
When did Mitochondria Evolve?
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Eukaryote evolution and cellular complexity
Historically, life is categorized into three broad domains: bacteria, archaea, and eukaryota. Whereas bacteria…

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,…

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…

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…

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…

Why Is the Speed of Light the Same in All Frames of Reference?
Why ask "why" about physical laws?
The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you…

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…

Learn All About Earth’s Gravity
Introduction
Earth's gravitational field at the surface is approximately 9.8 Newtons/kilogram or 9.8 meters/second/second. But how does that change due…

Do Black Holes Really Exist?
Introduction
The purpose of this article is to discuss the title question from several different viewpoints, to show that it isn't as simple as it looks.…

Frequently Made Errors in Climate Science – The Greenhouse Effect
1.What is meant by "The Greenhouse Effect"?
Many gases, such as H2O, CO2, CH4, are transparent to visible light but absorb and emit parts of the infrared…

Learn About the Speed of Light and Galilean Relativity
Introduction
In this article, I will discuss some experiments in the 19th and early 20th centuries that looked at how the velocity of a light source affects…

What Causes Cancer: Bad Luck or Bad Lifestyles?
What causes cancer?
For the most part, cancer is a disease that arises from mutations in the body that accumulate over time. These mutations knock…

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…

What Is Heat? Definition in Thermodynamics Explained
One of the most frustrating misconceptions in thermodynamics centers on the actual definition of heat. Many science and engineering students refer to a…

Why Electrons Don’t Crash Into the Nucleus — Quantum View
Atoms and Coulomb forces
If atoms were described only by Coulomb attraction, the electron and nucleus would attract each other and, according to classical…

How Does an Airplane Wing Work? A Primer on Lift
Many people ask how an airplane wing works, and several answers are commonly given. You might have even seen vigorous arguments between proponents…

Learn About Energy Gained by Charge in an Electrostatic Field
Energy gain of an electron in a potential V
I have seen this question being asked frequently on here. A lot of students have a bit of an issue in understanding…

Have Scientists Seen an Electron? How We Detect Them
Have Scientists Seen an Electron? Why Seeing Isn't Enough
This article is not about literally seeing a single electron with your eye; it addresses the…

A Geometrical View of Time Dilation and the Twin Paradox
Based on the number of questions we receive on the topic at Physics Forums, there is a lot of confusion in the general public about how time dilation works…

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…

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…

Atomic Positioning with DNA Hinges
I was perusing the Nature Nanotechnology website today when I came across an interesting article by Funke and Dietz, called "Placing molecules with Bohr…

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…

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…

Does Heisenberg Uncertainty Violate Energy Conservation?
The short answer is: No — there is no violation.
The longer answer
Given the probabilistic aspect of quantum theory, what do we mean now by "conservation…

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…

Examples of Prequantum Field Theories I: Gauge Fields
After having motivated the need for prequantum field theory and having laid out its principles (i. extremal action, ii. global…

Do Photons Move Slower in a Solid Medium?
Scope and context
This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower…

Time Dilation & Redshift of Schwarzschild Black Holes
Time dilation near a Schwarzschild black hole
The following is an overview of the time-dilation and gravitational-redshift effects of a static (Schwarzschild)…

Does Gravity Gravitate: The Wave
In the first two posts in this series, we looked at different ways of interpreting the question "does gravity gravitate?" We left off at…

Why Rigid Rods Can’t Send Faster-Than-Light Signals
Why a rigid rod can't send faster-than-light signals
One common proposal for achieving faster-than-light (FTL) communication is to use a long, perfectly…

Does Gravity Gravitate? Part 2
In the first post of this series, I talked about two ways to answer the title question, one leading to the answer "no" and the other leading…

PF’s policy on Lorentz Ether Theory and Block Universe
What is the PF's policy on Lorentz Ether Theory and Block Universe?Debates about the superiority or "truth" of modern Lorentz Ether Theory (LET) and…

Does Gravity Gravitate?
The title question of this article is one that often comes up in PF threads, and I would like to give my take on it. This will be the first…

Why Is Acceleration Due to Gravity a Constant?
This question has popped up many times. So here is an attempt to address it.To answer this question at the elementary level, several assumptions will…

Struggles With the Continuum: Point Particles and the Electromagnetic Field
In these posts, we're seeing how our favorite theories of physics deal with the idea that space and time are a continuum, with points described…

Explosion-Generated Collapsing Vacuum Bubbles Reach 20,000 Kelvin
Experiment overview
In a recent paper published in Physical Review Letters (PRL), one of the top physics journals, Jérôme Duplat and Emmanuel Villermaux…

What Is Evolution? How It Works — Mechanisms & Evidence
What is evolution?
In every field of scientific endeavor there sometimes comes a quantum shift in knowledge, a grand denouement that changes how we see…

Why Does C Have a Particular Value, and Can It Change?
Short answer:
Because c (speed of light) has units, its value is what it is only because of our choice of units, and there is no meaningful way to test…

What Planck Length Is and It’s Common Misconceptions
The Planck length is an extremely small distance constructed from physical constants. Many misconceptions overstate its physical significance, claiming…

