Science and Math Articles

Here is the collection of expert STEM articles that span all the sciences and mathematics. Some examples include physics, mathematics, biology, chemistry, cosmology, and earth sciences. For math, we cover algebra to advanced calculus.  These articles are all peer-reviewed by the community.

bubbles

Explosion-Generated Collapsing Vacuum Bubbles Reach 20,000 Kelvin

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5 Comments
Experiment overview In a recent paper published in Physical Review Letters (PRL), one of the top physics journals, Jérôme Duplat and Emmanuel Villermaux…
cmb

A Poor Man’s CMB Primer: Orientation of the Universe

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4 Comments
 This is a picture of the cosmic microwave background:Fig 1. The cosmic microwave background as seen by the European Space Agency's…
planck

What Planck Length Is and It’s Common Misconceptions

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33 Comments
The Planck length is an extremely small distance constructed from physical constants. Many misconceptions overstate its physical significance, claiming…
spacetime2

Struggles With The Continuum: Quantum Mechanics of Charged Particles

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39 Comments
 Last time we saw that nobody yet knows if Newtonian gravity, applied to point particles, truly succeeds in predicting the future. To be precise:…
imagination

Why Imagination Without Knowledge Is Ignorance Waiting to Happen

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15 Comments
Introduction My feelings on people who think that imagination is more important than knowledge are well-known. These people simply are parroting Einstein's…
animal speeds

Animal Speed Scaling: Body-Lengths per Second Across Sizes

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19 Comments
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…
infinity_faq

Infinity in Mathematics: Limits and Cardinality FAQ

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17 Comments
Introduction Understanding the behavior of infinity is one of the major accomplishments of mathematics. However, the infinite is often misunderstood and…
man_on_moon

Apollo Program: Moon Missions & Last Moonwalk 1972

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Eugene Cernan: Last to Walk on the Moon On December 11, 1972, astronaut Eugene Cernan became the last person to walk on the lunar surface, marking the…
spacetime

Is Spacetime Really a Continuum?

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29 Comments
  Introduction Is spacetime really a continuum?  That is, can points of spacetime really be described---at least locally---by lists of four…
photoelectric

“Violating” Einstein’s Photoelectric Effect Model

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4 Comments
Einstein's Photoelectric Insight One of the most spectacular theoretical descriptions that Einstein had ever produced is the corpuscular nature of light…
CosmologicalHorizons

Inflationary Misconceptions and the Basics of Cosmological Horizons

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46 Comments
Introduction It is a common saying that during inflation "space expanded faster than the speed of light."  This statement is meant to articulate the…
lightswitch

What Happens When You Flip the Light Switch: From Zero Seconds to 20 Years

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47 Comments
Introduction Few people know what happens when a customer does something like flipping a light switch. The full explanation requires descriptions of topics…
relativitytherorm

Learn the Relativistic Work-Kinetic Energy Theorem

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19 Comments
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…
supergravity

Emergence From the Superpoint

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6 Comments
 In the previous article we saw that the generalization of super-Lie algebras to homotopy super-Lie n-algebras (super L-infinity algebras)…
liealgebra

Homotopy Lie-n Algebras in Supergravity

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1 Comment
 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…
string theory

It Was 20 Years Ago Today — the M-theory Conjecture

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2 Comments
  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,…

Why You Should Not Use Wikipedia As Your Primary Source

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108 Comments
It is no secret to anyone who has read my posts in this forum for a while that I do not like Wikipedia. I think that there is a fundamental flaw with the…
hupmisconceptions1

Learn a Misconception of the Heisenberg Uncertainty Principle

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26 Comments
One of the common misconceptions about the Heisenberg Uncertainty Principle (HUP) is that it is the fault of our measurement accuracy.A description…
learnfrompf

The Most Important Thing You Can Learn from Physics Forums

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15 Comments
Introduction It is a bit pompous of me to think that I can tell you the most important thing you can learn from Physics Forums (PF). After all, each…
errorbars

Plus/minus What? How to Interpret Error Bars

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20 Comments
People sometimes find themselves staring at a number with a ± in it when a new physics result is presented. But what does it mean? This Insight aims to…
LCDM4

Approximate LCDM Expansion in Simplified Math (Part 4)

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14 Comments
  Part 4: Cosmic Recession Rates An astronomer, accompanied by his amateur relativist friend, aimed a telescope at a distant galaxy and measured…
theoex

False Physics Major Dichotomy: Theorist or Experimentalist?

