Physics Articles

Here contains the collection of expert physics articles that deal with physics topics. These span all skill ranges and may include astronomy and cosmology topics. Learn something new today by professionals in the fields you are interested in!

Epsilontic limits and continuity

Epsilontic – Limits and Continuity

Abstract I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I…

The Poor Man’s Milli-Ohm Meter

Introduction In a previous article on measuring battery internal resistance, a simple technique for low-resistance measurement was outlined. In this article,…
Differential Equation Systems and Nature

Differential Equation Systems and Nature

Abstract "Mathematics is the native language of nature." is a phrase that is often used when it comes to explaining why mathematics is all around in natural…
quantum information

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

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…
Carl Sagan

Opinion: When Pro Scientists Explain Using Pop Science

Abstract There is so much to say about the many endeavors by professional scientists to explain to us the world. The list is long: Carl Sagan, Harald…
white dwarfs

Why There Are Maximum Mass Limits for Compact Objects

In this article, we will look at why there are maximum mass limits for objects that are supported against gravity by degeneracy pressure instead of kinetic…
gravity collapse

Oppenheimer-Snyder Model of Gravitational Collapse: Implications

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

What Are Tensors and Why Are They Used in Relativity?

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

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

When Discussing the Twin Paradox: Read This First

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 here on…
gravity collapse

The Oppenheimer-Snyder Model of Gravitational Collapse: An Overview

Part 1: OverviewPart 2: Mathematical DetailsPart 3: ImplicationsMost people who have spent any time at all studying GR are familiar with the…
definition differences

Yardsticks to Metric Tensor Fields

I asked myself why different scientists understand the same thing seemingly differently, especially the concept of a metric tensor. If we ask a topologist,…
quantum computers 101

Quantum Computing for Beginners

Introduction to Quantum Computing This introduction to quantum computing is intended for everyone and especially those who have no knowledge of this relatively…
gauss law misconceptions

A Physics Misconception with Gauss’ Law

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…
why can we jump

How Can We Jump When the Ground Does No Work?

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

Symmetry Arguments and the Infinite Wire with a Current

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

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)

(based on and…
quantum mechanics new approach

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

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

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

This Insight is a condensed version of No Preferred Reference Frame at the Foundation of Quantum Mechanics. Reference numbers here correspond to that paper.…
quantum double slit experiment

Quantum Mechanics and the Famous Double-slit Experiment

Key PointsQuantum mechanics is known for its strangeness, including phenomena like wave-particle duality, which allows particles to behave like waves. …

When Science is Not Enough: Legal and Health Implications of Questions

There are often questions on Physics Forums related to building machines or structures that are left unanswered because of this guideline (found in the…
tolman law beginner

Tolman Law in a Nutshell

The Tolman law describes how the temperature in a fixed gravitational field depends on the position (see for a pedagogic…
Bayesian statistics part 4

Posterior Predictive Distributions in Bayesian Statistics

Confessions of a moderate Bayesian, part 4 Bayesian statistics by and for non-statisticiansRead part 1: How to Get Started with Bayesian StatisticsRead…
electric potential

Introduction to Electric Vector Potential and Its Applications

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

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

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?

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

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?

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

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

A Principle Explanation of the “Mysteries” of Modern Physics

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

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

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?

In this insight, we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko's…
pressure is a source of gravity

Is Pressure A Source Of Gravity?

In a previous series of articles, I posed the question "Does Gravity Gravitate?" and explained how, depending on how you interpreted the terms "gravity"…
Compton Scattering

Massive Meets Massless: Compton Scattering Revisited

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

Is Science an Authority? How to View Announcements from Scientists

In a previous article, I discussed why scientists (among others) are almost never interested in considering a new theory proposed by a non-scientist: because…
dark energy supernova

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

In Part 1 of this 3-part series, I explained kinematics in Einstien-deSitter (EdS) cosmology and in Part 2, I explained kinematics in ##\Lambda##CDM cosmology…
dark energy cosmology lcdm

Dark Energy Part 2: LCDM Cosmology

This is Part 2 of a 3-part series explaining evidence for so-called “dark energy” leading to a current positive cosmological acceleration. The evidence…
beginner guide to baryons

A Beginner Physics Guide to Baryon Particles

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

Slowly Lowering an Object in a Static, Spherically Symmetric Spacetime

In the first two articles in this series, we looked at the Einstein Field Equation and Maxwell's Equations in a static, spherically symmetric spacetime.…
supernova refsdal

The Reappearance of Supernova (SN) Refsdal

Key Points Astronomers have been trying to understand space for thousands of years. Supernova Refsdal was the first known multiply imaged supernova. …
Dark Energy Cosmology Part 1

Dark Energy Part 1: Einstein-deSitter Cosmology

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

The Evolution of the Universe, Cosmic Web and Connections

The universe was not perfectly uniform when it started, some areas had a higher density than others. During the evolution of the universe, these areas…
Gaia search for black holes

Gaia and the Race to Detect More Gravitational Waves

Gravitational waves (GW’s) are disturbances in spacetime produced by any massive object moving asymmetrically. However, only the most massive and most…
uranus spin

3 Possible Models For Why Uranus Spins on Its Side

Uranus spins on its side. Uranus has an obliquity (tilt) of 98º, making its axis of rotation closer to the ecliptic plane than any other planet. It is…
black holes are not empty

Black Holes Are Not Empty Voids. A Black Hole at the Heart!

