinates both…
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…
perpetual motion machines

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

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Authorship Authorship Contributions From Anorlunda Introduction You may want to believe the article you read, or the video you saw, or you may be very…
fluid dynamics experiment

Video Analysis of Spheres Falling Through Two Liquids

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3 Comments
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 About the author As a long-time woodworker, I enjoy being able to tell one wood from another. In the process of learning how to do that,…
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…
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 &=…
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…
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]…
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 Transit a Rotating Tunnel: Physics & Trajectories

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2 Comments
Introduction Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below. For the…
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…
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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3 Comments
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…
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…
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…
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…
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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Introduction Commonly there is a lot of imprecision in talking about ''indistinguishable'' (or ''identical'') particles, even in serious work. This Insight…
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…
Kerr Spacetime

Exploring Fermi-Walker Transport in Kerr Spacetime

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2 Comments
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…
quantum qubit

A Classical View of the Qubit

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2 Comments
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

Learning 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…
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…
What are virtual particles

Virtual Particles Explained — Quantum Field Theory

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Definition / Summary Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) for interactions…
quantum mechanics is incomplete

9 Reasons Quantum Mechanics is Incomplete

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Incomplete interpretations of quantum mechanics I argue that all interpretations of quantum mechanics (QM) are incomplete, each for its own reason. I…
Simple Harmonic Oscillator Laboratory

An Accurate Simple Harmonic Oscillator Laboratory

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[CONTENT] Learning ObjectivesExecute a specific experimental procedure to test a specific hypothesis. Use the Tracker video analysis software for…