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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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…
create a universe story

How to Create a Universe: Instructions for an Apprentice God

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11 Comments
(-: ##~~~## 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…
What is a Tangent Line

Tangent to a Curve: Definition, Equations & Examples

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0 Comments
Definition / Summary The tangent to a curve in a plane at a particular point has the same gradient as the curve at that point.More generally, the…
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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1 Comment
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…
science major advice

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

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

AVX-512 Programming: Extracting Column Subtotals from a Table

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

Fermi-Walker Transport in Minkowski Spacetime

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8 Comments
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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2 Comments
Definition / Summary Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) for interactions…
The Sum of Geometric Series from Probability Theory

The Sum of Geometric Series from Probability Theory

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12 Comments
Here I present a simple (but to the best of my knowledge, new) derivation of the formula for the sum of the infinite geometric series. The derivation is…
quantum mechanics is incomplete

9 Reasons Quantum Mechanics is Incomplete

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45 Comments
I argue that all interpretations of quantum mechanics (QM) are incomplete, each for its own reason. I also point out that for some interpretations (those…
AVX-512 conclusion

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

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

AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic

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

An Accurate Simple Harmonic Oscillator Laboratory

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

An Intro to AVX-512 Assembly Programming

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

Against “interpretation”

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195 Comments
I am against "interpretations" of Quantum Mechanics (QM) in a sense in which John Bell [1] was against measurement in QM and Travis Norsen [2] is against…
lie algebra representations

Learn Lie Algebras: A Walkthrough – The Representations

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1 Comment
  Part III: Representations  Sums and Products. Frobenius began in ##1896## to generalize Weber's group characters and soon investigated…
abacus introduction

Suanpan & Soroban Abacus: History, Use, How-To Guide

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7 Comments
Introduction Abacuses are commonly seen in ancient civilizations around the world as a convenient tool for simple calculations. In this article we focus…
Hooke's Law Experiement

An Example of An Accurate Hooke’s Law Laboratory

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16 Comments
Learning ObjectivesGain confidence and experimental care in making accurate measurements. Understand the relationship between force and spring…
Lie Algebra Structure

Learn Lie Algebras: A Walkthrough – The Structures

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2 Comments
  Part II: StructuresDecompositions.Lie algebra theory is to a large extend the classification of the semisimple Lie algebras which…
lie algebra basics

Learn Lie Algebras: A Walkthrough – The Basics

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7 Comments
  Part I: Basics Introduction. This article is meant to provide a quick reference guide to Lie algebras: the terminology, important theorems,…
Interview with Michio Kaku

Michio Kaku Interview — Peak Oil, String Theory & Space

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Don't forget to read Part 1 of this interview. Peak Oil and Future Energy Sources Professor Kaku, what do you think of "peak oil"? How serious is it,…
Michio Kaku Interview

Michio Kaku Interview — Physics, String Theory & Future

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1 Comment
We are happy to present this archived interview with Dr. Michio Kaku, conducted in 2004. Michio Kaku is an American theoretical physicist, futurist, and…
Data Structures Programming

Intro to Data Structures for Programming

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

Demystifying the Often Misunderstood Bernoulli’s Equation

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

Are Magnetic Field Lines Real?

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

When Vehicle Power Dictates Acceleration

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

The Quantum Mystery of Wigner’s Friend

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30 Comments
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

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9 Comments
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…
inventions

Inventions and Inventors Quiz and Trivia

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26 Comments
Time to test your inventions, inventors and patent knowledge. As always there is no prize, so try without Google. Post your score in the comment thread.…
Super Quantum

The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations

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3 Comments
In this Insight, I will show how the Popescu-Rohrlich (superquantum) correlations provide an unreasonable advantage in a particular "quantum guessing game''…
engineer anorlunda

Interview with Engineer Mentor anorlunda

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2 Comments
Tell us about your school years? Part of my story is sad but common. I was a poor student. I didn’t pay attention, and I never did homework even once;…
bhobba physics interview

Interview with Physics Mentor bhobba

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2 Comments
Give us an executive summary on bhobbaI was born in Toowong Brisbane Australia 17/11/1955, and was raised in suburbs around Toowong - Toowong itself,…
rotational mechanics

