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Learn About the FLRW Metric and The Friedmann Equation
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Previous Chapter: A Journey Into the Cosmos – The Friedmann Equation
Chapter 2- FLRW Metric and The Friedmann Equation
In…
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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…
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Learn Quantization in Mathematical Quantum Field Theory
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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…
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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…
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The Schwarzschild Metric: The Photon Sphere
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…
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Learn Gauge Fixing in Mathematical Quantum Field Theory
The following is one chapter in a series of Mathematical Quantum Field Theory.The previous chapter is 11. Reduced phase space.The next chapter…
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The Schwarzschild Metric: GPS Satellites
A Global Positioning System (GPS) device gives your precise location by receiving light pulses from satellites with synchronized clocks then…
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Learn About the Friedmann Equation and the Cosmos
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…
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Learn Reduced Phase Space in Mathematical Quantum Field Theory
The following is one chapter in a series on Mathematical Quantum Field Theory.The previous chapter is 10. Gauge symmetries.The next chapter is…
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Learn Gauge Symmetries in Mathematical Quantum Field Theory
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…
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Learn Propagators in Mathematical Quantum Field Theory
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.…
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What is the Homopolar Generator: An Analytical Example
Introduction
It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…
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Learn Phase Space in Mathematical Quantum Field Theory
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.…
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Learn Observables in Mathematical Quantum Field Theory
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…
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Learn Symmetries in Mathematical Quantum Field Theory
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.…
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Learn Lagrangians in Mathematical Quantum Field Theory
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.…
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Learn Field Variations in Mathematical Quantum Field Theory
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.…
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How to Use the Spaghetti-Twist Method to Align DNA
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…
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Learn the Fields of Mathematical Quantum Field Theory
The following is one chapter in a series on Mathematical Quantum Field TheoryThe previous chapter is 2. Spacetime.The next chapter is 4. Field…
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Learn Spacetime in Mathematical Quantum Field Theory
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.…
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Learn the Geometry of Mathematical Quantum Field Theory
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…
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A First Idea of Quantum Field Theory – 20 Part Series
These notes mean to give an expository but rigorous introduction to the basic concepts of relativistic perturbative quantum field theories, specifically…
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The What and Why of Circuit Analysis Assumptions
Probably everyone reading this article already has education on elementary circuit analysis (CA) and many of us are much more advanced. Typically, the…
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Introduction to Perturbative Quantum Field Theory
This is the beginning of a series that gives an introduction to perturbative quantum field theory (pQFT) on Lorentzian spacetime backgrounds in its…
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How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics
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…
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15 of the Best PF 2017 Eclipse Photos
The 2017 August Eclipse really was something special. Fortunately Physics Forums has great photographers and snapped some remarkable shots. Here are a…
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A Poor Man’s CMB Primer: Quantum Seeds
The CMB establishes a record of ancient acoustic oscillations in the baryon-photon plasma. We've been studying how these primordial sound…
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Find Out the Results Shown at 2017 CERN EPS Conference
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…
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Super p-Brane Theory Emerging from Super Homotopy Theory
A notorious open problem:
What is the non-perturbative theory formerly known as Strings?We still have no fundamental formulation of “M-theory”…
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Assessing the Physics in Edmond Hamilton’s “The Second Satellite”
This article won't contain much about physics that typical readers of this site don't already know. However, deconstructing improper physics in literature…
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Lesson on Entanglement Entropy in Quantum Field Theory
Part 1: Quantum Mechanics[This article expects the reader to have some experience with quantum field theory and path integrals][I should also…
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Learn Damped Motion in Classical and Quantum Mechanics
This Insights article is about dissipative forces (friction, air resistance, viscosity...).Damping by friction forces is one of the concepts that is…
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Exploring the Spectral Paradox in Physics
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…
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Learn Entanglement Entropy in Quantum Mechanics
Quantum Mechanics(QM) is one of the greatest intellectual achievements in human history. Not only because it describes the world at the microscopic level…
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The Diffraction Limited Spot Size with Perfect Focusing
Purpose
The purpose of this Insights article is to give the reader a brief introduction to the principles behind diffraction-limited focusing. The reader…
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Learn Frenet Equations in 2-D Which Result in the Cornu Spiral
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…
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Learn About Vacuum Fluctuations in Experimental Practice
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Permanent Magnets Explained by Magnetic Surface Currents
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…
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Why Higher Category Theory in Physics?
