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!

gps2

The Schwarzschild Metric: The Photon Sphere

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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…
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…
cosmosintro

Learn About the Friedmann Equation and the Cosmos

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6 Comments
 This article is part of our student writer series. The writer Arman777 is an undergraduate physics student at METUThis is an introduction…
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…
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…
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…
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…
quantumfieldtheory

A First Idea of Quantum Field Theory – 20 Part Series

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8 Comments
These notes mean to give an expository but rigorous introduction to the basic concepts of relativistic perturbative quantum field theories, specifically…
circuitanalysis

The What and Why of Circuit Analysis Assumptions

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15 Comments
Probably everyone reading this article already has education on elementary circuit analysis (CA) and many of us are much more advanced. Typically, the…
perturbation

Introduction to Perturbative Quantum Field Theory

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110 Comments
This is the beginning of a series that gives an introduction to perturbative quantum field theory (pQFT) on Lorentzian spacetime backgrounds in its…
quantumpeace

How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics

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289 Comments
Many people here know that I am a "Bohmian", i.e. an adherent of a very non-orthodox interpretation of quantum mechanics (QM). Indeed, in the past, I have…

15 of the Best PF 2017 Eclipse Photos

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69 Comments
The 2017 August Eclipse really was something special. Fortunately Physics Forums has great photographers and snapped some remarkable shots. Here are a…
inflation5

A Poor Man’s CMB Primer: Quantum Seeds

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11 Comments
 The CMB establishes a record of ancient acoustic oscillations in the baryon-photon plasma. We've been studying how these primordial sound…
epsresults

Find Out the Results Shown at 2017 CERN EPS Conference

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7 Comments
The EPS conference was a week ago, and many new results and future plans were shown. A good general overview has been collected by Paris Sphicas in his…
m-theory

Super p-Brane Theory Emerging from Super Homotopy Theory

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6 Comments
  A notorious open problem: What is the non-perturbative theory formerly known as Strings?We still have no fundamental formulation of “M-theory”…
EdmondHamilton

Assessing the Physics in Edmond Hamilton’s “The Second Satellite”

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2 Comments
This article won't contain much about physics that typical readers of this site don't already know. However,  deconstructing improper physics in literature…
entanglement_entropy2

Lesson on Entanglement Entropy in Quantum Field Theory

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3 Comments
Part 1: Quantum Mechanics[This article expects the reader to have some experience with quantum field theory and path integrals][I should also…
dampedforces

Learn Damped Motion in Classical and Quantum Mechanics

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21 Comments
This Insights article is about dissipative forces (friction, air resistance, viscosity...).Damping by friction forces is one of the concepts that is…
SpectralParadox

Exploring the Spectral Paradox in Physics

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17 Comments
In terms of wavelength, peak solar radiation occurs at about 500 nm.  Interestingly, this is well within the range of human vision.  When solar radiation…
entanglement_entropy

Learn Entanglement Entropy in Quantum Mechanics

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22 Comments
Quantum Mechanics(QM) is one of the greatest intellectual achievements in human history. Not only because it describes the world at the microscopic level…
diffractiontheory

The Diffraction Limited Spot Size with Perfect Focusing

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12 Comments
Purpose:  The purpose of this Insights article is to give the reader a brief introduction to the principles behind diffraction-limited focusing. The…
cornuspiral

Learn Frenet Equations in 2-D Which Result in the Cornu Spiral

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3 Comments
This Insights article is intended as an introduction to the Frenet-Serret equations by showing an interesting application that results from a case in two-dimensional…
quantumflux

Learn About Vacuum Fluctuations in Experimental Practice

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41 Comments
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles”, “Misconceptions about Virtual Particles“ , and ''The…
magnet

Permanent Magnets Explained by Magnetic Surface Currents

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38 Comments
Introduction: The purpose of this Insight is to explain permanent magnets in a way that is in agreement with advanced textbooks on the subject, and that…
highercategorytheory

Why Higher Category Theory in Physics?