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27 Comments
Figure showing links between ballistic pressure waves and traumatic brain injury.Many physics majors believe that pursuing a Ph.D. in…
LCDM3

The LCDM Cosmological Model in Simplified Math (Part 3)

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5 Comments
  Part 3: Important Cosmological Horizons and Distances A question that often comes up is: "how big is the observable universe?"The question…
lcdmjorrie

Approximate LCDM Expansion in Simplified Math (Part 2)

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14 Comments
  Part 2: Time and Distance In Part 1 we have seen how one of the simplest ways of expressing the fractional expansion rate of the universe,…
neutrino

Learn About Neutrino Masses and Speed

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28 Comments
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…
gravity

Understanding the General Relativity View of Gravity on Earth

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

Approximate LCDM Expansion in Simplified Math

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11 Comments
 If we restrict ourselves to a spatially flat LCDM universe model (and ignore the early radiation energy density), the first Friedmann equation…
math obvious

Teaching Math as Obvious Thinking | Make Math Click

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20 Comments
My goal when I teach math My #1 goal, when I teach a math class, is to convey a way of thinking about math. It's quite different from what most students…
physics love

Should You Do Science for Love or for Money

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19 Comments
While I served on the math faculty of the US Air Force Academy, we invited numerous cadets to participate in self-funded research…
measuringentanglement

Can You Measure Quantum Entanglement?

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24 Comments
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

Garrett Lisi’s Superparticle Bet With Frank Wilczek

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52 Comments
There is an interesting story unfolding in particle physics. The main motivation for building the Large Hadron Collider was to search for new particles.…
qftintegrals

Some Useful Integrals In Quantum Field Theory

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2 Comments
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.…
arrowoftime

Retrocausality: How Fundamental is the Arrow of Time?

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26 Comments
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…
research work

Initiating Physics PhD Research: Getting Started Effectively

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1 Comment
Full Chapter List - So You Want To Be A Physicist... Series Part I: Early Physics Education in High schools Part II: Surviving the First Year…
gas compression

Reversible vs Irreversible Gas Compression and Expansion Work

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26 Comments
Introduction In learning Thermodynamics, one of the difficult concepts that many students struggle with is the difference between reversible and irreversible…
perbation theory

Introduction to Causal Perturbation Theory

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30 Comments
Relativistic quantum field theory is notorious for the occurrence of divergent expressions that must be renormalized by recipes that on first sight sound…
cheshirecat

Weak Values Part 2: The Quantum Cheshire Cat Experiment

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

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 temperature

Negative Absolute Temperatures: Explanation & Examples

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9 Comments
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…
What is Energy

A Definition and Controversy of Energy

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44 Comments
[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…
LHC

LHC Part 3: Protons as Large as a Barn

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8 Comments
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…
earth year

How to Scientifically Measure How Many Days Are in a Year

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75 Comments
How many days are there in a year? Ask pretty much anyone and they will tell you 365, except for leaps years which have 366. In addition,…
Alzheimers

Can Gene Editing Eliminate Alzheimer’s Disease?

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14 Comments
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…
subway

Brachistochrone Subway Tunnel: Fastest Tunnel Shape Explained

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6 Comments
Introduction A subway tunnel could, in principle, operate without external energy (like electricity) if we assume zero friction everywhere. The train…
redlights

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…
mermin

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]…
classroom

Explore Some Sins in Physics Didactics

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Introduction There are many sins in physics didactics. Usually, they occur, because teachers, professors, textbook or popular-science-book writers, etc.…

LHC Part 2: Commissioning

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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…
CrispR DNA

Why CRISPR Technologies Won’t Lead to Designer Babies

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37 Comments
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…
abstract_algebra

Is Zero a Natural Number?

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Using: Anderson-Feil Chapter 1.1 Is zero a natural number? This is a pretty controversial question. Many mathematicians - especially those working in foundational…
micro1

Formal Syntax and WFFs in Set Theory (Hrbacek-Jech)

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Hrbacek–Jech Chapter 1.2: Formal Language and WFFs Introduction Hrbacek and Jech do not go into full detail about what a property is formally. This…
bioethics

Bioethics & Genetic Engineering: Ethics and Policy

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Bioethics Key PointsWorrying about the future now means recognizing advances in technology, such as genetic engineering, that have already arisen. …
supernova

Star Fate: From Nebulae to White Dwarfs and Black Holes

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Star Fate: From Birth to Black Holes Stars form in vast clouds of gas and dust called nebulae. Over time gravity pulls material together until the core…
hand_to_hand_combat

Hand-to-Hand Combat Physics — Force, Momentum, Speed

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1 Comment
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_evidence

5 Pieces of Evidence that Support Theory of Evolution

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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…