Struggles With The Continuum: Quantum Mechanics of Charged Particles
Last time we saw that nobody yet knows if Newtonian gravity, applied to point particles, truly succeeds in predicting the future. To be precise:…

How Fast Do Changes in the Gravitational Field Propagate?
Overview
General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational…

Animal Speed Scaling: Body-Lengths per Second Across Sizes
Introduction
In a recent American Journal of Physics issue, I read an interesting paper by Nicole Meyer-Vernet and Jean-Pierre Rospars examining the top…

“Violating” Einstein’s Photoelectric Effect Model
Einstein's Photoelectric Insight
One of the most spectacular theoretical descriptions that Einstein had ever produced is the corpuscular nature of light…

What Happens When You Flip the Light Switch: From Zero Seconds to 20 Years
Introduction
Few people know what happens when a customer does something like flipping a light switch. The full explanation requires descriptions of topics…

Do Photons have Mass?
Do photons have mass?
The quick answer: NOCommon source of confusion
However, this is where it gets a bit confusing for most people. This is because,…

Learn the Relativistic Work-Kinetic Energy Theorem
I was bothered for a long time by the reasons for the relativistic validity of the work-kinetic energy relation ##\Delta E=Fd##, which holds without any…

Emergence From the Superpoint
In the previous article we saw that the generalization of super-Lie algebras to homotopy super-Lie n-algebras (super L-infinity algebras)…

An Equation for the Centrifugal Force Reversal Near A Black Hole
My goal in this article is to derive a simple equation for the proper acceleration of an observer traveling on a circular path around a Schwarzschild black…

Homotopy Lie-n Algebras in Supergravity
The previous article in this series claimed that the mathematics of the 21st century that had fallen into the 1970s in the form of string…

Learn A Short Proof of Birkhoff’s Theorem
Birkhoff's theorem is a very useful result in General Relativity, and pretty much any textbook has a proof of it. The one I first read was in Misner, Thorne,…

It Was 20 Years Ago Today — the M-theory Conjecture
While the world didn't end, after all, 15 years back at the turn of the millennium, in hindsight it is curious that, almost unnoticed,…

Bell Spaceship Paradox: Why the String Breaks in SR
Bell spaceship paradox — setup
Bell describes two spaceships that start out at rest relative to each other with an elastic string between them, one…

Learn a Misconception of the Heisenberg Uncertainty Principle
One of the common misconceptions about the Heisenberg Uncertainty Principle (HUP) is that it is the fault of our measurement accuracy.A description…

Why You Can’t Quantum Tunnel Through a Wall
Can You Quantum Tunnel Through a Wall?
Short answer
The short and sweet answer if a tennis ball, a bowling ball, or any other kind of ordinary macroscopic…

What is relativistic mass and why it is not used much?
It happens that the term relativistic mass is used, in particular in the introductory text on special relativity. It should be noted that whether or not…

Learn About Neutrino Masses and Speed
It was hard to miss the 2011 OPERA neutrino speed measurement that indicated superluminal neutrino speeds (and turned out to be a measurement error), but…

Understanding the General Relativity View of Gravity on Earth
Often students have difficulty reconciling the General Relativity (GR) view of gravity versus their own experience with gravity on the surface of Earth.…

Can You Measure Quantum Entanglement?
What is Quantum Entanglement?
Though any pair of particles, given their history, might happen to be entangled, some pairs are more entangled than others.
…

Garrett Lisi’s Superparticle Bet With Frank Wilczek
There is an interesting story unfolding in particle physics. The main motivation for building the Large Hadron Collider was to search for new particles.…

Some Useful Integrals In Quantum Field Theory
In my paper on renormalisation I mentioned what most who have studied calculations in Quantum Field Theory find, it's rather complicated and mind-numbing.…

Retrocausality: How Fundamental is the Arrow of Time?
In this Insight, I'll discuss a recent experiment ([1] [2] [3]) by some Australian physicists that has brought a thought experiment into the real world…

Reversible vs Irreversible Gas Compression and Expansion Work
Introduction
In learning Thermodynamics, one of the difficult concepts that many students struggle with is the difference between reversible and irreversible…

Introduction to Causal Perturbation Theory
Relativistic quantum field theory is notorious for the occurrence of divergent expressions that must be renormalized by recipes that on first sight sound…

LHC Quiz: Think You Know about the LHC?
News of the LHC progress has dazzled scientists and hobbyists alike. It's now time to show just how much you know about the operation.Please share…

Frequently Made Errors in Heat: Elementary Level
1. Heat, Work, Internal Energy, and Kinetic Energy
"If heat is the motion of molecules, why isn't it Kinetic Energy?"In everyday use, we may think…

Weak Values Part 2: The Quantum Cheshire Cat Experiment
In a previous Insight, Weak Values Part 1: "Asking Photons Where They Have Been," I showed different methods for computing the relative intensities in…

Weak Values Part 1: Asking Photons Where They Have Been
In a previous Insight on retrocausality, I explained an experiment by Danan, Farfurnik, Bar-Ad, and Vaidman (DFBV)[1], “Asking Photons Where They Have…