An Example of Servo-Constraints in Mechanics

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5 Comments
Servo-constraint was invented by Henri Beghin in his Ph.D. thesis in 1922. For details see the celebrated monograph in rational mechanics by Paul Appell.To…
Telescope Buying Guide

Beginner Telescope Buyer’s Guide: Choose the Right Scope

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142 Comments
What telescope should a beginner buy? People often ask what telescope an aspiring amateur astronomer should buy. There isn't a single "correct" answer…
killing Fields and Black Holes

Killing Vector Field & Surface Gravity in Kerr BH Explained

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Killing Vector Field The Killing vector field is a vector field on a differentiable manifold that preserves the spacetime metric. In other words, it generates…
LHC Energies

LHC Relativistic Energies and Time Dilation at 3.5–14 TeV

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Large Hadron Collider and proton energies The Large Hadron Collider has produced collisions at 7 TeV. For collisions at 7 TeV, each proton must be ramped…
Falling in Black Holes

Radial Infall into a Static Mass: Equations & Guide

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From Exploring Black Holes by John Wheeler and Edwin Taylor. The relations below apply to any object falling radially toward a static, spherically symmetric…
physics blogs

What Are Your Favorite Science or Math Blogs?

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7 Comments
We asked our PF Advisors to tell us what their favorite science or math blog is (other than PF Insights).We also have a physics blog list here.Here…
stock options math

Intuitive Black‑Scholes Options Pricing Explained Simply

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19 Comments
Introduction Financial options — the right to purchase (call) or sell (put) stock or other assets at a fixed price on a future date — have been around…
unity orbital mechanics

Unity Orbital Mechanics and AR Scaling: Implementation Guide

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2 Comments
In this Insight I describe implementing basic orbital mechanics simulations in the Unity game engine and an approach to scaling the simulation for Augmented…
why quantum

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

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397 Comments
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…
whosaidwhat

Match the Scientist with the Story Quiz

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15 Comments
Among the most famous people are often geniuses. It's hard to tell whether this is the reason for the many anecdotes which are told about them, or whether…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

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16 Comments
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

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42 Comments
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…
walter lewin

Lewin’s Circuit Paradox: Distinguishing E_s and E_m

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65 Comments
Introduction Much has lately been said regarding this paradox that first appeared in one of W. Lewin's MIT lecture series on YouTube (see References [1]).…
information definition

How to Better Define Information in Physics

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12 Comments
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…
Sagittarius A

Calculate Sgr A* Spin from QPOs — Kerr Metric Derivation

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3 Comments
Introduction This Insight explains how it is possible to calculate the spin of Sagittarius A* — the supermassive black hole at the center of the Milky…
Niels_Tuning2

Interview: Niels Tuning — LHCb Run Coordinator at CERN

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2 Comments
Physics Forums is pleased to introduce Niels Tuning. He's a physicist working as the Run Coordinator for the LHCb experiment at CERN. Apart from the questions…

What Academic Advice Would You Tell Your 18 Year Old Self?

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27 Comments
We asked our PF Advisors to tell us what academic advice would you tell your 18 year old self. Here are their responses…Thanks to all the PF…
algorithms

Intro to Algorithms for Programming

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28 Comments
Many threads here at PF include some questions about how to learn to program. This is asked by Physics students who want to learn programming to help their…
maxima

How to Solve Einstein’s Field Equations in Maxima

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4 Comments
A few months ago, pervect pointed me to a post by Chris Hillman which is an introduction to the usage of Maxima for General Relativity. Maxima is a free…
advisor_textbooks

What’s Your Most Memorable Textbook?