Key PointsBlack Holes (BH’s) have a gravitational pull so strong that nothing, not even light, can escape it BH’s can be divided into two…
energy conservation can we do better

Can We Do Better Than Mechanical Energy Conservation?

Note: It is assumed that the reader has read part I of the series. Introduction The ambiguity and flaws discussed in part I can be resolved using the…
energy conservation ambiguity

Is Mechanical Energy Conservation Free of Ambiguity?

Introduction "Close to any question that is in the textbook, there is another question that has never been answered that is interesting." [Stephen Wolfram,…
fluid dynamics experiment

Accurate Fluid Dynamics By Video Analysis

IntroductionProviding accurate fluid dynamics experiments for undergraduate laboratories is challenging in several ways, including reproducibility,…
Diffraction Grating Spectrometer.

Learn the Fundamentals of the Diffraction Grating Spectrometer

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

Intro to the Ionization Energy of Atomic Hydrogen

Introduction In previous articles relating to various transition energies in Hydrogen, Helium and Deuterium we have employed the following formula for…
quantum entanglement

Answering Mermin’s Challenge with the Relativity Principle

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

In a recent thread, I outlined how to compute the correlation function for the Bell basis states\begin{equation}\begin{split}|\psi_-\rangle &=…
Kuhnian Revolution

Modern Physics Understood as an Unrecognized Kuhnian Revolution

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

Relativistic Treatment of the DC Conducting Straight Wire

Introduction The direct-current-conducting infinitely long wire is often discussed in the context of relativistic electrodynamics. It is of course a completely…
Deuterium Lyman Alpha Line

Revisiting The Deuterium Lyman Alpha Line Experiment

Introduction In this article, we will be revisiting a somewhat understudied (and seemingly unrepeated) experiment to measure the Deuterium Lyman Alpha…
Solar Balmer Lines

Signature of the Sun: Analyzing the Solar Balmer Series Lines

Introduction We are in many ways a fortunate generation having so many wonderful tools at our disposal on account of the "silicon revolution". The advent…
Bohr’s Helium Lines

Understanding Bohr’s Helium Lines

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

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

Preface While browsing through unanswered posts in the Classical Physics Workshop, I came across a gem at the link shown below.  For the reader's convenience,…
Balmer Alpha Line

Calculating the Balmer Alpha Line: Atomic Hydrogen

Introduction Most readers acquainted with the hydrogen spectrum will be familiar with the set of lines in the visible spectrum representing transitions…
spacetime maxwell

Maxwell’s Equations in a Static, Spherically Symmetric Spacetime

In the first article in this series, we looked at the Einstein Field Equations in a static, spherically symmetric spacetime. In this article, we are going…
quantum superposition

Understanding Superposition Physically and Mathematically

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

What Thermodynamics and Entropy Means

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

This will be the first of several articles which will provide, for reference, useful equations for static, spherically symmetric spacetimes. This is a…
Star Equations

Equations of State for Photon Gas and Relativistic Electron Gas

This Insight develops equations of state that are useful in calculations about cosmology and about the insides of stars. The first calculation is for a…
rules of quantum mechanics

The 7 Basic Rules of Quantum Mechanics

For reference purposes and to help focus discussions on Physics Forums in interpretation questions on the real issues, there is a need for fixing the common…
Quantum Particles

Clarifying Common Issues with Indistinguishable Particles

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

When Renewable Energy Meets Power Grid Operations

The electric power industry faces much turmoil in the coming decades.  The business model of the electric utility company (public or private) may not…
create a universe story

How to Create a Universe – Instructions for an Apprentice God

(-: ##~~~## A fantasy to be read at leisure time ##~~~## :-) Written October 7, 1999 to relax from the strains of working on a new interpretation of quantum…
quantum qubit

A Classical View of the Qubit

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

9 Reasons Quantum Mechanics is Incomplete

I argue that all interpretations of quantum mechanics (QM) are incomplete, each for its own reason. I also point out that for some interpretations (those…
against quantum interpretations

Against “interpretation”

I am against "interpretations" of Quantum Mechanics (QM) in a sense in which John Bell [1] was against measurement in QM and Travis Norsen [2] is against…
Hooke's Law Experiement

An Example of An Accurate Hooke’s Law Laboratory

Learning ObjectivesGain confidence and experimental care in making accurate measurements. Understand the relationship between force and spring…
Bernoulli's equation

Demystifying the Often Misunderstood Bernoulli’s Equation

Introduction Bernoulli's equation is one of the most useful equations in the field of fluid mechanics, owing to its simplicity and broad applicability.…
Magnetic Field Lines

Are Magnetic Field Lines Real?