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30 Comments
 This here is my personal story. For an alternative introduction see my talk: Higher Structures in Mathematics and Physics.Initially,…
SchwarzschildGeometry3

The Schwarzschild Geometry: Spacetime Diagrams

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12 Comments
 When we left off in part 2, we were looking at the metric for the Schwarzschild geometry in Kruskal-Szekeres coordinates:$$ ds^2 = \frac{32…
quantumapplitudes

Learn About Quantum Amplitudes, Probabilities and EPR

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83 Comments
This is a little note about quantum amplitudes. Even though quantum probabilities seem very mysterious, with weird interference effects and seemingly nonlocal…
vaccummyth

Explore The Vacuum Fluctuation Myth in Quantum Theory

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230 Comments
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles” and “Misconceptions about Virtual Particles“ which…
anyon

Learn The Main Conceptual Ideas of Anyon Particles

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55 Comments
Every quantum physicist knows that all particles are either bosons or fermions. And the standard textbook argues that this so does not depend on the number…
frameofreference2

Frames of Reference: A Skateboarder’s View

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22 Comments
My essay Explaining Rolling Motion raised some commentary about frames of reference and their equivalence when solving physics problems. I wish to pursue…
relativitygauge

Exploring General Relativity as a Gauge Theory

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24 Comments
The fundamental interactions of the Standard Model are described by Yang-Mills theory. This is a gauge theory, which means the following: (1) Choose a…
quantumparticle

Spectral Standard Model and String Compactifications

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28 Comments
 The Connes-Lott-Chamseddine-Barrett model is the observation that the standard model of particle physics -- as a classical action functional,…
cmbprimer4

A Poor Man’s CMB Primer: Cosmic Acoustics

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1 Comment
 Before decoupling, photons and charged particles were in good thermal contact: though the primordial plasma might have varied in temperature…
spacetimecon

Struggles with the Continuum: Spacetime Conclusion

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4 Comments
 We've been looking at how the continuum nature of spacetime poses problems for our favorite theories of physics --- problems with infinities.…
11dgravity

11d Gravity From Just the Torsion Constraint

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17 Comments
 It is familiar that Einstein gravity may be formulated in terms of a vielbein field together with a "spin connection", subject to the constraint…
spacetime7

Struggles with the Continuum: General Relativity

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2 Comments
 Combining electromagnetism with relativity and quantum mechanics led to QED. Last time we saw the immense struggles with the continuum this…
ohmslaw

Learn Why Ohm’s Law Is Not a Law

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41 Comments
At first, I wanted this title to say “Ohm’s law is not a Law.”  But someone else used that phrase in a recent PF thread, and a storm of protest…
carcapacity

Why Road Capacity Is Almost Independent of the Speed Limit

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29 Comments
Let us start with a familiar situation. Take a familiar part of a road, for example, the one from your home to work. How long will it take you to drive…
Supersymmetry

Learn About Supersymmetry and Deligne’s Theorem

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54 Comments
 In 2002, Pierre Deligne proved a remarkable theorem on what mathematically is called Tannakian reconstruction of tensor categories. Here…
LHC4

LHC Part 4: Searching for New Particles and Decays

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17 Comments
 The LHC experiments are in full swing collecting data this year (more information in the forum), and a while ago the collaboration of the…
acusticbeats

Acoustic ‘beats’ from Mismatched Musical Frequencies

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11 Comments
Introduction In late high school physics courses and first-year university courses, the phenomenon of acoustical 'beats' (digital audio) is often covered.…

Learn About Spacetime Diagrams of Light Clocks

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25 Comments
We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45 degrees. Many quantitative…

A Black Hole Problem From Greg Egan’s “Incandescence”

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8 Comments
The following problem was inspired by reading Greg Egan's "Incadescence".  Consider a body, orbiting a Schwarzschild black hole and tide locked to it,…
Photoacoustic

The Interaction of Sound and Light

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6 Comments
I recently wrote a post on my blog about a fairly esoteric idea regarding sound propagating through light. This inspired me to write an article about…
logicp2

Scientific Inference: Do We Really Need Induction?

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14 Comments
  Part 2. "We don't need no stinkin' induction" -- Sir Karl Popper The traditional scientific method supposedly employs induction both in the…
antigravity

Roger Babson’s Anti-Gravity Contest

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13 Comments
In the early 20th century, an eccentric businessman named Roger Babson declared gravity to be mankind's greatest threat. He devoted part of his fortune…
logic1

Scientific Inference: Logical Induction Ain’t Logical

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39 Comments
 Three million years ago, the grandfathers of our genus used sharpened stones to chop wood and cut bone. Today, surgeons use fiber optic-guided…
virtualparticlesmyths

Learn the Top Misconceptions about Virtual Particles

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1 Comment
This Insight Article is a sequel to the Insight Article ''The Physics of Virtual Particles'', which contains an exposition of definitions that are physically…
acpoweranalysisp3

AC Power Analysis: The 4 Levels of Cyber Resilience

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9 Comments
 Power system security is much too big a topic for this article.  But I can squeeze in a few points about vulnerability to cyber attacks.…
nightsky

How Representative is the Night Sky?