This here is my personal story. For an alternative introduction see my talk: Higher Structures in Mathematics and Physics.Initially,…
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The Schwarzschild Geometry: Spacetime Diagrams
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…
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Learn About Quantum Amplitudes, Probabilities and EPR
This is a little note about quantum amplitudes. Even though quantum probabilities seem very mysterious, with weird interference effects and seemingly nonlocal…
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Explore The Vacuum Fluctuation Myth in Quantum Theory
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles” and “Misconceptions about Virtual Particles“ which…
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Learn The Main Conceptual Ideas of Anyon Particles
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…
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Frames of Reference: A Skateboarder’s View
My essay Explaining Rolling Motion raised some commentary about frames of reference and their equivalence when solving physics problems. I wish to pursue…
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Exploring General Relativity as a Gauge Theory
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…
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Spectral Standard Model and String Compactifications
The Connes-Lott-Chamseddine-Barrett model is the observation that the standard model of particle physics -- as a classical action functional,…
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A Poor Man’s CMB Primer: Cosmic Acoustics
Before decoupling, photons and charged particles were in good thermal contact: though the primordial plasma might have varied in temperature…
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Struggles with the Continuum: Spacetime Conclusion
We've been looking at how the continuum nature of spacetime poses problems for our favorite theories of physics --- problems with infinities.…
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11d Gravity From Just the Torsion Constraint
It is familiar that Einstein gravity may be formulated in terms of a vielbein field together with a "spin connection", subject to the constraint…
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Struggles with the Continuum: General Relativity
Combining electromagnetism with relativity and quantum mechanics led to QED. Last time we saw the immense struggles with the continuum this…
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Learn Why Ohm’s Law Is Not a Law
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…
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Why Road Capacity Is Almost Independent of the Speed Limit
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…
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Learn About Supersymmetry and Deligne’s Theorem
In 2002, Pierre Deligne proved a remarkable theorem on what mathematically is called Tannakian reconstruction of tensor categories. Here…
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LHC Part 4: Searching for New Particles and Decays
The LHC experiments are in full swing collecting data this year (more information in the forum), and a while ago the collaboration of the…
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Acoustic ‘beats’ from Mismatched Musical Frequencies
Introduction
In late high school physics courses and first-year university courses, the phenomenon of acoustical 'beats' (digital audio) is often covered.…
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Learn About Spacetime Diagrams of Light Clocks
We demonstrate a method for constructing spacetime diagrams for special relativity on graph paper that has been rotated by 45 degrees. Many quantitative…
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A Black Hole Problem From Greg Egan’s “Incandescence”
The following problem was inspired by reading Greg Egan's "Incadescence". Consider a body, orbiting a Schwarzschild black hole and tide locked to it,…
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The Interaction of Sound and Light
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…
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Scientific Inference: Do We Really Need Induction?
Part 2. "We don't need no stinkin' induction" -- Sir Karl Popper
The traditional scientific method supposedly employs induction both in the…
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Roger Babson’s Anti-Gravity Contest
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…
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Scientific Inference: Logical Induction Ain’t Logical
Three million years ago, the grandfathers of our genus used sharpened stones to chop wood and cut bone. Today, surgeons use fiber optic-guided…
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Learn the Top Misconceptions about Virtual Particles
This Insight Article is a sequel to the Insight Article ''The Physics of Virtual Particles'', which contains an exposition of definitions that are physically…
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AC Power Analysis: The 4 Levels of Cyber Resilience
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.…
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How Representative is the Night Sky?
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…
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How the EPR Paradox Fits Between Entanglement and Nonlocality
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,…
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Intro to AC Power Analysis: Network Analysis
Let me use the terms “power grid” and “network” interchangeably.