Negative Absolute Temperatures: Explanation & Examples
It's a famous result in thermodynamics that you cannot reach absolute zero no matter how hard you try. Given the definition of absolute zero, it is also…

A Definition and Controversy of Energy
[CONTENT]
What is energy?
Energy is a fundamental concept that refers to the capacity of a system to do work. It is a scalar quantity, meaning it has magnitude…

Frequently Made Errors: Pseudo and Resultant Forces
1. Real versus Fictitious
Pseudo, or "fictitious", forces can arise when a non-inertial frame of reference is used. Using a non-inertial frame…

LHC Part 3: Protons as Large as a Barn
Introduction
See also part 1 and part 2 of the series.The LHC commissioning phase is coming to and end. On Wednesday May 20th 2015, the first collisions…

Why Renormalisation in Quantum Theory Needs a Cutoff
Introduction
This is a follow on from my paper explaining renormalization. A question was raised - why exactly do we need a cut-off. There is a deep reason…

Frequently Made Errors in Mechanics: Springs
1. Springs in Series
"A spring of constant ##k_1## is connected in series with a spring of constant ##k_2##. What is the spring constant…

Frequently Made Errors in Mechanics: Momentum and Impacts
An impact is an impulse (change of momentum) that involves arbitrarily large forces acting very briefly. These result in near-instantaneous…

Frequently Made Errors in Mechanics: Hydrostatics
1. Archimedes' Principle
X "When a body is placed in a liquid, the weight of the body equals the weight of the liquid displaced"That will…

Can Gene Editing Eliminate Alzheimer’s Disease?
The development of the CRISPR/Cas9 system has made gene editing a relatively simple task. While CRISPR and other gene-editing technologies stand to revolutionize…

Derivation of Gauss’s Law: Coulomb to Flux Explained
Gauss's law was formulated by Carl Friedrich Gauss in 1835. It is one of the four Maxwell's equations that form the basis of classical electrodynamics.…

Brachistochrone Subway Tunnels: Speed vs. Depth Tradeoffs
Introduction
A subway tunnel could, in principle, operate without external energy (like electricity) if we assume zero friction everywhere. The train would…

Frequently Made Errors: Kinematics Mistakes Explained
Kinematics is the subset of dynamics that only concerns itself with time, displacement, velocity, and acceleration. A problem is a kinematics problem…

Frequently Made Errors: Mechanics — Moments and Torque
Entire List for Frequently Made Errors Series
MechanicsForces
Friction
Moments
Kinematics
Hydrostatics
Momentum and Impacts
Springs
Pseudo…

Quantum Renormalisation Made Easy
What Is The Issue With Renormalisation
If you have an interest in physics you have likely come across renormalisation before, although what it really…

Mutual Inductance: When k≠1 and Two Coupling Coefficients
Mutual inductance and the coupling coefficient
A commonly used formula for mutual inductance M between two nearby coils L1 and L2 is M = k√(L1*L2).…

Learn About the Greenberger-Horne-Zeilinger Experiment
In two previous Insights, I shared Mermin's explanation of the Hardy experiment[1] and the Mermin device[2]. Both of his corresponding AJP papers presented…

The Quantum Liar Experiment: An Instantiation of the Mermin Device
In 1981, Mermin published a paper[1], "Bringing home the atomic world: Quantum mysteries for anybody" in which he explained the mystery of quantum nonlocality[2]…

Frequently Made Errors in Mechanics: Friction
1. Direction of the normalDefinition: The normal force that body A exerts on body B is that force of minimum magnitude which suffices to prevent penetration…

Frequently Made Errors in Mechanics: Forces
Entire List for Frequently Made Errors Series
Mechanics
Forces
Friction
Moments
Kinematics
Hydrostatics
Momentum and Impacts
…

Particle in a Box: 1D & 2D Quantum Visualizations
Introduction
The particle in a box is a staple of entry-level quantum mechanics courses because it provides a clear contrast between classical and quantum…

LHC Part 2: Commissioning
View All PartsPart 1: LHC about to restart - some FAQs
Part 2: Commissioning
Part 3: Protons as Large as a Barn
Part 4: Searching for New Particles…

Understanding the Second Law of Thermodynamics Clearly
Introduction
The second law of thermodynamics and the associated concept of entropy have been sources of confusion for thermodynamics students for centuries.…

Why CRISPR Technologies Won’t Lead to Designer Babies
The prospect of designer babies has been a staple of the dystopian futures imagined by science-fiction writers, evoking fears of eugenics (e.g. Brave…

Hand-to-Hand Combat Physics — Force, Momentum, Speed
Physics of Hand-to-Hand Combat
Hand-to-hand combat (often abbreviated H2H or HTH) refers to fighting at very close range, usually without weapons.
It includes…

Evolution Explained: FAQs, Evidence & Common Misconceptions
[CONTENT]
Key PointsEvolution is a scientific theory supported by multiple independent lines of evidence.
In science, the term "theory" denotes a…

5 Pieces of Evidence that Support Theory of Evolution
Evidence for Evolution
If you’re new to the topic, these primers provide helpful background:What is Evolution: A Beginner’s Guide
What Is Evolution…