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3 Comments
A couple of weeks back, a thread was started about whether or not most of the stars we see at night are brighter than our Sun. The consensus was yes. I'd…
quantumentanglement

How the EPR Paradox Fits Between Entanglement and Nonlocality

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11 Comments
If we violate a Bell inequality, we know we have quantum entanglement, and it used to be thought that these two notions were one and the same.At least,…
acpoweranalysisp2

Intro to AC Power Analysis: Network Analysis

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26 Comments
 Let me use the terms “power grid” and “network” interchangeably. What is the Power Grid Required to Do?Deliver energy to customers,…
Newton-Cartan-Theory

The Revival of Newton-Cartan Theory in General Relativity

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12 Comments
It's a calculation which you can find in any textbook on General Relativity (GR): when gravity is weak and does not vary with time, and when particles…
virtualparticles

Learn the Physics of Virtual Particles in Quantum Mechanics

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33 Comments
In discussions on the internet (including a number of Wikipedia pages) and in books and articles for non-experts in particle physics, there is considerable…
universeexpand

Learn about the Big Bang and the Expansion of the Universe

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29 Comments
The "ordinary Big Bang and expansion" (no inflation, no dark energy) Einstein's General Relativity allows a solution (FLRW metric) where an empty Universe…
acpoweranalysisp1

Intro to AC Power Analysis: Learn System Basics

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13 Comments
 Instantaneous PowerThe formula for power is: ##P=V\cdot I## , power= voltage*current.   We call that, instantaneous power.   Even…
pet_scan

Learn the Basics of Positron Emission Tomography (PET)

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7 Comments
Key PointsPaul Dirac first theorized positrons in 1928 and they were observed four years later by Carl Anderson. Positron Emission Tomography…
tcp_ip

How to Manage TCP/IP In Automation or Measurement Networks

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10 Comments
The 1990s saw the widespread adoption of network technology on two fronts: Office automation and factory automation. But while office automation soon standardized…
Ethernettime

Learn Time Synchronization Across Switched Ethernets

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18 Comments
Now and then you come across measurement problems that are tightly associated with the notion of synchronicity, meaning that things need to happen simultaneously.…
qminterpret

Tools to Enrich our Quantum Mechanics Interpretations Discourse

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13 Comments
IntroductionMany times, we encounter ourselves tangled into some Quantum Mechanics (QM) interpretations debates. Unfortunately, the standard…
spacetime6

Struggles with the Continuum – Freeman Dyson and QED

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24 Comments
 Last time I sketched how physicists use quantum electrodynamics, or 'QED', to compute answers to physics problems as power series in the…
islingmodel

High Temperature and Low Duality for the Ising Model on an Infinite Regular Tree

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1 Comment
Today I felt like sharing a computation that I thought was interesting. I'm sure I'm not the first to explore the Ising-Ising duality in this context,…
secondaryforces

Introduction to the Secondary Forces in Physics

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7 Comments
Many are familiar with the "fundamental forces" of nature: gravity, electromagnetism, and the strong and weak nuclear forces. Three of these have a tendency…
spacetime5

Struggles with the Continuum: Quantum Electrodynamics

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10 Comments
  Quantum field theory is the best method we have for describing particles and forces in a way that takes both quantum mechanics…
darkmatter

Learn About Knut Lundmark and the Prehistory of Dark Matter

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16 Comments
Look in your standard cosmology textbook (in my case, the closest one at hand is Barbara Ryden's Introduction to Cosmology) and go to the section which…
spacetime4

Struggles with the Continuum – Relativity and Quantum

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5 Comments
 In this series, we're looking at mathematical problems that arise in physics due to treating spacetime as a continuum---basically, problems…
theneedforinfinity

Why the Need of Infinity in Physics

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31 Comments
It is beyond doubt that the notion of infinity lies somewhere near the core of all mathematics, probably in a finite vicinity of zero. But where does it…
complexscience

Thoughts on the Complexity of Modern Science

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122 Comments
Science today is incredibly complex. Anyone who ever did scientific research knows that, but many in the general public seem to be completely unaware of…
rainbows