What is the Power Grid Required to Do?Deliver energy to customers,…
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The Revival of Newton-Cartan Theory in General Relativity
It's a calculation that you can find in any textbook on General Relativity (GR): when gravity is weak and does not vary with time, and when particles are…
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Learn the Physics of Virtual Particles in Quantum Mechanics
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…
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Learn about the Big Bang and the Expansion of the Universe
The "ordinary Big Bang and expansion" (no inflation, no dark energy)
Einstein's General Relativity allows a solution (FLRW metric) where an empty Universe…
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Intro to AC Power Analysis: Learn System Basics
Instantaneous PowerThe formula for power is: ##P=V\cdot I## , power= voltage*current. We call that, instantaneous power. Even…
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Learn the Basics of Positron Emission Tomography (PET)
PET Key PointsPaul Dirac first theorized positrons in 1928 and they were observed four years later by Carl Anderson.
Positron Emission Tomography…
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How to Manage TCP/IP In Automation or Measurement Networks
The 1990s saw the widespread adoption of network technology on two fronts: Office automation and factory automation. But while office automation soon standardized…
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Learn Time Synchronization Across Switched Ethernets
Now and then you come across measurement problems that are tightly associated with the notion of synchronicity, meaning that things need to happen simultaneously.…
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Tools to Enrich our Quantum Mechanics Interpretations Discourse
IntroductionMany times, we encounter ourselves tangled in some Quantum Mechanics (QM) interpretations debates. Unfortunately, the standard…
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Struggles with the Continuum – Freeman Dyson and QED
Last time I sketched how physicists use quantum electrodynamics, or 'QED', to compute answers to physics problems as power series in the…
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High Temperature and Low Duality for the Ising Model on an Infinite Regular Tree
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,…
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Introduction to the Secondary Forces in Physics
Many are familiar with the "fundamental forces" of nature: gravity, electromagnetism, and the strong and weak nuclear forces. Three of these tend to bind…
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Struggles with the Continuum: Quantum Electrodynamics
Quantum field theory is the best method we have for describing particles and forces in a way that takes both quantum mechanics…
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Learn About Knut Lundmark and the Prehistory of Dark Matter
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 that…
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Struggles with the Continuum – Relativity and Quantum
In this series, we're looking at mathematical problems that arise in physics due to treating spacetime as a continuum---basically, problems…
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Why the Need of Infinity in Physics
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…
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Thoughts on the Complexity of Modern Science
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…
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Exploration into the Physics of Rainbows
For several years, I have been contemplating this beautiful picture by photographer Brian McPhee. I have a personal interest in the photograph because…
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Learn All About Earth’s Gravity
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…
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Learn About the Speed of Light and Galilean Relativity
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Understanding Buoyancy: The Limits of Archimedes
It’s a principle as old as science itself, and remarkably, remains essentially unchanged in the light of revolution after revolution in our understanding…
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How to Self-Study Basic High School Mathematics
IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what mathematics should I study…
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The Essential Guide to Self Study Mathematics
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,…
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Have Scientists Seen an Electron?
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.…
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The Block Universe – Refuting a Common Argument
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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…
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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…
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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](https://www.physicsforums.com/insights/wp-content/uploads/2015/11/blockuniverse2.png)
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](https://www.physicsforums.com/insights/wp-content/uploads/2015/10/blockuniverse1.png)
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](https://www.physicsforums.com/insights/wp-content/uploads/2015/10/prequantum4.png)
Examples of Prequantum Field Theories IV: Wess-Zumino-Witten-type Theories
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](https://www.physicsforums.com/insights/wp-content/uploads/2015/10/prequantum3.png)
Examples of Prequantum Field Theories III: Chern-Simons-type Theories
After having constructed gauge fields and higher gauge fields in the previous article by systems of ##L_\infty##-algebroid-valued…
![guagetheory](https://www.physicsforums.com/insights/wp-content/uploads/2015/10/guagetheory.png)
Examples of Prequantum Field Theories II: Higher Gauge Fields
After having recalled ordinary gauge fields from a dg-algebraic perspective in the previous article, here I discuss…