We recently had a question in the relativity forums that mentioned the behavior of magnetic field lines and reminded me of my own confusion at school about…
vehicle power

When Vehicle Power Dictates Acceleration

One interesting problem when dealing with a vehicle of a certain mass is to determine what is required in order to get the maximum acceleration while going…
Quantum Eraser

The Quantum Mystery of Wigner’s Friend

In this Insight I will introduce the quantum mystery called ``Wigner's friend'' using Healey's version [1] of Frauchiger and Renner's (FR's) version [2]…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

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

The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

In this Insight, I will show how the Popescu-Rohrlich (superquantum) correlations provide an unreasonable advantage in a particular "quantum guessing game''…
killing Fields and Black Holes

Exploring the Math in Killing Fields and Black Holes

Killing Vector Field The Killing vector field is a vector field on a differentiable manifold that preserves the metric over spacetime (from this I assume,…
LHC Energies

Exploring the Energies in the Large Hadron Collider

The Large Hadron Collider has produced collisions at 7 TeV. For collisions at 7 TeV, protons need to be ‘ramped’ to 3.5 TeV, the proton has a mass…
Falling in Black Holes

Black Holes and the Properties of In-Falling Radial Plungers

From 'Exploring Black Holes' by John Wheeler and Edwin Taylor; can apply to any object falling radially towards a static spherical mass (where the mass…
why quantum

Why the Quantum | A Response to Wheeler’s 1986 Paper

Wheeler's opening statement in his 1986 paper, ``How Come the Quantum?'' holds as true today as it did then [1] The necessity of the quantum in the construction…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

Having more than 10 years of experience in teaching vector and tensor calculus and special and general relativity, I have noted that many people have the…
speed of sound

Direct Echo-Based Measurement of the Speed of Sound

Figure 1: Distance vs. time a firecracker report echoed off of a building at different distances on both a cold and a warm day.The speed of sound…
information definition

How to Better Define Information in Physics

When I ask questions about the conservation of information I frequently get the reply, “It depends on what you mean by information.”   So, I researched…
bizarro univerise

Lessons From the Bizzaro Universe

The terms Bizarro and Bizarro World originated in Superman comics, where strangely imperfect versions of Superman, other action characters, and even Earth…

Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

Paper discussion: Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Antonio Genova, Erwan Mazarico, Sander…

Learn Statistical Mechanics: The Ideal Gas

Read Part 1: Equilibrium Systems The Ideal Gas: Boltzmann's Approach (The Microcanonical Ensemble) Consider a monatomic gas of ##N## non-interacting…

Addressing the “Classical Physics Is Wrong” Fallacy

One of the common questions or comments we get on PF is the claim that classical physics or classical mechanics (i.e. Newton's laws, etc.) is wrong because…

Learn Renormalization in Mathematical Quantum Field Theory

This is one chapter in a series on Mathematical Quantum Field TheoryThe previous chapter is: 15. Interacting quantum fields. 16. Renormalization In…

Learn Interacting Quantum Fields in Mathematical Quantum Field Theory

This is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 14. Free quantum fields.The next chapter is 16. Renormalization. 15.…

Learn Free Quantum Fields in Mathematical Quantum Field Theory

This is one chapter in a series on Mathematical Quantum Field TheoryThe previous chapter is 13. Quantization.The next chapter is 15. Interacting…

Intro to the Big Bang and Infinity Concepts

This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METUIn the cosmology section of the…

Learn About the FLRW Metric and The Friedmann Equation

This article is part of our student writer series. The writer Arman777, is an undergraduate physics student at METUPrevious Chapter: A Journey Into…

The Fundamental Difference in Interpretations of Quantum Mechanics

A topic that continually comes up in discussions of quantum mechanics is the existence of many different interpretations. Not only are there different…

Learn Quantization in Mathematical Quantum Field Theory

The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 12. Gauge fixing.The next chapter is 14.…

Explore Coordinate Dependent Statements in an Expanding Universe

In this Insight we will discuss the general Robertson--Walker (RW) universe, in which a set of co-moving observers with proper time ##t## observe the universe…

The Schwarzschild Metric: A Newtonian Comparison

A Short Proof of Birkoff's Theorem derived the Schwarzschild metric in units of ##G = c = 1##:\begin{equation} ds^2 = -\left(1 - \frac{2M}{r}\right)dt^2…