Exploration into the Physics of Rainbows

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88 Comments
For several years, I have been contemplating this beautiful picture by photographer Brian McPhee.  I have a personal interest in the photograph because…
earthgravity

Learn All About Earth’s Gravity

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18 Comments
Earth's gravitational field at the surface is approximately 9.8 Newtons/kilogram, or equivalently, 9.8 meters/second/second. But how does that change due…
speedoflight1

Learn About the Speed of Light and Galilean Relativity

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43 Comments
Key PointsEarly experiments attempted to measure the speed of light, including Galileo's lantern experiment, Ole Rømer's eclipse experiment, and…
buoyancy

Understanding Buoyancy: The Limits of Archimedes

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19 Comments
It’s a principle as old as science itself, and remarkably, remains essentially unchanged in the light of revolution after revolution in our understanding…
studymath

How to Self-Study Basic High School Mathematics

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5 Comments
  IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study…
studymath1

The Essential Guide to Self Study Mathematics

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13 Comments
  How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead,…
seeelectron

Have Scientists Seen an Electron?

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18 Comments
This is not about seeing an electron, but rather, the notion that seeing something with our eyes is the end-all requirement for the validity of anything.…
peterblockuniverse

The Block Universe – Refuting a Common Argument

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153 Comments
The "block universe" interpretation of SR has come up repeatedly in threads here on PF. Rather than link to them, I want to summarize a common argument…
Retrocausality

Understanding Retrocausality and Blockworld

In an Insights series “Blockworld and its Foundational Implications,” I quoted Huw Price and Ken Wharton in several places advocating a blockworld…
blockuniverse5

Blockworld and its Foundational Implications: Delayed Choice and No Counterfactual Definiteness

 In parts 1 and 2 of this 5-part Insights series, I explained the blockworld (BW) implication of special relativity. In part 3, I introduced…
blockuniverse4

Blockworld and its Foundational Implications: General Relativity and Closed Timelike Curves

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2 Comments
 In parts 1 and 2 of this 5-part Insights series, I explained the blockworld (BW) implication of special relativity (SR). In part 3, I introduced…
blockuniverse3

Blockworld and its Foundational Implications: General Relativity and the Big Bang

 In parts 1 and 2 of this 5-part Insights series, I explained the blockworld (BW) implication of special relativity (SR). Geroch sums up the…
blockuniverse2

Blockworld and Its Foundational Implications: The Relativity of Simultaneity and Blockworld

 In part 1 of this 5-part Insights series, I introduced two consequences of the second postulate of special relativity (SR): time dilation…
blockuniverse1

Blockworld and Its Foundational Implications: Time Dilation and Length Contraction

 This is the first in a 5-part series of Insights that will introduce blockworld (aka "block universe”) and use it to address a puzzle…
prequantum4

Examples of Prequantum Field Theories IV: Wess-Zumino-Witten-type Theories

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4 Comments
  At the end of this page, we will have come full circle back to the first article in the series 20 years ago -- The M-Theory Conjecture.We…
prequantum3

Examples of Prequantum Field Theories III: Chern-Simons-type Theories

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1 Comment
  After having constructed gauge fields and higher gauge fields in the previous article by systems of ##L_\infty##-algebroid-valued…
guagetheory

Examples of Prequantum Field Theories II: Higher Gauge Fields

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1 Comment
   After having recalled ordinary gauge fields from a dg-algebraic perspective in the previous article, here I discuss…
prequantumft

Examples of Prequantum Field Theories I: Gauge Fields

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1 Comment
  After having motivated the need for prequantum field theory and having laid out its principles (i. extremal action, ii. global…
animationwalk

Fun with Self-Avoiding Walks Simulations

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16 Comments
This post is about some simulations I did of self-avoiding random walks. These are what they sound like: with each step, the position of the walk moves…
prequantumgeometry5

Higher Prequantum Geometry V: The Local Observables – Lie Theoretically

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1 Comment
 This article discusses how the previous considerations naturally follow the concepts of local observables of local field theories and of…
prequantumgeometry4

Higher Prequantum Geometry IV: The Covariant Phase Space – Transgressively

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13 Comments
  The Euler-Lagrange ##p##-gerbes discussed in the previous article are singled out as being exactly the right coherent refinement…
prequantumgeometry3

Higher Prequantum Geometry III: The Global Action Functional – Cohomologically

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9 Comments
  The previous article ended with the concept of classical locally variational field theories, of which a class of examples are…