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13 Comments
We asked our PF Advisors to tell us their most memorable or influential textbook and why. Here are their responses...Thanks to all the PF Advisors…
bizarro univerise

Lessons From the Bizzaro Universe

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23 Comments
The terms Bizarro and Bizarro World originated in Superman comics, where strangely imperfect versions of Superman, other action characters, and even Earth…
ridler_motion2

Rindler Motion in Special Relativity: Rindler Coordinates

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27 Comments
Our destination In our last article, Hyperbolic Trajectories, we derived some facts about the trajectory of a rocket that is undergoing constant (proper)…
sun_getting_smaller

Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

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

Rindler Motion in Special Relativity: Hyperbolic Trajectories

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5 Comments
Introduction: Why Rindler Motion? When students learn relativity, it's usually taught using inertial (constant velocity) motion. There are lots of reasons…
adam_becker

Adam Becker — What Is Real? Quantum Foundations Explained

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134 Comments
Adam Becker is an astrophysicist and science writer whose first book, What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics, has just…
statmech2

Learn Statistical Mechanics: The Ideal Gas

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

Addressing the “Classical Physics Is Wrong” Fallacy

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186 Comments
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…
hilbertspaces2

Learn the Basics of Hilbert Spaces and Their Relatives: Operators

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4 Comments
  Operators. The Maze Of Definitions. We will use the conventions of part I (Basics), which are ##\mathbb{F}\in \{\mathbb{R},\mathbb{C}\}##,…
cliffordjohnson

Clifford V. Johnson: The Dialogues & Science Outreach

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7 Comments
Clifford V. Johnson is a professor in the Physics and Astronomy Department at USC. He says, "I mainly work on (super)string theory, gravity, gauge theory…
hilbertspaces

Learn the Basics of Hilbert Spaces and Their Relatives: Definitions

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2 Comments
  Basics Language first: There is no such thing as the Hilbert space.Hilbert spaces can look rather different, and which one is used in…
qft_renormalization

Learn Renormalization in Mathematical Quantum Field Theory

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

Name the Science Book Author Quiz

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25 Comments
Let's see how well you know your science book authors. Some are classic, some modern! Don't forget to post your score in the comment thread linked at the…

Learn Interacting Quantum Fields in Mathematical Quantum Field Theory

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9 Comments
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.…
qft_freequantum

Learn Free Quantum Fields in Mathematical Quantum Field Theory

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1 Comment
This is one chapter in a series on Mathematical Quantum Field TheoryThe previous chapter is 13. Quantization.The next chapter is 15. Interacting…
bb_infinity2

Intro to the Big Bang and Infinity Concepts

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34 Comments
In the cosmology section of the Physics Forums, I encountered many Big Bang and related infinity problems. Hence, in this article, I want to explain the…
drak

Interview with a Mentor: Drakkith

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7 Comments
 Give us an early bio on yourselfWell, I was born and raised near Dallas, Texas as the only boy of 4 children. I grew up with 3 sisters, though…
journeycosmos3

Learn About the FLRW Metric and The Friedmann Equation

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1 Comment
Previous Chapter: A Journey Into the Cosmos – The Friedmann Equation                Chapter 2- FLRW Metric and The Friedmann Equation In…
qm_interpretations

The Fundamental Difference in Interpretations of Quantum Mechanics

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

Learn Quantization in Mathematical Quantum Field Theory

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14 Comments
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.…
statmech1

Learn Statistical Mechanics: Equilibrium Systems

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20 Comments
This is the first of a multi-part series of articles intended to give a concise overview of statistical mechanics and some of its applications. These articles…
expandinguniverse

Explore Coordinate Dependent Statements in an Expanding Universe

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5 Comments
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…

Demystifying the Chain Rule in Calculus

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8 Comments
Introduction There are a  number of posts on PF involving a general confusion over the multi-variable chain rule.  The problem is often caused by…
gps3

The Schwarzschild Metric: A Newtonian Comparison

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2 Comments
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…
debatetips

Learn 3 Tips For Cooling Off Hot Debates and Win The Argument

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22 Comments
 Civil discussion and debate are critical to Physics Forums. But it is also important in everyday life. When arguments get overheated, people…
gps2

The Schwarzschild Metric: The Photon Sphere

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3 Comments
 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…
qft_gauge

Learn Gauge Fixing in Mathematical Quantum Field Theory

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1 Comment
The following is one chapter in a series of Mathematical Quantum Field Theory.The previous chapter is 11. Reduced phase space.The next chapter…
gps1

The Schwarzschild Metric: GPS Satellites

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4 Comments
 A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then…
textbook

The Birth of a Physics Textbook: An Author’s Journey

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74 Comments
 It is said that you should accomplish three things in life:Plant a tree. Have a child. Write a book.Out of the three, I have…
cosmosintro

Learn About the Friedmann Equation and the Cosmos

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6 Comments
This is an introduction to cosmology for someone who has some knowledge of calculus and basic physics. In this tutorial, we will take a journey into the…
qtf_phased_space

Learn Reduced Phase Space in Mathematical Quantum Field Theory

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4 Comments
The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 10. Gauge symmetries.The next chapter is…
workethic

Why Work Ethic Is a Key to Success for Science Majors

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25 Comments
After earning a 4.0 GPA in his first semester as a Physics major at an esteemed state university, our son (and homeschool grad) attributes his…
arnold

Arnold Neumaier Interview: QFT Foundations & Thermal

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39 Comments
Please give us a brief background on yourself Over 40 years ago, I studied mathematics, physics and computer science in Freiburg and Berlin (Germany).…
dice

Learn About Intransitive Dice with a Twist

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6 Comments
Intransitive dice are sets of dice that don't follow the usual rules for "is better/larger than". If A<B and B<C, then A<C. If Bob runs faster…
qtf_guagesym

Learn Gauge Symmetries in Mathematical Quantum Field Theory

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18 Comments
This is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 9. Propagators.The next chapter is 11. Reduced phase…
unitsworkforyou

How to Make Units of Measurement Work for You

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13 Comments
How do we use units? You may see one of these speed limit signs, nearly every day. Even though neither of them displays units, drivers know they are implied.…
qft_prapagators

Learn Propagators in Mathematical Quantum Field Theory

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8 Comments
This is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 8. Phase space.The next chapter is 10. Gauge symmetries. 9.…
Maxwell equations

What is the Homopolar Generator: An Analytical Example

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8 Comments
Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…
qtf_phasespace

Learn Phase Space in Mathematical Quantum Field Theory

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7 Comments
The following is one chapter of a series on Mathematical Quantum Field Theory.The previous chapter is 7. Observables.The next chapter is 9. Propagators. 8.…
qtf_observables

Learn Observables in Mathematical Quantum Field Theory

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8 Comments
The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 6. Symmetries.The next chapter is 8. Phase…
dna_stretch

Learn the Amazing New Research on Untying Knots in Polymers

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4 Comments
Macromolecules A joint computational-experimental paper that I worked on was just published in MacroLetters, a journal that covers all topics relating…
qtf_symmerities

Learn Symmetries in Mathematical Quantum Field Theory

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4 Comments
The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 5. Lagrangians.The next chapter is 7. Observables.  6.…
qft_lang

Learn Lagrangians in Mathematical Quantum Field Theory

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42 Comments
This is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 4. Field Variations.The next chapter is 6. Symmetries.  5.…
qtf_field_variations2

Learn Field Variations in Mathematical Quantum Field Theory

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6 Comments
This is chapter 4 of a series on Mathematical Quantum Field Theory.The previous chapter is 3. Fields.The next chapter is 5. Lagrangians.  4.…
dna_twist

How to Use the Spaghetti-Twist Method to Align DNA

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1 Comment
A new paper from a collaboration of Canadian physicists has demonstrated how simply twirling a wire through a solution of DNA molecules can align the molecules…
qtf_fields

Learn the Fields of Mathematical Quantum Field Theory

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82 Comments
The following is one chapter in a series on Mathematical Quantum Field TheoryThe previous chapter is 2. Spacetime.The next chapter is 4. Field…
qft_spacetime

Learn Spacetime in Mathematical Quantum Field Theory

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9 Comments
The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 1. Geometry.The next chapter is 3. Fields  2.…
qtf_geometry

Learn the Geometry of Mathematical Quantum Field Theory

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33 Comments
This is the first chapter in a series on Mathematical Quantum Field Theory.The next chapter is 2. Spacetime. 1. Geometry The geometry of physics…